Optimism in Reinforcement Learning and Kullback-Leibler Divergence

Details Optimism in Reinforcement Learning and Kullback-Leibler Divergence Optimism in Reinforcement Learning and Kullback-Leibler Divergence

2010-04-29

arxiv.org/abs/1004.5229v3

Computer Science

Learning

This work has been accepted and presented at ALLERTON 2010; Communication, Control, and Computing (Allerton), 2010 48th Annual

Scientific paper

10.1109/ALLERTON.2010.5706896

We consider model-based reinforcement learning in finite Markov De- cision Processes (MDPs), focussing on so-called optimistic strategies. In MDPs, optimism can be implemented by carrying out extended value it- erations under a constraint of consistency with the estimated model tran- sition probabilities. The UCRL2 algorithm by Auer, Jaksch and Ortner (2009), which follows this strategy, has recently been shown to guarantee near-optimal regret bounds. In this paper, we strongly argue in favor of using the Kullback-Leibler (KL) divergence for this purpose. By studying the linear maximization problem under KL constraints, we provide an ef- ficient algorithm, termed KL-UCRL, for solving KL-optimistic extended value iteration. Using recent deviation bounds on the KL divergence, we prove that KL-UCRL provides the same guarantees as UCRL2 in terms of regret. However, numerical experiments on classical benchmarks show a significantly improved behavior, particularly when the MDP has reduced connectivity. To support this observation, we provide elements of com- parison between the two algorithms based on geometric considerations.

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