Multi Batch Reinforcement Learning

We consider the problem of Reinforcement Learning (RL) in a multi-batch setting, also sometimes called growing-batch setting. It consists in successive rounds: at each round, a batch of data is collected with a fixed policy, then the policy may be updated for the next round. In comparison with the more classical online setting, one cannot afford to train and use a bad policy and therefore exploration must be carefully controlled. This is even more dramatic when the batch size is indexed on the past policies performance. In comparison with the mono-batch setting, also called offline setting, one should not be too conservative and keep some form of exploration because it may compromise the asymptotic convergence to an optimal policy.In this article, we investigate the desired properties of RL algorithms in the multi-batch setting. Under some minimal assumptions, we show that the population of subjects either depletes or grows geometrically over time. This allows us to characterize conditions under which a safe policy update is preferred, and those conditions may be assessed in-between batches. We conclude the paper by advocating the benefits of using a portfolio of policies, to better control the desired amount of risk.