Distributional reinforcement learning using quantile function neural networks
Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for selecting an action to be performed by a reinforcement learning agent interacting with an environment. In one aspect, a method comprises: receiving a current observation; for each action of a plurality of actions: randomly sampling one or more probability values; for each probability value: processing the action, the current observation, and the probability value using a quantile function network to generate an estimated quantile value for the probability value with respect to a probability distribution over possible returns that would result from the agent performing the action in response to the current observation; determining a measure of central tendency of the one or more estimated quantile values; and selecting an action to be performed by the agent in response to the current observation using the measures of central tendency for the actions.
1. A method performed by one or more computers, the method comprising:
selecting an action to be performed by a reinforcement learning agent interacting with an environment, comprising:
receiving a current observation characterizing a current state of the environment;
for each action of a plurality of actions that can be performed by the agent to interact with the environment:
sampling one or more random values;
for each random value:
processing a network input that comprises the action, the current observation, and the random value using an action selection neural network, in accordance with values of a set of action selection neural network parameters, to generate a network output that defines a sample from a return distribution,
wherein the return distribution defines a probability distribution over possible returns that would result from the agent performing the action in response to the observation; and
determining a measure of central tendency of the samples from the return distribution; and
selecting an action from the plurality of actions to be performed by the agent in response to the current observation using the measures of central tendency for the actions.
2. The method of claim 1 , wherein selecting an action to be performed by the agent comprises: selecting an action having the highest measure of central tendency.
3. The method of claim 1 , wherein selecting an action to be performed by the agent comprises:
selecting an action having the highest measure of central tendency with probability 1−ε and selecting an action randomly from the plurality of actions with probability ε.
4. The method of claim 1 , wherein each of the random values are sampled from a uniform distribution over an interval [0,1].
5. The method of claim 1 , wherein each of the random values is transformed by a distortion risk measure function prior to being processed by the action selection neural network.
6. The method of claim 5 , wherein:
the distortion risk measure function is a non-decreasing function mapping a domain [0,1] to a range [0,1];
the distortion risk measure function maps the point 0 in the domain to the point 0 in the range; and
the distortion risk measure function maps the point 1 in the domain to the point 1 in the range.
7. The method of claim 1 , wherein the measure of central tendency is a mean of the samples from the return distribution for the action.
8. The method of claim 1 , wherein processing the action, the current observation, and the random value using the action selection neural network comprises:
processing the current observation using one or more convolutional neural network layers to generate an encoded representation of the current observation;
processing the random value using one or more neural network layers to generate an encoded representation of the random value that has a same dimensionality as the encoded representation of the current observation;
determining a combined representation by pointwise multiplying the encoded representation of the current observation and the encoded representation of the random value; and
processing the combined representation and a numerical representation of the action using one or more fully-connected neural network layers.
9. A system comprising:
one or more computers; and
one or more storage devices communicatively coupled to the one or more computers, wherein the one or more storage devices store instructions that, when executed by the one or more computers, cause the one or more computers to perform operations comprising:
selecting an action to be performed by a reinforcement learning agent interacting with an environment, comprising:
receiving a current observation characterizing a current state of the environment;
for each action of a plurality of actions that can be performed by the agent to interact with the environment:
sampling one or more random values;
for each random value:
processing a network input that comprises the action, the current observation, and the random value using an action selection neural network, in accordance with values of a set of action selection neural network parameters, to generate a network output that defines a sample from a return distribution,
wherein the return distribution defines a probability distribution over possible returns that would result from the agent performing the action in response to the observation; and
determining a measure of central tendency of the samples from the return distribution; and
selecting an action from the plurality of actions to be performed by the agent in response to the current observation using the measures of central tendency for the actions.
10. The system of claim 9 , wherein selecting an action to be performed by the agent comprises:
selecting an action having the highest measure of central tendency.
11. The system of claim 9 , wherein selecting an action to be performed by the agent comprises:
selecting an action having the highest measure of central tendency with probability 1−ε and selecting an action randomly from the plurality of actions with probability ε.
12. The system of claim 9 , wherein each of the random values are sampled from a uniform distribution over an interval [0,1].
13. The system of claim 9 , wherein each of the random values is transformed by a distortion risk measure function prior to being processed by the action selection neural network.
14. The system of claim 13 , wherein:
the distortion risk measure function is a non-decreasing function mapping a domain [0,1] to a range [0,1];
the distortion risk measure function maps the point 0 in the domain to the point 0 in the range; and
the distortion risk measure function maps the point 1 in the domain to the point 1 in the range.
15. The system of claim 9 , wherein the measure of central tendency is a mean of the samples from the return distribution for the action.
16. The system of claim 9 , wherein processing the action, the current observation, and the random value using the action selection neural network comprises:
processing the current observation using one or more convolutional neural network layers to generate an encoded representation of the current observation;
processing the random value using one or more neural network layers to generate an encoded representation of the random value that has a same dimensionality as the encoded representation of the current observation;
determining a combined representation by pointwise multiplying the encoded representation of the current observation and the encoded representation of the random value; and
processing the combined representation and a numerical representation of the action using one or more fully-connected neural network layers.
17. One or more non-transitory computer storage media storing instructions that when executed by one or more computers cause the one or more computers to perform operations comprising:
selecting an action to be performed by a reinforcement learning agent interacting with an environment, comprising:
receiving a current observation characterizing a current state of the environment;
for each action of a plurality of actions that can be performed by the agent to interact with the environment:
sampling one or more random values;
for each random value:
processing a network input that comprises the action, the current observation, and the random value using an action selection neural network, in accordance with values of a set of action selection neural network parameters, to generate a network output that defines a sample from a return distribution,
wherein the return distribution defines a probability distribution over possible returns that would result from the agent performing the action in response to the observation; and
determining a measure of central tendency of the samples from the return distribution; and
selecting an action from the plurality of actions to be performed by the agent in response to the current observation using the measures of central tendency for the actions.
18. The non-transitory computer storage media of claim 17 , wherein selecting an action to be performed by the agent comprises:
selecting an action having the highest measure of central tendency.
19. The non-transitory computer storage media of claim 17 , wherein selecting an action to be performed by the agent comprises:
selecting an action having the highest measure of central tendency with probability 1−ε and selecting an action randomly from the plurality of actions with probability ε.
20. The non-transitory computer storage media of claim 17 , wherein each of the random values are sampled from a uniform distribution over an interval [0,1].