Last Switch Dependent Bandits with Monotone Payoff Functions

Ayoub Foussoul*, Vineet Goyal, Orestis Papadigenopoulos*, Assaf Zeevi

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation, where consecutive plays of the same action lead to decreased performance, or deprivation, where the payoff of an action increases after an interval of inactivity. In this work, we take a step towards understanding the approximability of planning LSD bandits, namely, the (NP-hard) problem of computing an optimal arm-pulling strategy under complete knowledge of the model. In particular, we design the first efficient constant approximation algorithm for the problem and show that, under a natural monotonicity assumption on the payoffs, its approximation guarantee (almost) matches the state-of-the-art for the special and well-studied class of recharging bandits (also known as delay-dependent). In this attempt, we develop new tools and insights for this class of problems, including a novel higher-dimensional relaxation and the technique of mirroring the evolution of virtual states. We believe that these novel elements could potentially be used for approaching richer classes of action-induced nonstationary bandits (e.g., special instances of restless bandits). In the case where the model parameters are initially unknown, we develop an online learning adaptation of our algorithm for which we provide sublinear regret guarantees against its full-information counterpart.

Original languageEnglish
Pages (from-to)10265-10284
Number of pages20
JournalProceedings of Machine Learning Research
Volume202
StatePublished - 2023
Externally publishedYes
Event40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States
Duration: 23 Jul 202329 Jul 2023

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