The Optimal Approximation Factors in Misspecified Off-Policy Value Function Estimation

Philip Amortila, Nan Jiang, Csaba Szepesvari
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:768-790, 2023.

Abstract

Theoretical guarantees in reinforcement learning (RL) are known to suffer multiplicative blow-up factors with respect to the misspecification error of function approximation. Yet, the nature of such approximation factors—especially their optimal form in a given learning problem—is poorly understood. In this paper we study this question in linear off-policy value function estimation, where many open questions remain. We study the approximation factor in a broad spectrum of settings, such as presence vs. absence of state aliasing and full vs. partial coverage of the state space. Our core results include instance-dependent upper bounds on the approximation factors with respect to both the weighted $L_2$-norm (where the weighting is the offline state distribution) and the $L_\infty$ norm. We show that these approximation factors are optimal (in an instance-dependent sense) for a number of these settings. In other cases, we show that the instance-dependent parameters which appear in the upper bounds are necessary, and that the finiteness of either alone cannot guarantee a finite approximation factor even in the limit of infinite data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-amortila23a, title = {The Optimal Approximation Factors in Misspecified Off-Policy Value Function Estimation}, author = {Amortila, Philip and Jiang, Nan and Szepesvari, Csaba}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {768--790}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/amortila23a/amortila23a.pdf}, url = {https://proceedings.mlr.press/v202/amortila23a.html}, abstract = {Theoretical guarantees in reinforcement learning (RL) are known to suffer multiplicative blow-up factors with respect to the misspecification error of function approximation. Yet, the nature of such approximation factors—especially their optimal form in a given learning problem—is poorly understood. In this paper we study this question in linear off-policy value function estimation, where many open questions remain. We study the approximation factor in a broad spectrum of settings, such as presence vs. absence of state aliasing and full vs. partial coverage of the state space. Our core results include instance-dependent upper bounds on the approximation factors with respect to both the weighted $L_2$-norm (where the weighting is the offline state distribution) and the $L_\infty$ norm. We show that these approximation factors are optimal (in an instance-dependent sense) for a number of these settings. In other cases, we show that the instance-dependent parameters which appear in the upper bounds are necessary, and that the finiteness of either alone cannot guarantee a finite approximation factor even in the limit of infinite data.} }
Endnote
%0 Conference Paper %T The Optimal Approximation Factors in Misspecified Off-Policy Value Function Estimation %A Philip Amortila %A Nan Jiang %A Csaba Szepesvari %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-amortila23a %I PMLR %P 768--790 %U https://proceedings.mlr.press/v202/amortila23a.html %V 202 %X Theoretical guarantees in reinforcement learning (RL) are known to suffer multiplicative blow-up factors with respect to the misspecification error of function approximation. Yet, the nature of such approximation factors—especially their optimal form in a given learning problem—is poorly understood. In this paper we study this question in linear off-policy value function estimation, where many open questions remain. We study the approximation factor in a broad spectrum of settings, such as presence vs. absence of state aliasing and full vs. partial coverage of the state space. Our core results include instance-dependent upper bounds on the approximation factors with respect to both the weighted $L_2$-norm (where the weighting is the offline state distribution) and the $L_\infty$ norm. We show that these approximation factors are optimal (in an instance-dependent sense) for a number of these settings. In other cases, we show that the instance-dependent parameters which appear in the upper bounds are necessary, and that the finiteness of either alone cannot guarantee a finite approximation factor even in the limit of infinite data.
APA
Amortila, P., Jiang, N. & Szepesvari, C.. (2023). The Optimal Approximation Factors in Misspecified Off-Policy Value Function Estimation. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:768-790 Available from https://proceedings.mlr.press/v202/amortila23a.html.

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