Deep Q-Learning: From Q-Tables to Neural Networks

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February 10, 2025

Introduction

This lecture concludes our course with an exploration of Deep Q-Learning, a cutting-edge technique in Reinforcement Learning that builds upon the foundational principles of Q-Learning we’ve discussed. As we approach the culmination of this course, our objective is to provide a comprehensive yet accessible understanding of Deep Q-Learning. This topic is not only academically significant but also holds substantial real-world relevance in the rapidly evolving landscape of Artificial Intelligence.

We will begin by revisiting the traditional Q-Learning algorithm, pinpointing its inherent limitations, particularly concerning scalability in complex environments. This understanding will naturally lead us to appreciate the innovative solutions offered by Deep Q-Learning, primarily through the integration of deep neural networks. This transition marks a significant step towards handling more intricate problems in reinforcement learning, paving the way for applications in domains previously intractable with classical methods. This lecture will systematically unfold the concepts, starting from the motivations for Deep Q-Learning to its algorithmic details and practical considerations.

Q-Learning Recap and Transition to Deep Learning

Review of Reinforcement Learning Fundamentals

Recall that Reinforcement Learning (RL) is concerned with training agents to make optimal decisions within an environment to maximize cumulative rewards. At its core, RL involves an agent interacting with an environment, observing its state ($s$), taking an action ($a$), and receiving a reward ($r$). The sequence of these interactions defines the learning process. A crucial element in RL is the concept of cumulative discounted reward. This is not simply the immediate reward received after an action, but the total reward expected over time, discounted by a factor $\gamma$ (gamma). The discount factor, $0 \leq \gamma \leq 1$, determines the importance of future rewards relative to immediate ones. A higher $\gamma$ emphasizes long-term rewards, encouraging the agent to consider the future consequences of its actions. This discounted cumulative reward is what the agent aims to maximize over time, guiding its learning process towards optimal behavior.

Q-Learning Algorithm and Q-Table

In our exploration of RL algorithms, we focused on Q-Learning, a model-free, off-policy algorithm. Q-Learning centers around the concept of a Q-table (or action-value function), denoted as $Q(s, a)$. This table is a mapping from state-action pairs to Q-values, where each Q-value $Q(s, a)$ represents the expected discounted cumulative reward of taking action $a$ in state $s$ and following an optimal policy thereafter.

The Q-table is typically initialized before the learning process begins. Common initialization strategies include setting all Q-values to zero or to small random values. Initializing to zero is often preferred as it provides a neutral starting point without introducing bias. The Q-Learning algorithm then iteratively updates these Q-values based on interactions with the environment.

The update process is driven by the Bellman equation, specifically the Q-learning update rule. In each step, the agent:

Observes the current state $s_t$.
Selects an action $a_t$ based on a policy (e.g., $\epsilon$-greedy, which balances exploration and exploitation).
Executes action $a_t$ in the environment.
Receives a reward $r_t$ and observes the next state $s_{t+1}$.
Updates the Q-value for the state-action pair $(s_t, a_t)$ using the following update rule:

\[Q(s_t, a_t) \leftarrow Q(s_t, a_t) + \alpha [r_t + \gamma \max_{a} Q(s_{t+1}, a) - Q(s_t, a_t)]\] where $\alpha$ is the learning rate, determining the step size of the update, and $\gamma$ is the discount factor.

where $\alpha$ is the learning rate, determining the step size of the update, and $\gamma$ is the discount factor.

This update rule is derived from the Bellman optimality equation and iteratively refines the Q-values to converge towards the optimal Q-function, $Q^*(s, a)$. The asterisk in $Q^*(s, a)$ denotes the optimal Q-function, representing the maximum possible Q-value for each state-action pair. The goal of Q-Learning is to learn a Q-table that approximates this optimal Q-function. Through repeated interactions and updates, the Q-table gradually converges to represent the optimal action values, enabling the agent to make decisions that maximize long-term rewards.

Limitations of Q-Learning: The Curse of Dimensionality

While Q-Learning is conceptually simple and has proven effective in many scenarios, its practical application faces significant challenges when dealing with complex environments. The primary bottleneck is the scalability issue arising from the use of the Q-table. The size of the Q-table grows exponentially with the number of states and actions, a problem known as the curse of dimensionality.

Consider an environment with a moderately large state space, for instance, 10,000 possible states, and for each state, suppose there are 1,000 possible actions. In this scenario, the Q-table would require storing $10,000 \times 1,000 = 10,000,000$ Q-values. This demands substantial memory for storage. Furthermore, updating each of these values efficiently during the learning process becomes computationally expensive.

Definition 1 (Curse of Dimensionality in Q-Learning). The curse of dimensionality in Q-Learning refers to the exponential increase in the size of the Q-table with the number of states and actions, leading to impractical memory and computational requirements for complex environments.

In many real-world problems, especially those involving continuous state spaces (e.g., robotics, autonomous driving) or high-dimensional sensory inputs (e.g., images, videos), the number of states can be effectively infinite or astronomically large. For such problems, maintaining and updating a Q-table becomes entirely impractical. The memory requirements become unmanageable, and the exploration of such a vast state-action space to adequately populate the Q-table becomes infeasible within reasonable timeframes.

This fundamental limitation of Q-Learning motivates the need for alternative approaches that can handle large and continuous state spaces. The solution lies in approximating the Q-function using function approximation techniques, rather than explicitly tabulating it. This is where Deep Q-Learning (DQN) comes into play. DQN leverages the power of deep neural networks to approximate the Q-function, offering a scalable and effective approach to tackle complex reinforcement learning problems that are beyond the reach of traditional Q-Learning. By replacing the Q-table with a neural network, DQN overcomes the memory and computational bottlenecks, paving the way for applying reinforcement learning to high-dimensional and complex environments.

Deep Q-Learning (DQN)

Approximating the Q-Function with Neural Networks

As discussed, the primary bottleneck of traditional Q-Learning lies in its reliance on Q-tables, which become computationally and memory-wise prohibitive for large state spaces. To overcome this limitation, Deep Q-Learning (DQN) replaces the Q-table with a deep neural network, known as a Q-network. This network serves as a function approximator to estimate the Q-values.

Definition 2 (Q-Network). A Q-Network in Deep Q-Learning is a deep neural network that approximates the Q-function. It takes a state as input and outputs the estimated Q-values for all possible actions in that state.

In contrast to Q-Learning where we perform a direct lookup in the Q-table for a given state-action pair to retrieve the Q-value, DQN utilizes a neural network. This Q-network, parameterized by weights $\theta$, takes the state $s$ as input and outputs a vector of Q-values, where each component corresponds to the Q-value $Q(s, a; \theta)$ for each possible action $a$ in that state. Mathematically, we represent this as $Q(s; \theta) \approx Q^*(s)$, where $Q^*(s)$ is the optimal action-value function for state $s$.

