On the Optimality of Batch Policy Optimization Algorithms

Chenjun Xiao, Yifan Wu, Jincheng Mei, Bo Dai, Tor Lattimore, Lihong Li, Csaba Szepesvari, Dale Schuurmans
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:11362-11371, 2021.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-xiao21b, title = {On the Optimality of Batch Policy Optimization Algorithms}, author = {Xiao, Chenjun and Wu, Yifan and Mei, Jincheng and Dai, Bo and Lattimore, Tor and Li, Lihong and Szepesvari, Csaba and Schuurmans, Dale}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {11362--11371}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/xiao21b/xiao21b.pdf}, url = {https://proceedings.mlr.press/v139/xiao21b.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T On the Optimality of Batch Policy Optimization Algorithms %A Chenjun Xiao %A Yifan Wu %A Jincheng Mei %A Bo Dai %A Tor Lattimore %A Lihong Li %A Csaba Szepesvari %A Dale Schuurmans %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-xiao21b %I PMLR %P 11362--11371 %U https://proceedings.mlr.press/v139/xiao21b.html %V 139 %X 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.
APA
Xiao, C., Wu, Y., Mei, J., Dai, B., Lattimore, T., Li, L., Szepesvari, C. & Schuurmans, D.. (2021). On the Optimality of Batch Policy Optimization Algorithms. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:11362-11371 Available from https://proceedings.mlr.press/v139/xiao21b.html.

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