OPERATIONS, TECHNOLOGY, AND INFORMATION MANAGEMENT


Fast Rates for the Regret of


Offline Reinforcement Learning Mathematics of Operations Research, 50, 1, February 2025 LINK TO PAPER


YICHUN HU ASSISTANT PROFESSOR


Samuel Curtis Johnson Graduate School of Management


Cornell SC Johnson College of Business Cornell University


Co-authors • Yichun Hu


Assistant Professor , Samuel Curtis Johnson Graduate School of Management, Cornell SC Johnson College of Business, Cornell University


• Nathan Kallus, Cornell Tech, Cornell University • Masatoshi Uehara, Evolutionary Scale/CSI Biohub


Summary Te authors study the regret of offline reinforcement learning in an in-


finite-horizon discounted Markov decision process (MDP). While existing analyses of common approaches, such as fitted Q-iteration (FQI), suggest root-n convergence for regret, empirical behavior exhibits much faster con- vergence. In this paper, the authors present a finer regret analysis that exactly characterizes this phenomenon by providing fast rates for the regret conver- gence.


First, they show that given any estimate for the optimal quality function, the regret of the policy it defines converges at a rate given by the exponentiation of the estimate’s pointwise convergence rate, thus speeding up the rate. Te level of exponentiation depends on the level of noise in the decision-making problem, rather than the estimation problem. Tey establish such noise levels for linear and tabular MDPs as examples. Second, they provide new analyses of FQI and Bellman residual minimization to establish the correct pointwise convergence guarantees. Tese results imply one-over-n rates in linear cases and exponential-in-n rates in tabular cases. Te authors extend their findings to general function approximation by extending the results to regret guaran- tees based on Lp-convergence rates for estimating the optimal quality function rather than pointwise rates, where L2 guarantees for nonparametric estima- tion can be ensured under mild conditions.S


CONTENTS TO MAIN


| RESEARCH WITH IMPACT: CORNELL SC JOHNSON COLLEGE OF BUSINESS • 2025 EDITION


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