A single algorithm for both restless and rested rotting bandits

TL;DR

This paper introduces RAW-UCB, a novel algorithm that effectively handles both rested and restless rotting bandit problems, achieving near-optimal regret without prior knowledge of the setting or non-stationarity type.

Contribution

The paper presents RAW-UCB, the first algorithm to adaptively perform well in both rested and restless rotting bandit scenarios without prior setting knowledge.

Findings

RAW-UCB achieves near-optimal regret in synthetic experiments.

The algorithm performs well on dataset-based experiments.

It outperforms existing algorithms in both settings.

Abstract

In many application domains (e.g., recommender systems, intelligent tutoring systems), the rewards associated to the actions tend to decrease over time. This decay is either caused by the actions executed in the past (e.g., a user may get bored when songs of the same genre are recommended over and over) or by an external factor (e.g., content becomes outdated). These two situations can be modeled as specific instances of the rested and restless bandit settings, where arms are rotting (i.e., their value decrease over time). These problems were thought to be significantly different, since Levine et al. (2017) showed that state-of-the-art algorithms for restless bandit perform poorly in the rested rotting setting. In this paper, we introduce a novel algorithm, Rotting Adaptive Window UCB (RAW-UCB), that achieves near-optimal regret in both rotting rested and restless bandit, without any prior knowledge of the setting (rested or restless) and the type of non-stationarity (e.g., piece-wise constant, bounded variation). This is in striking contrast with previous negative results showing that no algorithm can achieve similar results as soon as rewards are allowed to increase. We confirm our theoretical findings on a number of synthetic and dataset-based experiments.