SARSA Agent

The SARSA algorithm is an on-policy reinforcement learning method for environments with a discrete action space. A SARSA agent trains a value function based critic to estimate the expected discounted cumulative long-term reward of the current policy. Therefore, SARSA is the on-policy version of Q-learning. For more information on the different types of reinforcement learning agents, see Reinforcement Learning Agents.

In Reinforcement Learning Toolbox™, a SARSA agent is implemented by an rlSARSAAgent object.

Note

SARSA agents do not support recurrent networks.

SARSA agents can be trained in environments with the following observation and action spaces.

Observation Space	Action Space
Continuous or discrete	Discrete

SARSA agents use the following critic.

Critic	Actor
Q-value function critic Q(S,A), which you create using rlQValueFunction or rlVectorQValueFunction	SARSA agents do not use an actor.

During training, the agent explores the action space using epsilon-greedy exploration. During each control interval the agent selects a random action with probability ϵ, otherwise it selects the action for which the action-value function is greatest with probability 1–ϵ.

Critic Used by the SARSA Agent

To estimate the value of the current policy, a SARSA agent uses a critic. The critic is a function approximator object that implements the parametrized action-value function Q(S,A;ϕ), using parameters ϕ. For a given observation S and action A, the critic stores the corresponding estimate of the expected discounted cumulative long-term reward given the current policy. During training, the critic tunes the parameters in ϕ to improve its action-value function estimation. After training, the parameters remain at their tuned values in the critic internal to the trained agent.

For critics that use table-based value functions, the parameters in ϕ are the actual Q(S,A) values in the table.

For more information on creating critics, see Create Policies and Value Functions.

SARSA Agent Creation

To create a SARSA agent:

1. Create observation specifications for your environment. If you already have an environment object, you can obtain these specifications using getObservationInfo.

2. Create action specifications for your environment. If you already have an environment object, you can obtain these specifications using getActionInfo.

3. Create an approximation model for your critic. Depending on the type of problem and on the specific critic you use in the next step, this model can be an rlTable object (only for discrete observation spaces), a custom basis function with initial parameter values, or a neural network object. The inputs and outputs of the model you create depend on the type of critic you use in the next step.

4. Create a critic using rlQValueFunction or rlVectorQValueFunction. Use the model you created in the previous step as a first input argument.

5. Specify agent options using an rlSARSAAgentOptions object. Alternatively, you can skip this step and modify the agent options later using dot notation.

6. Create the agent using rlSARSAAgent.

SARSA Training Algorithm

SARSA agents use the following training algorithm. To configure the training algorithm, specify options using an rlSARSAAgentOptions object.

• Initialize the critic Q(S,A;ϕ) with random parameter values in ϕ.

• For each training episode:

  1. At the beginning of the episode, get the initial observation from the environment.

  2. For the current observation S, select a random action A with probability ϵ. Otherwise, select the action for which the critic value function is greatest.

     $$A=\arg \underset{A}{\max }Q\left(S,A;\varphi \right)$$

     To specify ϵ and its decay rate, use the EpsilonGreedyExploration option.

  3. Repeat the following operations for each step of the episode until S is a terminal state:

     1. Execute action A₀. Observe the reward R and the next observation S'.

     2. For the current observation S', select a random action A' with probability ϵ. Otherwise, select the action for which the critic value function is greatest.

        $$A\text{'}=\underset{A\text{'}}{\arg \max }Q\left(S\text{'},A\text{'};\varphi \right)$$

     3. If S' is a terminal state, set the value function target y to R. Otherwise, set it to

        $$y=R+\gamma Q\left(S\text{'},A\text{'};\varphi \right)$$

        To set the discount factor γ, use the DiscountFactor option.

     4. Compute the difference ΔQ between the value function target and the current Q(S,A;ϕ) value.

        $$\Delta Q=y-Q\left(S,A;\varphi \right)$$

     5. Update the critic using the learning rate α. Specify the learning rate when you create the critic by setting the LearnRate option in the rlCriticOptimizerOptions property within the agent options object.

        • For table-based critics, update the corresponding Q(S,A) value in the table.

          $$Q\left(S,A\right)=Q\left(S,A;\varphi \right)+\alpha \cdot \Delta Q$$

        • For all other types of critics, compute the gradients Δϕ of the loss function with respect to the parameters ϕ. Then, update the parameters based on the computed gradients. In this case, the loss function is the square of ΔQ.

          $$\begin{array}{l}\Delta \varphi =\frac{1}{2}{\nabla }_{\varphi }{\left(\Delta Q\right)}^2\\ \varphi =\varphi +\alpha \cdot \Delta \varphi \end{array}$$

     6. Set the observation S to S'.

     7. Set the action A to A'.

References

[1] Sutton, Richard S., and Andrew G. Barto. Reinforcement Learning: An Introduction. Second edition. Adaptive Computation and Machine Learning. Cambridge, Mass: The MIT Press, 2018.