Comparison of Q-Table and Q-Network approaches for Q-value estimation.

Consider an environment with $n$ possible actions. For a given state $s$, the Q-network outputs a vector of $n$ values, $[Q(s, a_1; \theta), Q(s, a_2; \theta), \dots, Q(s, a_n; \theta)]$. Each value $Q(s, a_i; \theta)$ approximates the expected discounted cumulative reward if action $a_i$ is taken in state $s$ and the agent follows an optimal policy thereafter. When deciding which action to take in state $s$, the agent selects the action $a^* = \operatorname{argmax}_{a} Q(s, a; \theta)$ that corresponds to the highest Q-value predicted by the network.

The critical advantage of using a neural network is its ability to generalize. Unlike a Q-table, which can only store and retrieve values for states it has explicitly encountered, a neural network can generalize from seen states to unseen states. This generalization is crucial for handling large or continuous state spaces. Furthermore, neural networks, especially deep networks, are capable of learning complex, hierarchical representations from high-dimensional input data, making them well-suited for complex RL environments. The learning process in DQN then shifts to training the Q-network by adjusting its weights $\theta$ to minimize the error between the network’s Q-value estimations and the target Q-values derived from the Bellman equation.

Deep Q-Network Architecture for High-Dimensional Inputs

DeepMind’s pioneering work with DQN famously applied it to playing Atari 2600 games, demonstrating the power of this approach in complex, visually rich environments. In this context, the raw input to the agent is the game screen, which is a high-dimensional visual input. To handle this, DQN architectures typically employ Convolutional Neural Networks (CNNs).

For Atari games, and similar visual environments, the state $s_t$ is often represented as a sequence of frames rather than a single static frame. Using a sequence of, for example, four consecutive frames, provides the network with temporal context, allowing it to perceive motion and changes in the game environment. Preprocessing steps are usually applied to these frames, such as converting them to grayscale and downsampling to reduce dimensionality and computational cost.

Example 1 (DQN Architecture for Image-Based States). A typical DQN architecture for processing image-based states might consist of convolutional layers followed by fully connected layers.

Input Layer: Accepts a preprocessed state, which is a sequence of frames. For instance, a stack of 4 grayscale frames of size $84 \times 84$ pixels each.
Convolutional Layers: Several convolutional layers are used to automatically extract spatial features from the input frames. These layers learn hierarchical representations, starting from simple edges and corners in early layers to more complex object features in deeper layers. Common configurations include:
- Convolutional layer 1: e.g., 32 filters of size $8 \times 8$ with stride 4, followed by ReLU activation.
- Convolutional layer 2: e.g., 64 filters of size $4 \times 4$ with stride 2, followed by ReLU activation.
- Convolutional layer 3: e.g., 64 filters of size $3 \times 3$ with stride 1, followed by ReLU activation.
- These parameters (number of filters, kernel size, stride) are examples and can be adjusted.
Fully Connected Layers: After the convolutional layers, one or more fully connected layers are used to process the high-level features extracted by the convolutional layers. These layers learn complex relationships between the extracted features and the Q-values. A typical setup might include:
- Fully connected layer 1: e.g., 512 units, followed by ReLU activation.
Output Layer: The final layer is a fully connected output layer with a linear activation function. The number of neurons in this layer is equal to the number of possible actions in the environment. Each neuron outputs the estimated Q-value for a specific action. For example, if the game has 4 possible actions (e.g., up, down, left, right), the output layer will have 4 neurons, outputting $[Q(s, \text{up}; \theta), Q(s, \text{down}; \theta), Q(s, \text{left}; \theta), Q(s, \text{right}; \theta)]$.

This architecture effectively transforms raw visual input into meaningful representations and then maps these representations to action values, enabling the agent to learn directly from visual inputs in complex environments. The network is trained end-to-end to predict Q-values that guide the agent’s decision-making process.

Training Instability due to Non-Stationary Targets

Training deep neural networks to approximate Q-functions introduces a significant challenge: training instability arising from non-stationary targets. This issue stems from the fact that the target values used to train the Q-network are themselves dependent on the parameters of the Q-network being trained.

Recall the Q-learning update rule, which forms the basis for defining the target Q-value. In DQN, we aim to minimize the loss between the predicted Q-value $Q(s_t, a_t; \theta)$ and a target value $y_t$. A simplified target value, based on the Bellman equation, can be expressed as:

\[y_t = r_t + \gamma \max_{a'} Q(s_{t+1}, a'; \theta)\]

Here, the target value $y_t$ is calculated using the same Q-network that we are trying to train. This creates a circular dependency. The network’s current weights $\theta$ are used to both predict the Q-value for the current state-action pair and to estimate the maximum Q-value for the next state, which is used to form the target.

As the Q-network’s weights $\theta$ are updated during training to reduce the error between $Q(s_t, a_t; \theta)$ and $y_t$, the values of $Q(s_{t+1}, a'; \theta)$ also change. This means that with every update, the target values $y_t$ are also shifting. In essence, the target is constantly moving, making the learning process unstable. It’s akin to trying to hit a moving target that is moving in response to your own movements.

This non-stationarity of the targets can lead to oscillations and divergence during training. The network might chase after targets that are constantly changing, preventing it from converging to a stable and optimal Q-function. This instability is a major hurdle in training DQNs and requires specific techniques to mitigate.

Stabilizing Training with Target Networks

To address the issue of non-stationary targets and stabilize the training process in DQN, the concept of target networks was introduced.

Definition 3 (Target Network). In Deep Q-Learning, a target network is a separate neural network, with the same architecture as the Q-network, used to compute target Q-values. Its weights are updated less frequently than the Q-network’s weights to stabilize training.

The core idea is to decouple the computation of target Q-values from the Q-network that is being updated in each training step. This is achieved by using two separate neural networks:

Q-Network (Prediction Network): Denoted as $Q(s, a; \theta)$, this is the primary network that is trained and updated at each step. It is used to select actions based on the current state and to predict Q-values for the current state-action pairs for training.
Target Network: Denoted as $Q'(s, a; \theta')$, this network is used to calculate the target Q-values. It has the same architecture as the Q-network, but its parameters $\theta'$ are updated less frequently. Typically, the parameters of the target network are periodically updated to match the parameters of the Q-network, but with a delay.

The target Q-value $y_t$ is then calculated using the target network instead of the Q-network:

\[y_t = r_t + \gamma \max_{a'} Q'(s_{t+1}, a'; \theta')\]

During training, only the weights $\theta$ of the Q-network are updated using gradient descent to minimize the loss between $Q(s_t, a_t; \theta)$ and $y_t$. The weights $\theta'$ of the target network are held fixed for a number of steps. After a fixed interval of $C$ steps, the weights of the target network are updated by copying the weights from the Q-network: $\theta' \leftarrow \theta$. This periodic update synchronizes the target network with the Q-network, but the delay in updates provides stability.

