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Title: Explicit Mean-Square Error Bounds for Monte-Carlo and Linear Stochastic Approximation
This paper concerns error bounds for recursive equations subject to Markovian disturbances. Motivating examples abound within the fields of Markov chain Monte Carlo (MCMC) and Reinforcement Learning (RL), and many of these algorithms can be interpreted as special cases of stochastic approximation (SA). It is argued that it is not possible in general to obtain a Hoeffding bound on the error sequence, even when the underlying Markov chain is reversible and geometrically ergodic, such as the M/M/1 queue. This is motivation for the focus on mean square error bounds for parameter estimates. It is shown that mean square error achieves the optimal rate of $O(1/n)$, subject to conditions on the step-size sequence. Moreover, the exact constants in the rate are obtained, which is of great value in algorithm design  more » « less
Award ID(s):
1935389
NSF-PAR ID:
10483723
Author(s) / Creator(s):
Publisher / Repository:
Proceedings of Machine Learning Research
Date Published:
Journal Name:
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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