Jointly learning exploratory and non-exploratory action selection policies

Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for training an action selection neural network that is used to select actions to be performed by an agent interacting with an environment. In one aspect, the method comprises: receiving an observation characterizing a current state of the environment; processing the observation and an exploration importance factor using the action selection neural network to generate an action selection output; selecting an action to be performed by the agent using the action selection output; determining an exploration reward; determining an overall reward based on: (i) the exploration importance factor, and (ii) the exploration reward; and training the action selection neural network using a reinforcement learning technique based on the overall reward.