By using a target network with delayed updates, the target values become more stationary for a period of time. This allows the Q-network to learn more effectively and reduces oscillations in training. The Q-network learns to predict Q-values that are closer to a more stable target, leading to more reliable convergence. The frequency of updating the target network (parameter $C$) is a hyperparameter that needs to be tuned. A smaller $C$ means more frequent updates, potentially leading to instability, while a larger $C$ might slow down learning.

Experience Replay: Breaking Correlation and Stabilizing Updates

Another crucial technique for stabilizing DQN training and improving data efficiency is experience replay.

Definition 4 (Experience Replay). Experience replay is a technique used in Deep Q-Learning to stabilize training by storing past experiences in a replay buffer and sampling mini-batches from it for training updates. This breaks correlations in sequential data and improves data efficiency.

In standard online reinforcement learning, agents learn from experiences sequentially as they are generated through interaction with the environment. However, consecutive experiences are often highly correlated, especially in environments where the agent’s actions have inertia or the environment changes slowly. Training directly on correlated experiences can lead to inefficient learning and instability because updates are based on highly similar data points, increasing variance and potentially leading to overfitting to recent experiences.

Experience replay addresses this issue by storing past experiences in a replay buffer (or replay memory) and then sampling mini-batches of experiences randomly from this buffer to perform updates. The process works as follows:

Experience Storage: As the agent interacts with the environment at each time step $t$, it generates an experience tuple $(s_t, a_t, r_t, s_{t+1})$, consisting of the current state $s_t$, the action taken $a_t$, the reward received $r_t$, and the next state $s_{t+1}$. These experience tuples are stored in a replay buffer $D$ with a fixed capacity $N$. When the buffer is full, new experiences overwrite the oldest ones, implementing a FIFO (First-In, First-Out) mechanism.
Mini-batch Sampling: To perform a training update, a mini-batch of $K$ experiences is randomly sampled from the replay buffer $D$. Sampling is typically uniform random, ensuring that all experiences in the buffer have an equal chance of being selected.
Q-Network Update: The Q-network is then trained using this randomly sampled mini-batch of experiences. For each experience $(s_j, a_j, r_j, s_{j+1})$ in the mini-batch, the target Q-value $y_j$ is calculated (using the target network as described in the previous subsection), and gradient descent is performed to minimize the loss function: $L = \mathbb{E}_{(s, a, r, s') \sim U(D)} [(y - Q(s, a; \theta))^2]$, where $U(D)$ denotes uniform sampling from the replay buffer $D$.

Experience replay offers several key benefits:

Decorrelation of Experiences: Randomly sampling experiences from the replay buffer breaks the temporal correlations present in sequential experiences. This results in training on a more diverse and less correlated dataset, which is closer to the assumption of independent and identically distributed (i.i.d.) data often made in machine learning. Decorrelation leads to more stable and efficient learning.
Data Efficiency and Reuse of Experiences: Experience replay allows for the reuse of past experiences multiple times. Each experience stored in the replay buffer can be used in multiple training updates, as it can be sampled in different mini-batches. This significantly improves data efficiency, as the agent learns from past interactions more effectively, rather than discarding them after a single update.
Stabilization of Training Updates: By averaging updates over a mini-batch of experiences, experience replay smooths out the learning process. It reduces the variance of updates compared to online learning, where updates are performed after each single experience. This batching effect contributes to more stable and robust training, preventing drastic changes in network weights based on single, potentially noisy, experiences.

Experience replay, combined with target networks, is a cornerstone of the DQN algorithm, enabling stable and efficient learning in complex reinforcement learning environments.

Deep Q-Learning Algorithm

The Deep Q-Learning algorithm integrates the Q-network, target network, and experience replay to learn effective policies in complex environments. The algorithm is summarized in Algorithm 1.

Algorithm 1 (Deep Q-Learning with Experience Replay and Target Network).

Initialize: Initialize Q-network $Q(s, a; \theta)$ with random weights $\theta$. Initialize target network $Q'(s, a; \theta')$ with weights $\theta' \leftarrow \theta$. Initialize replay memory $D$ with capacity $N$. Initialize starting state $s_1$. Action Selection: Select action $a_t$ using $\epsilon$-greedy policy based on $Q(s_t, a; \theta)$: $a_t = \begin{cases} \text{random action} & \text{with probability } \epsilon \\ \operatorname{argmax}_{a} Q(s_t, a; \theta) & \text{with probability } 1 - \epsilon \end{cases}$ Execute action $a_t$ in the environment and observe reward $r_t$ and next state $s_{t+1}$. Store Transition: Store transition $(s_t, a_t, r_t, s_{t+1})$ in replay memory $D$. Sample Batch: Sample random mini-batch of transitions $(s_j, a_j, r_j, s_{j+1})_{j=1}^K$ from $D$. Compute Target Q-values: For each transition in the batch, calculate target $y_j$: $y_j = \begin{cases} r_j & \text{if episode terminates at step } j+1 \\ r_j + \gamma \max_{a'} Q'(s_{j+1}, a'; \theta') & \text{otherwise} \end{cases}$ Gradient Descent Update: Perform gradient descent to update Q-network weights $\theta$ by minimizing the loss: $L = \frac{1}{K} \sum_{j=1}^K (y_j - Q(s_j, a_j; \theta))^2$ Update Target Network: Every $C$ steps, update target network weights: $\theta' \leftarrow \theta$. $s_t \leftarrow s_{t+1}$ break

Complexity Analysis of DQN Algorithm:

Let’s analyze the computational complexity of one training step within the DQN algorithm:

Action Selection: Selecting an action using the Q-network involves a forward pass through the network, which depends on the network architecture. For a deep CNN, this could be roughly proportional to the number of weights in the network, let’s denote it as $O(W_{forward})$.
Storing Transition: Storing a transition in the replay buffer is $O(1)$ on average, assuming efficient data structures.
Sampling Batch: Sampling a mini-batch of size $K$ from the replay buffer is $O(K)$.
Compute Target Q-values: For each sample in the batch, computing the target Q-value involves a forward pass through the target network to find the maximum Q-value for the next state, which is again $O(W'_{forward})$, where $W'_{forward}$ is the complexity of a forward pass in the target network (similar to $W_{forward}$). This is done for each of the $K$ samples, so $O(K \cdot W'_{forward})$.
Gradient Descent Update: Performing gradient descent involves backpropagation through the Q-network to compute gradients and update weights. The complexity of backpropagation is also roughly proportional to the number of weights and the batch size, let’s denote it as $O(K \cdot W_{backward})$.
Target Network Update: Updating the target network every $C$ steps by copying weights is approximately $O(W_{copy})$, where $W_{copy}$ is the number of weights to copy. However, amortized over each step, this cost is less significant if $C$ is reasonably large.

