Model Selection in Batch Policy Optimization

Jonathan Lee, George Tucker, Ofir Nachum, Bo Dai
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:12542-12569, 2022.

Abstract

We study the problem of model selection in batch policy optimization: given a fixed, partial-feedback dataset and M model classes, learn a policy with performance that is competitive with the policy derived from the best model class. We formalize the problem in the contextual bandit setting with linear model classes by identifying three sources of error that any model selection algorithm should optimally trade-off in order to be competitive: (1) approximation error, (2) statistical complexity, and (3) coverage. The first two sources are common in model selection for supervised learning, where optimally trading off these two is well-studied. In contrast, the third source is unique to batch policy optimization and is due to dataset shift inherent to the setting. We first show that no batch policy optimization algorithm can achieve a guarantee addressing all three simultaneously, revealing a stark contrast between difficulties in batch policy optimization and the positive results available in supervised learning. Despite this negative result, we show that relaxing any one of the three error sources enables the design of algorithms achieving near-oracle inequalities for the remaining two. We conclude with experiments demonstrating the efficacy of these algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-lee22k, title = {Model Selection in Batch Policy Optimization}, author = {Lee, Jonathan and Tucker, George and Nachum, Ofir and Dai, Bo}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {12542--12569}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/lee22k/lee22k.pdf}, url = {https://proceedings.mlr.press/v162/lee22k.html}, abstract = {We study the problem of model selection in batch policy optimization: given a fixed, partial-feedback dataset and M model classes, learn a policy with performance that is competitive with the policy derived from the best model class. We formalize the problem in the contextual bandit setting with linear model classes by identifying three sources of error that any model selection algorithm should optimally trade-off in order to be competitive: (1) approximation error, (2) statistical complexity, and (3) coverage. The first two sources are common in model selection for supervised learning, where optimally trading off these two is well-studied. In contrast, the third source is unique to batch policy optimization and is due to dataset shift inherent to the setting. We first show that no batch policy optimization algorithm can achieve a guarantee addressing all three simultaneously, revealing a stark contrast between difficulties in batch policy optimization and the positive results available in supervised learning. Despite this negative result, we show that relaxing any one of the three error sources enables the design of algorithms achieving near-oracle inequalities for the remaining two. We conclude with experiments demonstrating the efficacy of these algorithms.} }
Endnote
%0 Conference Paper %T Model Selection in Batch Policy Optimization %A Jonathan Lee %A George Tucker %A Ofir Nachum %A Bo Dai %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-lee22k %I PMLR %P 12542--12569 %U https://proceedings.mlr.press/v162/lee22k.html %V 162 %X We study the problem of model selection in batch policy optimization: given a fixed, partial-feedback dataset and M model classes, learn a policy with performance that is competitive with the policy derived from the best model class. We formalize the problem in the contextual bandit setting with linear model classes by identifying three sources of error that any model selection algorithm should optimally trade-off in order to be competitive: (1) approximation error, (2) statistical complexity, and (3) coverage. The first two sources are common in model selection for supervised learning, where optimally trading off these two is well-studied. In contrast, the third source is unique to batch policy optimization and is due to dataset shift inherent to the setting. We first show that no batch policy optimization algorithm can achieve a guarantee addressing all three simultaneously, revealing a stark contrast between difficulties in batch policy optimization and the positive results available in supervised learning. Despite this negative result, we show that relaxing any one of the three error sources enables the design of algorithms achieving near-oracle inequalities for the remaining two. We conclude with experiments demonstrating the efficacy of these algorithms.
APA
Lee, J., Tucker, G., Nachum, O. & Dai, B.. (2022). Model Selection in Batch Policy Optimization. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:12542-12569 Available from https://proceedings.mlr.press/v162/lee22k.html.

Related Material