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On Abruptly-Changing and Slowly-Varying Multiarmed Bandit Problems

33 citations0/0 files storedProceedings of the ... American Control Conference/Proceedings of the American Control Conference

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Advanced Bandit Algorithms Research Reinforcement Learning in Robotics Optimization and Search Problems

Abstract

We study the non-stationary stochastic multi-armed bandit (MAB) problem and propose two generic algorithms, namely, Limited Memory Deterministic Sequencing of Exploration and Exploitation (LM-DSEE) and Sliding-Window Upper Confidence Bound# (SW-UCB#). We rigorously analyze these algorithms in abruptly-changing and slowly-varying environments and characterize their performance. We show that the expected cumulative regret for these algorithms in either of the environments is upper bounded by sublinear functions of time, i.e., the time average of the regret asymptotically converges to zero. We complement our analysis with numerical illustrations.

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References

2002Finite-time Analysis of the Multiarmed Bandit Problem 2002The Nonstochastic Multiarmed Bandit Problem 2008On Upper-Confidence Bound Policies for Non-Stationary Bandit Problems 2012Learning in a Changing World: Restless Multiarmed Bandit With Unknown Dynamics 1988Asymptotically efficient adaptive allocation rules for the multiarmed bandit problem with switching cost 2019Optimal Exploration–Exploitation in a Multi-armed Bandit Problem with Non-stationary Rewards 2018A Change-Detection Based Framework for Piecewise-Stationary Multi-Armed Bandit Problem 2013Deterministic Sequencing of Exploration and Exploitation for Multi-Armed Bandit Problems

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2019Hedging the Drift: Learning to Optimize under Non-Stationarity

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