Therefore, the dominant complexities in each step are typically the forward and backward passes through the neural networks, and these are performed for each sample in the mini-batch. The approximate complexity per training step is $O(W_{forward} + K + K \cdot W'_{forward} + K \cdot W_{backward} + W_{copy}/C) \approx O(K \cdot (W_{forward} + W_{backward}))$, assuming $W_{forward} \approx W'_{forward}$ and $W_{backward}$ is of similar order. The overall complexity per episode and for the entire training process depends on the number of episodes, the length of each episode, and the number of training steps performed. In practice, DQN training is computationally intensive, primarily due to the repeated forward and backward passes through deep neural networks.

Course Conclusion and Exam Information

Summary of Reinforcement Learning Concepts

In this lecture, we have synthesized the core concepts of Reinforcement Learning, starting from the fundamental definitions of environments, states, actions, and rewards. We have traced the evolution from basic Q-Learning, which utilizes Q-tables and is well-suited for problems with limited state and action spaces, to the more advanced Deep Q-Learning. DQN leverages the power of neural networks to approximate the Q-function, thereby overcoming the scalability issues inherent in traditional Q-Learning and enabling the application of reinforcement learning to complex, high-dimensional environments. Crucially, we explored the techniques of target networks and experience replay, which are essential for stabilizing the training process of Deep Q-Networks and ensuring robust learning. These advancements represent a significant step forward in making reinforcement learning applicable to real-world problems of increasing complexity.

Exam Question Overview and Preparation Guidance

As we approach the final assessment, the exam will cover the key topics discussed throughout this course, encompassing Reinforcement Learning, Supervised Learning, and related areas of Artificial Intelligence. To guide your preparation, we present a set of example questions that are representative of the format and scope you can expect in the exam:

Example 2 (Example Exam Questions).

Supervised vs. Self-Supervised Learning: Delineate the fundamental differences between supervised and self-supervised learning paradigms. Emphasize the nature of labels, learning objectives, and typical applications for each.
Learning Modes in ChatGPT: Identify and describe the three primary learning modes employed in the training of ChatGPT. Explain the role and contribution of each mode to the overall capabilities of the model.
Entropy in Decision Trees: Define the concept of entropy as it pertains to a node in a decision tree. Provide the formula for calculating entropy and explain its significance in the context of decision tree construction.
Information Gain: Define information gain in the context of decision trees. Explain how it is calculated and why it is used as a criterion for feature selection during tree induction.
Information Gain Calculation: Given a specific dataset or scenario, calculate the information gain for a particular feature. Alternatively, construct a simple example dataset and demonstrate the calculation of information gain for a chosen feature.
Decision Tree Learning Algorithm (Pseudocode): Write the pseudocode for a standard decision tree learning algorithm (e.g., ID3, C4.5). Ensure your pseudocode clearly outlinesthe recursive process of tree construction, including feature selection and stopping conditions.
Discrete vs. Continuous Features in Decision Trees: Compare and contrast the handling of discrete and continuous features in decision trees. Discuss any necessary modifications or techniques required to accommodate continuous features.
Decision Trees for Classification vs. Regression: Explain the differences in using decision trees for classification versus regression tasks. Highlight variations in splitting criteria, prediction methods, and evaluation metrics.
Recommendation Systems (One-Page Description): Provide a concise, one-page description of recommendation systems. Cover the fundamental goals, types of recommendation systems (e.g., content-based, collaborative filtering), and key challenges in the field.
Factor Creation in Recommendation Systems: Describe the process of creating factors in recommendation systems, particularly in the context of matrix factorization techniques. Explain how latent factors are learned and used to generate recommendations.
Exploration vs. Exploitation in Reinforcement Learning: Clearly differentiate between exploration and exploitation in reinforcement learning. Discuss the importance of balancing these two aspects and common strategies for achieving this balance (e.g., $\epsilon$-greedy policy).
Policy in Reinforcement Learning: Define the concept of a policy in reinforcement learning. Explain its role in guiding an agent’s behavior and the different types of policies (e.g., deterministic, stochastic).
Q-Table Update using Q-Learning: Given a partially filled Q-table and a specific transition (state, action, reward, next state), demonstrate how to update a Q-value using the Q-learning algorithm. Ensure you apply the Q-learning update rule correctly.
Deep Q-Learning (DQN) Description: Provide a comprehensive description of Deep Q-Learning. Explain the motivation behind DQN, its key components (Q-network, target network, experience replay), and how these components work together to enable learning in complex environments.

These questions are designed to evaluate your understanding of the fundamental principles, algorithms, and concepts covered in this course. When answering descriptive questions, aim to provide a high-level overview, focusing on the most critical aspects and mechanisms. Where applicable, incorporating illustrative examples, including numerical examples, can significantly enhance the clarity and depth of your answers. Focus on demonstrating not just factual recall but also conceptual understanding and the ability to apply your knowledge to explain and analyze AI techniques.

Research and Engagement Opportunities in the AI Lab

For students with a continued interest in Artificial Intelligence and Machine Learning, our AI Laboratory offers a vibrant and engaging research environment. We provide numerous opportunities to deepen your involvement through:

Thesis Projects: Engage in cutting-edge research by undertaking thesis projects in various AI domains. We offer guidance and resources to support in-depth exploration and contribution to specific AI topics.
Internships: Gain practical experience through internships in the lab. Work alongside our research team on ongoing projects, contributing to real-world AI applications and development.
Doctoral Studies (Ph.D.): For those aspiring to pursue advanced research, we offer doctoral positions. Join our Ph.D. program to conduct original research, contribute to the AI field, and work towards becoming an expert in a specialized area of AI.

Our laboratory, located on the second floor of this building, is currently home to a dynamic team of 10-12 researchers. We encourage interested students to visit our lab to experience our research environment firsthand and learn more about our ongoing projectsand learn more about our ongoing projects. To arrange a visit or discuss potential opportunities, please feel free to send us an email. We are enthusiastic about fostering the next generation of AI researchers and practitioners and welcome your engagement.

Concluding Remarks

This lecture and this course have aimed to provide you with a robust foundation in key areas of Artificial Intelligence, culminating in an understanding of Deep Q-Learning, a powerful technique for tackling complex decision-making problems. We hope this journey has been both informative and inspiring, sparking your curiosity and preparing you for further exploration in this rapidly evolving field. We thank you for your active participation and engagement throughout the course and wish you success in your upcoming exams and future endeavors in Artificial Intelligence.

