Abstract: Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for training an action selection system using reinforcement learning techniques. In one aspect, a method comprises at each of multiple iterations: obtaining a batch of experience, each experience tuple comprising: a first observation, an action, a second observation, and a reward; for each experience tuple, determining a state value for the second observation, comprising: processing the first observation using a policy neural network to generate an action score for each action in a set of possible actions; sampling multiple actions from the set of possible actions in accordance with the action scores; processing the second observation using a Q neural network to generate a Q value for each sampled action; and determining the state value for the second observation; and determining an update to current values of the Q neural network parameters using the state values.