## 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 which trains a critic to estimate the return or future rewards.

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

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 an action greedily with respect to the value function with probability 1-ϵ. This greedy action is the action for which the value function is greatest.

### Critic Function

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

For more information on creating critics for value function approximation, see Create Policy and Value Function Representations.

When training is complete, 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 `rlQValueRepresentation` 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 `rlQAgentOptions`.

• Initialize the critic Q(S,A) with random values.

• For each training episode:

1. Set the initial observation S.

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.

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

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:

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

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

4. Compute the critic parameter update.

`$\Delta Q=y-Q\left(S,A\right)$`
5. Update the critic using the learning rate α.

`$Q\left(S,A\right)=Q\left(S,A\right)+\alpha \ast \Delta Q$`

Specify the learning rate when you create the critic representation by setting the `LearnRate` option in the `rlRepresentationOptions` object.

6. Set the observation S to S'.