--- title: "Deep Q-Learning: From Q-Tables to Neural Networks" author: "Your Name" date: "2025-02-10" format: html: toc: true # Table of Contents toc-depth: 2 code-tools: true theme: cosmo # Or "journal" for Distill-like minimalism --- # Introduction This lecture concludes our course with an exploration of Deep Q-Learning, a cutting-edge technique in Reinforcement Learning that builds upon the foundational principles of Q-Learning we've discussed. As we approach the culmination of this course, our objective is to provide a comprehensive yet accessible understanding of Deep Q-Learning. This topic is not only academically significant but also holds substantial real-world relevance in the rapidly evolving landscape of Artificial Intelligence. We will begin by revisiting the traditional Q-Learning algorithm, pinpointing its inherent limitations, particularly concerning scalability in complex environments. This understanding will naturally lead us to appreciate the innovative solutions offered by Deep Q-Learning, primarily through the integration of deep neural networks. This transition marks a significant step towards handling more intricate problems in reinforcement learning, paving the way for applications in domains previously intractable with classical methods. This lecture will systematically unfold the concepts, starting from the motivations for Deep Q-Learning to its algorithmic details and practical considerations. # Q-Learning Recap and Transition to Deep Learning ## Review of Reinforcement Learning Fundamentals Recall that Reinforcement Learning (RL) is concerned with training agents to make optimal decisions within an environment to maximize cumulative rewards. At its core, RL involves an agent interacting with an environment, observing its **state** ($s$), taking an **action** ($a$), and receiving a **reward** ($r$). The sequence of these interactions defines the learning process. A crucial element in RL is the concept of **cumulative discounted reward**. This is not simply the immediate reward received after an action, but the total reward expected over time, discounted by a factor $\gamma$ (gamma). The discount factor, $0 \leq \gamma \leq 1$, determines the importance of future rewards relative to immediate ones. A higher $\gamma$ emphasizes long-term rewards, encouraging the agent to consider the future consequences of its actions. This discounted cumulative reward is what the agent aims to maximize over time, guiding its learning process towards optimal behavior. ## Q-Learning Algorithm and Q-Table In our exploration of RL algorithms, we focused on Q-Learning, a model-free, off-policy algorithm. Q-Learning centers around the concept of a **Q-table** (or action-value function), denoted as $Q(s, a)$. This table is a mapping from state-action pairs to Q-values, where each Q-value $Q(s, a)$ represents the expected discounted cumulative reward of taking action $a$ in state $s$ and following an optimal policy thereafter. The Q-table is typically initialized before the learning process begins. Common initialization strategies include setting all Q-values to zero or to small random values. Initializing to zero is often preferred as it provides a neutral starting point without introducing bias. The Q-Learning algorithm then iteratively updates these Q-values based on interactions with the environment. The update process is driven by the Bellman equation, specifically the Q-learning update rule. In each step, the agent: 1. Observes the current state $s_t$. 2. Selects an action $a_t$ based on a policy (e.g., $\epsilon$-greedy, which balances exploration and exploitation). 3. Executes action $a_t$ in the environment. 4. Receives a reward $r_t$ and observes the next state $s_{t+1}$. 5. Updates the Q-value for the state-action pair $(s_t, a_t)$ using the following update rule: ::: tcolorbox $$Q(s_t, a_t) \leftarrow Q(s_t, a_t) + \alpha [r_t + \gamma \max_{a} Q(s_{t+1}, a) - Q(s_t, a_t)]$$ where $\alpha$ is the learning rate, determining the step size of the update, and $\gamma$ is the discount factor. ::: where $\alpha$ is the learning rate, determining the step size of the update, and $\gamma$ is the discount factor. This update rule is derived from the Bellman optimality equation and iteratively refines the Q-values to converge towards the optimal Q-function, $Q^*(s, a)$. The asterisk in $Q^*(s, a)$ denotes the optimal Q-function, representing the maximum possible Q-value for each state-action pair. The goal of Q-Learning is to learn a Q-table that approximates this optimal Q-function. Through repeated interactions and updates, the Q-table gradually converges to represent the optimal action values, enabling the agent to make decisions that maximize long-term rewards. ## Limitations of Q-Learning: The Curse of Dimensionality While Q-Learning is conceptually simple and has proven effective in many scenarios, its practical application faces significant challenges when dealing with complex environments. The primary bottleneck is the **scalability issue** arising from the use of the Q-table. The size of the Q-table grows exponentially with the number of states and actions, a problem known as the **curse of dimensionality**. Consider an environment with a moderately large state space, for instance, 10,000 possible states, and for each state, suppose there are 1,000 possible actions. In this scenario, the Q-table would require storing $10,000 \times 1,000 = 10,000,000$ Q-values. This demands substantial memory for storage. Furthermore, updating each of these values efficiently during the learning process becomes computationally expensive. ::: {.def:curse_dimensionality .definition} **Definition 1** (Curse of Dimensionality in Q-Learning). *The curse of dimensionality in Q-Learning refers to the exponential increase in the size of the Q-table with the number of states and actions, leading to impractical memory and computational requirements for complex environments.* ::: In many real-world problems, especially those involving continuous state spaces (e.g., robotics, autonomous driving) or high-dimensional sensory inputs (e.g., images, videos), the number of states can be effectively infinite or astronomically large. For such problems, maintaining and updating a Q-table becomes entirely impractical. The memory requirements become unmanageable, and the exploration of such a vast state-action space to adequately populate the Q-table becomes infeasible within reasonable timeframes. This fundamental limitation of Q-Learning motivates the need for alternative approaches that can handle large and continuous state spaces. The solution lies in approximating the Q-function using function approximation techniques, rather than explicitly tabulating it. This is where **Deep Q-Learning (DQN)** comes into play. DQN leverages the power of deep neural networks to approximate the Q-function, offering a scalable and effective approach to tackle complex reinforcement learning problems that are beyond the reach of traditional Q-Learning. By replacing the Q-table with a neural network, DQN overcomes the memory and computational bottlenecks, paving the way for applying reinforcement learning to high-dimensional and complex environments. # Deep Q-Learning (DQN) ## Approximating the Q-Function with Neural Networks As discussed, the primary bottleneck of traditional Q-Learning lies in its reliance on Q-tables, which become computationally and memory-wise prohibitive for large state spaces. To overcome this limitation, Deep Q-Learning (DQN) replaces the Q-table with a **deep neural network**, known as a **Q-network**. This network serves as a function approximator to estimate the Q-values. ::: definition **Definition 2** (Q-Network). *A Q-Network in Deep Q-Learning is a deep neural network that approximates the Q-function. It takes a state as input and outputs the estimated Q-values for all possible actions in that state.* ::: In contrast to Q-Learning where we perform a direct lookup in the Q-table for a given state-action pair to retrieve the Q-value, DQN utilizes a neural network. This Q-network, parameterized by weights $\theta$, takes the state $s$ as input and outputs a vector of Q-values, where each component corresponds to the Q-value $Q(s, a; \theta)$ for each possible action $a$ in that state. Mathematically, we represent this as $Q(s; \theta) \approx Q^*(s)$, where $Q^*(s)$ is the optimal action-value function for state $s$. <figure id="fig:q_table_vs_nn"> <figcaption>Comparison of Q-Table and Q-Network approaches for Q-value estimation.