Q-Learning Agents

The Q-learning algorithm is a model-free, online, off-policy reinforcement learning method. A Q-learning agent is a value-based reinforcement learning agent that trains a critic to estimate the return or future rewards. For a given observation, the agent selects and outputs the action for which the estimated return is greatest.

For more information on the different types of reinforcement learning agents, see Reinforcement Learning Agents.

Q-learning agents can be trained in environments with the following observation and action spaces.

Observation SpaceAction Space
Continuous or discreteDiscrete

Q agents use the following critic.

CriticActor

Q-value function critic Q(S,A), which you create using `rlQValueFunction` or `rlVectorQValueFunction`

Q 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 value function greatest with probability 1–ϵ.

Critic Function Approximator

To estimate the value function, a Q-learning agent maintains a critic Q(S,A;ϕ), which is a function approximator with parameters ϕ. The critic takes observation S and action A as inputs and returns the corresponding expectation of the long-term reward.

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 for value function approximation, see Create Policies and Value Functions.

During training, the agent tunes the parameter values in ϕ. After training, the parameters remain at their tuned value and the trained value function approximator is stored in critic Q(S,A).

Agent Creation

To create a Q-learning agent:

1. Create a critic using an `rlQValueFunction` object.

2. Specify agent options using an `rlQAgentOptions` object.

3. Create the agent using an `rlQAgent` object.

Training Algorithm

Q-learning agents use the following training algorithm. To configure the training algorithm, specify options using an `rlQAgentOptions` object.

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

• For each training episode:

1. Get the initial observation S from the environment.

2. Repeat the following for each step of the episode until S is a terminal state.

1. 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.

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

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

2. Execute action A. Observe the reward R and next observation S'.

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

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

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'.