Distributional reinforcement learning for continuous control tasks

1. A computer-implemented method for training an action selection neural network having a plurality of action selection parameters and used to select actions to be performed by an agent interacting with an environment, wherein the action selection neural network is configured to receive an input observation characterizing a state of the environment and to map the input observation to an action, the method comprising:

maintaining a respective replica of the action selection neural network;

receiving an observation characterizing a current state of an instance of the environment;

generating a respective transition starting from the received observation by selecting actions to be performed by the agent using the action selection neural network replica and in accordance with current values of the action selection parameters;

storing respective data for the respective transition in a memory; and

using a transition sampled from the memory to train the action selection neural network, the sampled transition comprising at least an observation-action-reward triple, and the training comprising:

processing an observation-action pair in the observation-action-reward triple of the sampled transition to generate, for the triple, a distribution over possible returns that could result if the action is performed in response to the observation; and

determining an update to the action selection parameters using the distribution over the possible returns.

2. The method of claim 1 wherein processing the observation-action pair in the sampled transition to generate the distribution over the possible returns comprises:

processing the observation-action pair in the sampled transition using a critic model having critic parameters to generate, for the triple, the distribution over possible returns that could result if the action in the triple is performed in response to the observation.

3. The method of claim 2 , wherein the critic model comprises a distributional Q network.

4. The method of claim 2 , wherein determining the update to the action selection parameters comprises:

determining an update to the critic parameters of the critic model based on a target distribution for the triple and the distribution over the possible returns generated by the critic model for the triple; and

determining the update to the action selection parameters using the critic model.

5. The method of claim 4 , wherein determining the update to the action selection parameters using the critic model comprises:

processing the observation in the triple using the action selection neural network to generate a predicted action for the observation; and

determining a parameter update for the action selection neural network based on (i) an expectation of a gradient of a critic model output with respect to the predicted action and at an observation-predicted action input pair and (ii) a gradient of the action selection neural network output with respect to the action selection parameters of the action selection neural network taken at the observation.

6. The method of claim 4 , wherein determining the update to the critic parameters of the critic model comprises:

determining a gradient of a critic objective that depends on a distance between the target distribution for the triple and the distribution generated by the critic model for the triple.

7. The method of claim 4 , wherein the sampled transition further comprises a last observation, and the method further comprises:

generating a distribution over possible returns for the last observation that represents a distribution over possible returns that could result if a next action is performed in response to the last observation, wherein the next action has been determined from the last observation using a target action selection network; and

determining the target distribution for the triple from the reward in the triple and the distribution over possible returns for the last observation.

8. The method of claim 1 , wherein the transitions in the memory are each associated with a respective priority, and wherein the sampling is biased by the priorities for the transitions in the memory.

9. The method of claim 1 , wherein the transition is a single step transition.

10. The method of claim 1 , wherein the transition is an N-step transition.

11. The method of claim 1 , wherein:

the distribution over the possible returns is a categorical distribution.

12. A computer-implemented system training an action selection neural network having a plurality of action selection parameters and used to select actions to be performed by an agent interacting with an environment, wherein the action selection neural network is configured to receive an input observation characterizing a state of the environment and to map the input observation to an action, the system comprising:

one or more processors; and

one or more storage devices storing instructions that when executed by the one or more computers, cause the one or more processors to perform learner operations comprising:

maintaining a respective replica of the action selection neural network;

receiving an observation characterizing a current state of an instance of the environment;

generating a respective transition starting from the received observation by selecting actions to be performed by the agent using the action selection neural network replica and in accordance with current values of the action selection parameters;

storing respective data for the respective transition in a memory; and

using a transition sampled from the memory to train the action selection neural network, the sampled transition comprising at least an observation-action-reward triple, and the training comprising:

processing an observation-action pair in the observation-action-reward triple of the sampled transition to generate, for the triple, a distribution over possible returns that could result if the action is performed in response to the observation; and

determining an update to the action selection parameters using the distribution over the possible returns.

13. The system of claim 12 , wherein processing the observation-action pair in the sampled transition to generate the distribution over the possible returns comprises:

processing the observation-action pair in the sampled transition using a critic model having critic parameters to generate, for the triple, the distribution over possible returns that could result if the action is performed in response to the observation.

14. The system of claim 13 , wherein the critic model comprises a distributional Q network.

15. The system of claim 13 , wherein determining the update to the action selection parameters comprises:

determining an update to the critic parameters of the critic model based on a target distribution for the triple and the distribution over the possible returns generated by the critic model for the triple; and

determining the update to the action selection parameters using the critic model.

16. The system of claim 15 , wherein determining the update to the action selection parameters using the critic model comprises:

processing the observation in the triple using the action selection neural network to generate a predicted action for the observation; and

determining a parameter update for the action selection neural network based on (i) an expectation of a gradient of the critic model output with respect to the predicted action and at an observation-predicted action input pair and (ii) a gradient of the action selection neural network output with respect to the action selection parameters of the action selection neural network taken at the observation.

17. The system of claim 15 , wherein determining the update to the critic parameters of the critic model comprises:

determining a gradient of a critic objective that depends on a distance between the target distribution for the triple and the distribution generated by the critic model for the triple.

18. One or more non-transitory computer-readable storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations for training an action selection neural network having a plurality of action selection parameters and used to select actions to be performed by an agent interacting with an environment, wherein the action selection neural network is configured to receive an input observation characterizing a state of the environment and to map the input observation to an action, the operations comprising:

maintaining a respective replica of the action selection neural network;

receiving an observation characterizing a current state of an instance of the environment;

generating a respective transition starting from the received observation by selecting actions to be performed by the agent using the action selection neural network replica and in accordance with current values of the action selection parameters;

storing respective data for the respective transition in a memory; and

using a transition sampled from the memory to train the action selection neural network, the sampled transition comprising at least an observation-action-reward triple, and the training comprising:

processing an observation-action pair in the observation-action-reward triple of the sampled transition to generate, for the triple, a distribution over possible returns that could result if the action is performed in response to the observation; and

determining an update to the action selection parameters using the distribution over the possible returns.

19. The non-transitory computer-readable storage media of claim 18 , wherein the transitions in the memory are each associated with a respective priority, and wherein the sampling is biased by the priorities for the transitions in the memory.

20. The non-transitory computer-readable storage media of claim 18 , wherein the transition is a single step transition.