</figcaption> </figure> Consider an environment with $n$ possible actions. For a given state $s$, the Q-network outputs a vector of $n$ values, $[Q(s, a_1; \theta), Q(s, a_2; \theta), \dots, Q(s, a_n; \theta)]$. Each value $Q(s, a_i; \theta)$ approximates the expected discounted cumulative reward if action $a_i$ is taken in state $s$ and the agent follows an optimal policy thereafter. When deciding which action to take in state $s$, the agent selects the action $a^* = \operatorname{argmax}_{a} Q(s, a; \theta)$ that corresponds to the highest Q-value predicted by the network. The critical advantage of using a neural network is its ability to **generalize**. Unlike a Q-table, which can only store and retrieve values for states it has explicitly encountered, a neural network can generalize from seen states to unseen states. This generalization is crucial for handling large or continuous state spaces. Furthermore, neural networks, especially deep networks, are capable of learning complex, hierarchical representations from high-dimensional input data, making them well-suited for complex RL environments. The learning process in DQN then shifts to training the Q-network by adjusting its weights $\theta$ to minimize the error between the network's Q-value estimations and the target Q-values derived from the Bellman equation. ## Deep Q-Network Architecture for High-Dimensional Inputs DeepMind's pioneering work with DQN famously applied it to playing Atari 2600 games, demonstrating the power of this approach in complex, visually rich environments. In this context, the raw input to the agent is the game screen, which is a high-dimensional visual input. To handle this, DQN architectures typically employ Convolutional Neural Networks (CNNs). For Atari games, and similar visual environments, the state $s_t$ is often represented as a sequence of frames rather than a single static frame. Using a sequence of, for example, four consecutive frames, provides the network with temporal context, allowing it to perceive motion and changes in the game environment. Preprocessing steps are usually applied to these frames, such as converting them to grayscale and downsampling to reduce dimensionality and computational cost. ::: example **Example 1** (DQN Architecture for Image-Based States). *A typical DQN architecture for processing image-based states might consist of convolutional layers followed by fully connected layers.* 1. ***Input Layer**: Accepts a preprocessed state, which is a sequence of frames. For instance, a stack of 4 grayscale frames of size $84 \times 84$ pixels each.* 2. ***Convolutional Layers**: Several convolutional layers are used to automatically extract spatial features from the input frames. These layers learn hierarchical representations, starting from simple edges and corners in early layers to more complex object features in deeper layers. Common configurations include:* - *Convolutional layer 1: e.g., 32 filters of size $8 \times 8$ with stride 4, followed by ReLU activation.* - *Convolutional layer 2: e.g., 64 filters of size $4 \times 4$ with stride 2, followed by ReLU activation.* - *Convolutional layer 3: e.g., 64 filters of size $3 \times 3$ with stride 1, followed by ReLU activation.* - *These parameters (number of filters, kernel size, stride) are examples and can be adjusted.* 3. ***Fully Connected Layers**: After the convolutional layers, one or more fully connected layers are used to process the high-level features extracted by the convolutional layers. These layers learn complex relationships between the extracted features and the Q-values. A typical setup might include:* - *Fully connected layer 1: e.g., 512 units, followed by ReLU activation.* 4. ***Output Layer**: The final layer is a fully connected output layer with a linear activation function. The number of neurons in this layer is equal to the number of possible actions in the environment. Each neuron outputs the estimated Q-value for a specific action. For example, if the game has 4 possible actions (e.g., up, down, left, right), the output layer will have 4 neurons, outputting $[Q(s, \text{up}; \theta), Q(s, \text{down}; \theta), Q(s, \text{left}; \theta), Q(s, \text{right}; \theta)]$.* ::: This architecture effectively transforms raw visual input into meaningful representations and then maps these representations to action values, enabling the agent to learn directly from visual inputs in complex environments. The network is trained end-to-end to predict Q-values that guide the agent's decision-making process. ## Training Instability due to Non-Stationary Targets Training deep neural networks to approximate Q-functions introduces a significant challenge: **training instability** arising from **non-stationary targets**. This issue stems from the fact that the target values used to train the Q-network are themselves dependent on the parameters of the Q-network being trained. Recall the Q-learning update rule, which forms the basis for defining the target Q-value. In DQN, we aim to minimize the loss between the predicted Q-value $Q(s_t, a_t; \theta)$ and a target value $y_t$. A simplified target value, based on the Bellman equation, can be expressed as: ::: tcolorbox $$y_t = r_t + \gamma \max_{a'} Q(s_{t+1}, a'; \theta)$$ ::: Here, the target value $y_t$ is calculated using the *same* Q-network that we are trying to train. This creates a circular dependency. The network's current weights $\theta$ are used to both predict the Q-value for the current state-action pair and to estimate the maximum Q-value for the next state, which is used to form the target. As the Q-network's weights $\theta$ are updated during training to reduce the error between $Q(s_t, a_t; \theta)$ and $y_t$, the values of $Q(s_{t+1}, a'; \theta)$ also change. This means that with every update, the target values $y_t$ are also shifting. In essence, the target is constantly moving, making the learning process unstable. It's akin to trying to hit a moving target that is moving in response to your own movements. This non-stationarity of the targets can lead to oscillations and divergence during training. The network might chase after targets that are constantly changing, preventing it from converging to a stable and optimal Q-function. This instability is a major hurdle in training DQNs and requires specific techniques to mitigate. ## Stabilizing Training with Target Networks To address the issue of non-stationary targets and stabilize the training process in DQN, the concept of **target networks** was introduced. ::: definition **Definition 3** (Target Network). *In Deep Q-Learning, a target network is a separate neural network, with the same architecture as the Q-network, used to compute target Q-values. Its weights are updated less frequently than the Q-network's weights to stabilize training.