Expected Sarsa is a type of reinforcement learning algorithm that is similar to Q-learning but instead of always choosing the action with the maximum reward, it takes into account the likelihood of each action under the current policy. This helps to eliminate the variance caused by randomly selecting actions.

What is Reinforcement Learning?

Reinforcement learning is a type of machine learning that involves an agent interacting with an environment to learn the optimal actions to take in order to receive the highest reward. The agent receives feedback in the form of rewards or punishments for each action it takes, and its goal is to learn how to maximize its reward over time.

Reinforcement learning is commonly used in applications such as gaming, robotics, and autonomous vehicles.

What is Expected Sarsa?

Expected Sarsa is a variation of the Sarsa algorithm, which is a type of reinforcement learning algorithm that uses a table to store the expected value of each state-action pair. In the Sarsa algorithm, the agent selects an action based on the current state, receives a reward, and then updates the expected value of the state-action pair using the reward and the estimated value of the next state-action pair.

Expected Sarsa is similar to the Sarsa algorithm, but instead of always selecting the action with the maximum expected value, it takes into account the likelihood of each action under the current policy. This helps to reduce the variance that can be introduced by randomly selecting actions. The update rule for Expected Sarsa is:

$$Q(S_t, A_t) \leftarrow Q(S_t, A_t) + \alpha[R_{t+1} + \gamma \sum_{a} \pi(a|S_{t+1})Q(S_{t+1}, a) - Q(S_t, A_t)] $$

Where Q(S_t, A_t) represents the expected value of the state-action pair, alpha is the learning rate, R_{t+1} is the reward for taking action A_t and transitioning to state S_{t+1}, gamma is the discount factor that determines the relative importance of future rewards, and pi(a|S_{t+1}) is the probability of selecting action a in state S_{t+1} under the current policy.

What are the Advantages of Expected Sarsa?

Expected Sarsa has several advantages over the traditional Sarsa algorithm:

  • Reduced Variance: By taking into account the likelihood of each action under the current policy, Expected Sarsa reduces the variance caused by randomly selecting actions.
  • Improved Convergence: By reducing the variance, Expected Sarsa can converge more quickly to the optimal policy.
  • Generality: Expected Sarsa can be applied to a wide range of reinforcement learning problems, including both episodic and continuing tasks.

What are the Disadvantages of Expected Sarsa?

Despite its advantages, Expected Sarsa also has some disadvantages:

  • Increased Computational Complexity: Because Expected Sarsa involves calculating the expected value of each action, it can be more computationally expensive than Sarsa.
  • Not Always Optimal: In some cases, selecting the action with the maximum expected value may be the optimal strategy, in which case Expected Sarsa may not perform as well as traditional Sarsa or Q-learning.
  • Sensitivity to Policy: Expected Sarsa is sensitive to the policy used to select actions. If the policy is not well optimized, then the algorithm may not perform as well.

When is Expected Sarsa Used?

Expected Sarsa is typically used when the environment is characterized by high variability, and traditional Sarsa may have difficulty converging to the optimal policy. It is also used in situations where the optimal action may not always be the action with the maximum expected value.

Expected Sarsa has been successfully applied in a variety of reinforcement learning problems, including robotics, gaming, and autonomous driving.

Expected Sarsa is a useful variation of the Sarsa algorithm that reduces variance by taking into account the likelihood of each action under the current policy. While it may be more computationally expensive and not always optimal in all situations, it is a valuable tool for reinforcement learning in situations where high variability is present.

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