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On the Optimality of Batch Policy Optimization Algorithms
Chenjun Xiao · Yifan Wu · Jincheng Mei · Bo Dai · Tor Lattimore · Lihong Li · Csaba Szepesvari · Dale Schuurmans

Tue Jul 20 05:40 AM -- 05:45 AM (PDT) @
in Deep Reinforcement Learning 2 »

Batch policy optimization considers leveraging existing data for policy construction before interacting with an environment. Although interest in this problem has grown significantly in recent years, its theoretical foundations remain under-developed. To advance the understanding of this problem, we provide three results that characterize the limits and possibilities of batch policy optimization in the finite-armed stochastic bandit setting. First, we introduce a class of confidence-adjusted index algorithms that unifies optimistic and pessimistic principles in a common framework, which enables a general analysis. For this family, we show that any confidence-adjusted index algorithm is minimax optimal, whether it be optimistic, pessimistic or neutral. Our analysis reveals that instance-dependent optimality, commonly used to establish optimality of on-line stochastic bandit algorithms, cannot be achieved by any algorithm in the batch setting. In particular, for any algorithm that performs optimally in some environment, there exists another environment where the same algorithm suffers arbitrarily larger regret. Therefore, to establish a framework for distinguishing algorithms, we introduce a new weighted-minimax criterion that considers the inherent difficulty of optimal value prediction. We demonstrate how this criterion can be used to justify commonly used pessimistic principles for batch policy optimization.

Keywords: Reinforcement Learning and Planning

Author Information

Chenjun Xiao (Google / University of Alberta)
Yifan Wu (Carnegie Mellon University)
Jincheng Mei (University of Alberta / Google Brain)
Bo Dai (Google Brain)
Tor Lattimore (DeepMind)
Lihong Li (Amazon)
Csaba Szepesvari (DeepMind/University of Alberta)
Dale Schuurmans (Google / University of Alberta)

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