* ::: The core idea is to decouple the computation of target Q-values from the Q-network that is being updated in each training step. This is achieved by using two separate neural networks: - **Q-Network (Prediction Network)**: Denoted as $Q(s, a; \theta)$, this is the primary network that is trained and updated at each step. It is used to select actions based on the current state and to predict Q-values for the current state-action pairs for training. - **Target Network**: Denoted as $Q'(s, a; \theta')$, this network is used to calculate the target Q-values. It has the same architecture as the Q-network, but its parameters $\theta'$ are updated less frequently. Typically, the parameters of the target network are periodically updated to match the parameters of the Q-network, but with a delay. The target Q-value $y_t$ is then calculated using the target network instead of the Q-network: ::: tcolorbox $$y_t = r_t + \gamma \max_{a'} Q'(s_{t+1}, a'; \theta')$$ ::: During training, only the weights $\theta$ of the Q-network are updated using gradient descent to minimize the loss between $Q(s_t, a_t; \theta)$ and $y_t$. The weights $\theta'$ of the target network are held fixed for a number of steps. After a fixed interval of $C$ steps, the weights of the target network are updated by copying the weights from the Q-network: $\theta' \leftarrow \theta$. This periodic update synchronizes the target network with the Q-network, but the delay in updates provides stability. By using a target network with delayed updates, the target values become more stationary for a period of time. This allows the Q-network to learn more effectively and reduces oscillations in training. The Q-network learns to predict Q-values that are closer to a more stable target, leading to more reliable convergence. The frequency of updating the target network (parameter $C$) is a hyperparameter that needs to be tuned. A smaller $C$ means more frequent updates, potentially leading to instability, while a larger $C$ might slow down learning. ## Experience Replay: Breaking Correlation and Stabilizing Updates Another crucial technique for stabilizing DQN training and improving data efficiency is **experience replay**. ::: definition **Definition 4** (Experience Replay). *Experience replay is a technique used in Deep Q-Learning to stabilize training by storing past experiences in a replay buffer and sampling mini-batches from it for training updates. This breaks correlations in sequential data and improves data efficiency.* ::: In standard online reinforcement learning, agents learn from experiences sequentially as they are generated through interaction with the environment. However, consecutive experiences are often highly correlated, especially in environments where the agent's actions have inertia or the environment changes slowly. Training directly on correlated experiences can lead to inefficient learning and instability because updates are based on highly similar data points, increasing variance and potentially leading to overfitting to recent experiences. Experience replay addresses this issue by storing past experiences in a **replay buffer** (or replay memory) and then sampling mini-batches of experiences randomly from this buffer to perform updates. The process works as follows: 1. **Experience Storage**: As the agent interacts with the environment at each time step $t$, it generates an experience tuple $(s_t, a_t, r_t, s_{t+1})$, consisting of the current state $s_t$, the action taken $a_t$, the reward received $r_t$, and the next state $s_{t+1}$. These experience tuples are stored in a replay buffer $D$ with a fixed capacity $N$. When the buffer is full, new experiences overwrite the oldest ones, implementing a FIFO (First-In, First-Out) mechanism. 2. **Mini-batch Sampling**: To perform a training update, a mini-batch of $K$ experiences is randomly sampled from the replay buffer $D$. Sampling is typically uniform random, ensuring that all experiences in the buffer have an equal chance of being selected. 3. **Q-Network Update**: The Q-network is then trained using this randomly sampled mini-batch of experiences. For each experience $(s_j, a_j, r_j, s_{j+1})$ in the mini-batch, the target Q-value $y_j$ is calculated (using the target network as described in the previous subsection), and gradient descent is performed to minimize the loss function: $L = \mathbb{E}_{(s, a, r, s') \sim U(D)} [(y - Q(s, a; \theta))^2]$, where $U(D)$ denotes uniform sampling from the replay buffer $D$. Experience replay offers several key benefits: - **Decorrelation of Experiences**: Randomly sampling experiences from the replay buffer breaks the temporal correlations present in sequential experiences. This results in training on a more diverse and less correlated dataset, which is closer to the assumption of independent and identically distributed (i.i.d.) data often made in machine learning. Decorrelation leads to more stable and efficient learning. - **Data Efficiency and Reuse of Experiences**: Experience replay allows for the reuse of past experiences multiple times. Each experience stored in the replay buffer can be used in multiple training updates, as it can be sampled in different mini-batches. This significantly improves data efficiency, as the agent learns from past interactions more effectively, rather than discarding them after a single update. - **Stabilization of Training Updates**: By averaging updates over a mini-batch of experiences, experience replay smooths out the learning process. It reduces the variance of updates compared to online learning, where updates are performed after each single experience. This batching effect contributes to more stable and robust training, preventing drastic changes in network weights based on single, potentially noisy, experiences. Experience replay, combined with target networks, is a cornerstone of the DQN algorithm, enabling stable and efficient learning in complex reinforcement learning environments. ## Deep Q-Learning Algorithm The Deep Q-Learning algorithm integrates the Q-network, target network, and experience replay to learn effective policies in complex environments. The algorithm is summarized in Algorithm [1](#alg:dqn){reference-type="ref" reference="alg:dqn"}. :::: {.alg:dqn .algorithm_env} **Algorithm 1** (Deep Q-Learning with Experience Replay and Target Network). ::: algorithmic ***Initialize:** Initialize Q-network $Q(s, a; \theta)$ with random weights $\theta$. Initialize target network $Q'(s, a; \theta')$ with weights $\theta' \leftarrow \theta$. Initialize replay memory $D$ with capacity $N$. Initialize starting state $s_1$. **Action Selection**: Select action $a_t$ using $\epsilon$-greedy policy based on $Q(s_t, a; \theta)$: $a_t = \begin{cases} \text{random action} & \text{with probability } \epsilon \\ \operatorname{argmax}_{a} Q(s_t, a; \theta) & \text{with probability } 1 - \epsilon \end{cases}$ Execute action $a_t$ in the environment and observe reward $r_t$ and next state $s_{t+1}$. **Store Transition**: Store transition $(s_t, a_t, r_t, s_{t+1})$ in replay memory $D$. **Sample Batch**: Sample random mini-batch of transitions $(s_j, a_j, r_j, s_{j+1})_{j=1}^K$ from $D$. **Compute Target Q-values**: For each transition in the batch, calculate target $y_j$: $y_j = \begin{cases} r_j & \text{if episode terminates at step } j+1 \\ r_j + \gamma \max_{a'} Q'(s_{j+1}, a'; \theta') & \text{otherwise} \end{cases}$ **Gradient Descent Update**: Perform gradient descent to update Q-network weights $\theta$ by minimizing the loss: $L = \frac{1}{K} \sum_{j=1}^K (y_j - Q(s_j, a_j; \theta))^2$ **Update Target Network**: Every $C$ steps, update target network weights: $\theta' \leftarrow \theta$. $s_t \leftarrow s_{t+1}$ break* ::: :::: **Complexity Analysis of DQN Algorithm:** Let's analyze the computational complexity of one training step within the DQN algorithm: - **Action Selection**: Selecting an action using the Q-network involves a forward pass through the network, which depends on the network architecture. For a deep CNN, this could be roughly proportional to the number of weights in the network, let's denote it as $O(W_{forward})$. - **Storing Transition**: Storing a transition in the replay buffer is $O(1)$ on average, assuming efficient data structures. - **Sampling Batch**: Sampling a mini-batch of size $K$ from the replay buffer is $O(K)$. - **Compute Target Q-values**: For each sample in the batch, computing the target Q-value involves a forward pass through the target network to find the maximum Q-value for the next state, which is again $O(W'_{forward})$, where $W'_{forward}$ is the complexity of a forward pass in the target network (similar to $W_{forward}$). This is done for each of the $K$ samples, so $O(K \cdot W'_{forward})$. - **Gradient Descent Update**: Performing gradient descent involves backpropagation through the Q-network to compute gradients and update weights. The complexity of backpropagation is also roughly proportional to the number of weights and the batch size, let's denote it as $O(K \cdot W_{backward})$. - **Target Network Update**: Updating the target network every $C$ steps by copying weights is approximately $O(W_{copy})$, where $W_{copy}$ is the number of weights to copy. However, amortized over each step, this cost is less significant if $C$ is reasonably large. Therefore, the dominant complexities in each step are typically the