What are the key differences between on-policy methods like SARSA and off-policy methods like Q-learning in the context of deep reinforcement learning?

/ / Published in Artificial Intelligence, EITC/AI/ARL Advanced Reinforcement Learning, Deep reinforcement learning, Function approximation and deep reinforcement learning, Examination review

In the realm of deep reinforcement learning (DRL), the distinction between on-policy and off-policy methods is fundamental, particularly when considering algorithms such as SARSA (State-Action-Reward-State-Action) and Q-learning. These methods differ in their approach to learning and policy evaluation, which has significant implications for their performance and applicability in various environments.

On-policy methods, such as SARSA, learn the value of the policy that is currently being followed by the agent. This means that the agent updates its policy based on the actions it actually takes and the rewards it actually receives. In SARSA, the update rule for the Q-value function is given by:

    \[ Q(s_t, a_t) \leftarrow Q(s_t, a_t) + \alpha \left[ r_{t+1} + \gamma Q(s_{t+1}, a_{t+1}) - Q(s_t, a_t) \right] \]

Here, s_t and a_t represent the state and action at time t, r_{t+1} is the reward received after taking action a_t, s_{t+1} is the subsequent state, and a_{t+1} is the action chosen in state s_{t+1}. The parameters \alpha and \gamma denote the learning rate and discount factor, respectively. The key aspect of SARSA is that the action a_{t+1} is selected according to the current policy, which means that the learning process is inherently tied to the policy being executed.

In contrast, off-policy methods like Q-learning learn the value of the optimal policy independently of the agent's actions. Q-learning updates the Q-values using the maximum reward of the next state, regardless of the policy currently being followed. The update rule for Q-learning is:

    \[ Q(s_t, a_t) \leftarrow Q(s_t, a_t) + \alpha \left[ r_{t+1} + \gamma \max_{a} Q(s_{t+1}, a) - Q(s_t, a_t) \right] \]

In this formula, \max_{a} Q(s_{t+1}, a) represents the maximum estimated value of the next state-action pair, which does not depend on the action actually taken by the agent. This distinction allows Q-learning to evaluate and improve the policy without being constrained by the specific actions taken during learning, making it an off-policy method.

The differences between these approaches have several important implications:

1. Exploration vs. Exploitation: On-policy methods like SARSA are more sensitive to the exploration strategy employed by the agent. Since SARSA updates its policy based on the actions actually taken, it directly incorporates the exploration strategy (e.g., epsilon-greedy) into the learning process. This can lead to more conservative policies that are safer in environments where certain actions can lead to highly variable outcomes. Conversely, Q-learning, being off-policy, separates the exploration strategy from the policy evaluation, which can sometimes lead to more aggressive exploitation of the learned Q-values.

2. Convergence and Stability: The convergence properties of on-policy and off-policy methods can differ significantly. On-policy methods like SARSA typically converge more slowly and can be more stable, especially in stochastic environments where the outcomes of actions are uncertain. This is because SARSA takes into account the actual sequence of actions and rewards, leading to a more realistic evaluation of the policy. Off-policy methods like Q-learning, while often converging faster, can be less stable in such environments due to the maximization step, which might overestimate the value of certain actions if the Q-values are not well estimated.

3. Sample Efficiency: Off-policy methods can be more sample efficient because they can reuse past experience to update the Q-values. This is particularly advantageous in environments where collecting new samples is expensive or time-consuming. In the context of deep reinforcement learning, this ability to leverage past experiences is often implemented through experience replay, where the agent stores past transitions and samples from this memory to update the Q-value function. On-policy methods, by contrast, must update their policy based on the current trajectory, which can be less efficient in terms of sample usage.

4. Applicability to Function Approximation: When extending these methods to deep reinforcement learning, where function approximation (e.g., using neural networks) is employed to estimate Q-values, the differences become even more pronounced. On-policy methods like SARSA can be more robust when using function approximators because they inherently incorporate the exploration strategy into the learning process. This can mitigate some of the issues associated with overestimation and instability. Off-policy methods like Q-learning, however, can suffer from divergence and instability when combined with function approximators, particularly due to the maximization step. Techniques such as Double Q-learning and Dueling Network Architectures have been developed to address these issues by providing more stable and accurate value estimates.

5. Policy Improvement: On-policy methods improve the policy gradually based on the actual experiences of the agent, leading to a more incremental and sometimes safer policy improvement process. Off-policy methods, on the other hand, aim to directly improve the policy towards the optimal policy, which can result in more significant policy changes. This difference can be important in environments where drastic policy changes can lead to undesirable or dangerous outcomes.

To illustrate these differences with an example, consider a robot navigating a maze to reach a goal. Using SARSA, the robot would update its policy based on the actual paths it takes, incorporating the exploration strategy into the learning process. This might lead to more cautious navigation, avoiding paths that have previously led to high penalties. With Q-learning, the robot would update its policy based on the maximum estimated reward of the next state, potentially leading to more aggressive exploration of new paths that might offer higher rewards, even if they have not been directly experienced by the robot.

The choice between on-policy methods like SARSA and off-policy methods like Q-learning depends on the specific requirements of the task at hand, the characteristics of the environment, and the desired balance between exploration and exploitation, convergence stability, sample efficiency, and the robustness of function approximation.

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