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Title: Is Q-Learning Minimax Optimal? A Tight Sample Complexity Analysis

This paper investigates a model-free algorithm of broad interest in reinforcement learning, namely, Q-learning. Whereas substantial progress had been made toward understanding the sample efficiency of Q-learning in recent years, it remained largely unclear whether Q-learning is sample-optimal and how to sharpen the sample complexity analysis of Q-learning. In this paper, we settle these questions: (1) When there is only a single action, we show that Q-learning (or, equivalently, TD learning) is provably minimax optimal. (2) When there are at least two actions, our theory unveils the strict suboptimality of Q-learning and rigorizes the negative impact of overestimation in Q-learning. Our theory accommodates both the synchronous case (i.e., the case in which independent samples are drawn) and the asynchronous case (i.e., the case in which one only has access to a single Markovian trajectory).

 
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Award ID(s):
1806154 2106778 2134080
NSF-PAR ID:
10501626
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
INFORMS
Date Published:
Journal Name:
Operations Research
Volume:
72
Issue:
1
ISSN:
0030-364X
Page Range / eLocation ID:
222 to 236
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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