forward and backward passes through the neural networks, and these are performed for each sample in the mini-batch. The approximate complexity per training step is $O(W_{forward} + K + K \cdot W'_{forward} + K \cdot W_{backward} + W_{copy}/C) \approx O(K \cdot (W_{forward} + W_{backward}))$, assuming $W_{forward} \approx W'_{forward}$ and $W_{backward}$ is of similar order. The overall complexity per episode and for the entire training process depends on the number of episodes, the length of each episode, and the number of training steps performed. In practice, DQN training is computationally intensive, primarily due to the repeated forward and backward passes through deep neural networks. # Course Conclusion and Exam Information ## Summary of Reinforcement Learning Concepts In this lecture, we have synthesized the core concepts of Reinforcement Learning, starting from the fundamental definitions of environments, states, actions, and rewards. We have traced the evolution from basic Q-Learning, which utilizes Q-tables and is well-suited for problems with limited state and action spaces, to the more advanced Deep Q-Learning. DQN leverages the power of neural networks to approximate the Q-function, thereby overcoming the scalability issues inherent in traditional Q-Learning and enabling the application of reinforcement learning to complex, high-dimensional environments. Crucially, we explored the techniques of target networks and experience replay, which are essential for stabilizing the training process of Deep Q-Networks and ensuring robust learning. These advancements represent a significant step forward in making reinforcement learning applicable to real-world problems of increasing complexity. ## Exam Question Overview and Preparation Guidance As we approach the final assessment, the exam will cover the key topics discussed throughout this course, encompassing Reinforcement Learning, Supervised Learning, and related areas of Artificial Intelligence. To guide your preparation, we present a set of example questions that are representative of the format and scope you can expect in the exam: ::: example **Example 2** (Example Exam Questions). 1. ***Supervised vs. Self-Supervised Learning**: Delineate the fundamental differences between supervised and self-supervised learning paradigms. Emphasize the nature of labels, learning objectives, and typical applications for each.* 2. ***Learning Modes in ChatGPT**: Identify and describe the three primary learning modes employed in the training of ChatGPT. Explain the role and contribution of each mode to the overall capabilities of the model.* 3. ***Entropy in Decision Trees**: Define the concept of entropy as it pertains to a node in a decision tree. Provide the formula for calculating entropy and explain its significance in the context of decision tree construction.* 4. ***Information Gain**: Define information gain in the context of decision trees. Explain how it is calculated and why it is used as a criterion for feature selection during tree induction.* 5. ***Information Gain Calculation**: Given a specific dataset or scenario, calculate the information gain for a particular feature. Alternatively, construct a simple example dataset and demonstrate the calculation of information gain for a chosen feature.* 6. ***Decision Tree Learning Algorithm (Pseudocode)**: Write the pseudocode for a standard decision tree learning algorithm (e.g., ID3, C4.5). Ensure your pseudocode clearly outlinesthe recursive process of tree construction, including feature selection and stopping conditions.* 7. ***Discrete vs. Continuous Features in Decision Trees**: Compare and contrast the handling of discrete and continuous features in decision trees. Discuss any necessary modifications or techniques required to accommodate continuous features.* 8. ***Decision Trees for Classification vs. Regression**: Explain the differences in using decision trees for classification versus regression tasks. Highlight variations in splitting criteria, prediction methods, and evaluation metrics.* 9. ***Recommendation Systems (One-Page Description)**: Provide a concise, one-page description of recommendation systems. Cover the fundamental goals, types of recommendation systems (e.g., content-based, collaborative filtering), and key challenges in the field.* 10. ***Factor Creation in Recommendation Systems**: Describe the process of creating factors in recommendation systems, particularly in the context of matrix factorization techniques. Explain how latent factors are learned and used to generate recommendations.* 11. ***Exploration vs. Exploitation in Reinforcement Learning**: Clearly differentiate between exploration and exploitation in reinforcement learning. Discuss the importance of balancing these two aspects and common strategies for achieving this balance (e.g., $\epsilon$-greedy policy).* 12. ***Policy in Reinforcement Learning**: Define the concept of a policy in reinforcement learning. Explain its role in guiding an agent's behavior and the different types of policies (e.g., deterministic, stochastic).* 13. ***Q-Table Update using Q-Learning**: Given a partially filled Q-table and a specific transition (state, action, reward, next state), demonstrate how to update a Q-value using the Q-learning algorithm. Ensure you apply the Q-learning update rule correctly.* 14. ***Deep Q-Learning (DQN) Description**: Provide a comprehensive description of Deep Q-Learning. Explain the motivation behind DQN, its key components (Q-network, target network, experience replay), and how these components work together to enable learning in complex environments.* ::: These questions are designed to evaluate your understanding of the fundamental principles, algorithms, and concepts covered in this course. When answering descriptive questions, aim to provide a high-level overview, focusing on the most critical aspects and mechanisms. Where applicable, incorporating illustrative examples, including numerical examples, can significantly enhance the clarity and depth of your answers. Focus on demonstrating not just factual recall but also conceptual understanding and the ability to apply your knowledge to explain and analyze AI techniques. ## Research and Engagement Opportunities in the AI Lab For students with a continued interest in Artificial Intelligence and Machine Learning, our AI Laboratory offers a vibrant and engaging research environment. We provide numerous opportunities to deepen your involvement through: - **Thesis Projects**: Engage in cutting-edge research by undertaking thesis projects in various AI domains. We offer guidance and resources to support in-depth exploration and contribution to specific AI topics. - **Internships**: Gain practical experience through internships in the lab. Work alongside our research team on ongoing projects, contributing to real-world AI applications and development. - **Doctoral Studies (Ph.D.)**: For those aspiring to pursue advanced research, we offer doctoral positions. Join our Ph.D. program to conduct original research, contribute to the AI field, and work towards becoming an expert in a specialized area of AI. Our laboratory, located on the second floor of this building, is currently home to a dynamic team of 10-12 researchers. We encourage interested students to visit our lab to experience our research environment firsthand and learn more about our ongoing projectsand learn more about our ongoing projects. To arrange a visit or discuss potential opportunities, please feel free to send us an email. We are enthusiastic about fostering the next generation of AI researchers and practitioners and welcome your engagement. # Concluding Remarks This lecture and this course have aimed to provide you with a robust foundation in key areas of Artificial Intelligence, culminating in an understanding of Deep Q-Learning, a powerful technique for tackling complex decision-making problems. We hope this journey has been both informative and inspiring, sparking your curiosity and preparing you for further exploration in this rapidly evolving field. We thank you for your active participation and engagement throughout the course and wish you success in your upcoming exams and future endeavors in Artificial Intelligence.