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Transferring knowledge across a sequence of related tasks is an importantchallenge in reinforcement learning (RL). Despite much encouraging empiricalevidence, there has been little theoretical analysis. In this paper, we study aclass of lifelong RL problems: the agent solves a sequence of tasks modeled asfinite Markov decision processes (MDPs), each of which is from a finite set ofMDPs with the same state/action sets and different transition/reward functions.Motivated by the need for cross-task exploration in lifelong learning, weformulate a novel online coupon-collector problem and give an optimalalgorithm. This allows us to develop a new lifelong RL algorithm, whose overallsample complexity in a sequence of tasks is much smaller than single-tasklearning, even if the sequence of tasks is generated by an adversary. Benefitsof the algorithm are demonstrated in simulated problems, including a recentlyintroduced human-robot interaction problem.

The Online Coupon-Collector Problem and Its Application to Lifelong Reinforcement Learning