Abstract: Methods, systems and apparatus, including computer programs encoded on computer storage media, for training a policy neural network by repeatedly updating the policy neural network at each of a plurality of training iterations. One of the methods includes generating training data for the training iteration by controlling the agent in accordance with an improved policy that selects actions in response to input state representations. A best response computation is performed using (i) a candidate policy generated from respective policy neural networks as of one or more preceding iterations and (ii) a candidate value neural network. The candidate value neural network is configured to generate a value output that is an estimate of a value of the environment being in the state characterized by a state representation to complete a particular task. The policy neural network is updated by training the policy neural network on the training data.