Reinforcement Learning in the Presence of Rare Events

We consider the task of reinforcement learning in an environment in which rare significant events occur independently of the actions selected by the controlling agent. If these events are sampled according to their natural probability of occurring, convergence of standard reinforcement learning algorithms is likely to be very slow, and the learning algorithms may exhibit high variance. In this work, we assume that we have access to a simulator, in which the rare event probabilities can be artificially altered. Then, importance sampling can be used to learn with this simulation data. We introduce algorithms for policy evaluation, both using tabular and function approximation representation of the value function. We prove that in both cases, the reinforcement learning algorithms converge. In the tabular case, we also analyze the bias and variance of our approach compared to TD-learning. We evaluate empirically the performance of the algorithm on random Markov Decision Processes, as well as on a large network planning task.