Mitigating Covariate Shift in Misspecified Regression with Applications to Reinforcement Learning

Fuente: arXiv
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Main Authors: Amortila, Philip, Cao, Tongyi, Krishnamurthy, Akshay
Format: Preprint
Published: 2024
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author Amortila, Philip
Cao, Tongyi
Krishnamurthy, Akshay
author_facet Amortila, Philip
Cao, Tongyi
Krishnamurthy, Akshay
contents A pervasive phenomenon in machine learning applications is distribution shift, where training and deployment conditions for a machine learning model differ. As distribution shift typically results in a degradation in performance, much attention has been devoted to algorithmic interventions that mitigate these detrimental effects. In this paper, we study the effect of distribution shift in the presence of model misspecification, specifically focusing on $L_{\infty}$-misspecified regression and adversarial covariate shift, where the regression target remains fixed while the covariate distribution changes arbitrarily. We show that empirical risk minimization, or standard least squares regression, can result in undesirable misspecification amplification where the error due to misspecification is amplified by the density ratio between the training and testing distributions. As our main result, we develop a new algorithm -- inspired by robust optimization techniques -- that avoids this undesirable behavior, resulting in no misspecification amplification while still obtaining optimal statistical rates. As applications, we use this regression procedure to obtain new guarantees in offline and online reinforcement learning with misspecification and establish new separations between previously studied structural conditions and notions of coverage.
format Preprint
id arxiv_https___arxiv_org_abs_2401_12216
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Mitigating Covariate Shift in Misspecified Regression with Applications to Reinforcement Learning
Amortila, Philip
Cao, Tongyi
Krishnamurthy, Akshay
Machine Learning
Optimization and Control
A pervasive phenomenon in machine learning applications is distribution shift, where training and deployment conditions for a machine learning model differ. As distribution shift typically results in a degradation in performance, much attention has been devoted to algorithmic interventions that mitigate these detrimental effects. In this paper, we study the effect of distribution shift in the presence of model misspecification, specifically focusing on $L_{\infty}$-misspecified regression and adversarial covariate shift, where the regression target remains fixed while the covariate distribution changes arbitrarily. We show that empirical risk minimization, or standard least squares regression, can result in undesirable misspecification amplification where the error due to misspecification is amplified by the density ratio between the training and testing distributions. As our main result, we develop a new algorithm -- inspired by robust optimization techniques -- that avoids this undesirable behavior, resulting in no misspecification amplification while still obtaining optimal statistical rates. As applications, we use this regression procedure to obtain new guarantees in offline and online reinforcement learning with misspecification and establish new separations between previously studied structural conditions and notions of coverage.
title Mitigating Covariate Shift in Misspecified Regression with Applications to Reinforcement Learning
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2401.12216