# What is SARSA? An Introduction

SARSA (State-Action-Reward-State-Action) is a fundamental algorithm in the field of Reinforcement Learning (RL) that aims to learn an optimal policy for an agent interacting with an environment. In RL, the primary objective is to maximize the cumulative reward obtained by the agent over time, and SARSA provides a well-defined framework for achieving this goal.

At its core, SARSA is an on-policy temporal difference learning algorithm. It updates the action-value function, denoted as Q(s, a), which represents the expected return (discounted sum of rewards) when starting from state s, taking action a, and following the current policy thereafter. The algorithm operates by estimating the Q-values iteratively based on the agent’s experiences in the environment.

The update rule for SARSA is as follows:

Q(s, a) ← Q(s, a) + α[r + γQ(s’, a’) — Q(s, a)]

where:

- s represents the current state
- a represents the action taken in state s
- r represents the immediate reward received
- s’ represents the next state
- a’ represents the action selected in state s’ based on the current policy
- α represents the learning rate (0 < α ≤ 1)
- γ represents the discount factor (0 ≤ γ ≤ 1)

The learning rate, α, determines the extent to which the Q-value is updated based on the new information. A higher learning rate results in faster learning but may lead to instability, while a lower learning rate promotes slower but more stable learning. The discount factor, γ, determines the importance of future rewards. A value close to 0 prioritizes immediate rewards, while a value close to 1 places more emphasis on long-term rewards.

The learning process in SARSA involves the agent interacting with the environment in a sequence of episodes. In each episode, the agent starts in an initial state and selects actions based on its current policy (e.g., ε-greedy policy). The ε-greedy policy balances exploration and exploitation by selecting the action with the highest estimated Q-value with probability 1-ε and selecting a random action with probability ε. This allows the agent to explore the environment and potentially discover better actions while still exploiting its current knowledge.

After selecting an action, the agent takes the action, observes the resulting next state (s’) and the immediate reward (r). It then selects the next action (a’) based on the current policy and the Q-values of the next state. The Q-value of the current state-action pair, Q(s, a), is then updated using the SARSA update rule mentioned above. This process continues until the episode terminates, either by reaching a terminal state or exceeding a maximum number of steps.

One of the key characteristics of SARSA is its on-policy nature. Unlike off-policy algorithms such as Q-learning, SARSA updates the Q-values based on the actions actually taken by the current policy. This means that the agent learns from its own experiences and refines its policy based on the observed rewards and state transitions. The on-policy nature of SARSA allows for a more direct connection between the learned Q-values and the actual behavior of the agent.

SARSA has several advantages that make it a valuable algorithm in the RL toolkit. It is relatively straightforward to implement and has a solid theoretical foundation. SARSA can handle both discrete and continuous state and action spaces, making it applicable to a wide range of RL problems. Additionally, under certain conditions, SARSA has convergence guarantees, ensuring that the learned Q-values will converge to the optimal values given sufficient exploration and learning.

However, SARSA also has some limitations that should be considered. The algorithm can be sensitive to the choice of hyperparameters, such as the learning rate (α) and discount factor (γ). Selecting appropriate values for these parameters can significantly impact the algorithm’s performance and convergence properties. If the learning rate is set too high, the Q-values may oscillate and fail to converge, while setting it too low can result in slow learning. Similarly, the discount factor determines the balance between short-term and long-term rewards, and an inappropriate value can lead to suboptimal policies.

Moreover, SARSA may suffer from slow convergence in large state and action spaces. As the number of states and actions increases, the algorithm needs to explore and update the Q-values for all possible state-action pairs, which can be computationally expensive and time-consuming. This limitation can be partially addressed by using function approximation techniques, such as neural networks, to represent the Q-values more compactly.

When compared to other RL algorithms, SARSA shares similarities with Q-learning, another popular temporal difference learning algorithm. Both algorithms aim to learn the optimal action-value function and use similar update rules. However, the key difference lies in their learning strategies. While Q-learning is an off-policy algorithm that updates the Q-values based on the maximum expected future reward, regardless of the action taken, SARSA updates the Q-values based on the actual action taken by the current policy. This difference can lead to different learning dynamics and performance characteristics in certain scenarios.

Q-learning tends to be more optimistic in its value estimates, as it always considers the best possible future action, even if that action is not actually taken by the current policy. This optimism can lead to faster convergence in some cases but may also result in overestimation of Q-values. On the other hand, SARSA’s on-policy nature ensures that the learned Q-values are more closely tied to the actual behavior of the agent, which can be advantageous in scenarios where the optimal policy is not easily reachable or when the exploration-exploitation trade-off is critical.

In practice, the choice between SARSA and Q-learning often depends on the specific problem domain and the characteristics of the environment. SARSA may be preferred when the agent’s behavior during learning is important, and the on-policy nature is desirable. Q-learning, on the other hand, may be favored when the goal is to learn the optimal policy independently of the exploration strategy.

It’s worth noting that there are various extensions and modifications to the basic SARSA algorithm that aim to improve its performance and address specific challenges. For example, Expected SARSA is a variant that uses the expected value of the next action, rather than the actual action taken, in the update rule. This modification can help reduce the variance in the updates and improve the stability of learning. Other extensions, such as Backward SARSA and n-step SARSA, incorporate additional information from future rewards and states to enhance the learning process.

In summary, SARSA is a fundamental RL algorithm that learns an optimal policy by estimating action-value functions through on-policy temporal difference learning. It provides a principled framework for agents to interact with an environment, receive rewards, and iteratively refine their decision-making process. Despite its limitations, such as sensitivity to hyperparameters and potential slow convergence in large state and action spaces, SARSA remains a valuable tool in the RL toolkit. Its on-policy nature, simplicity, and theoretical grounding make it a go-to choice for many RL problems. By understanding the core concepts and mathematical formulation of SARSA, researchers and practitioners can effectively apply and adapt the algorithm to suit their specific needs and advance the field of reinforcement learning.