Rebounding Bandits for Modeling Satiation Effects
Authors: Liu Leqi, Fatma Kilinc Karzan, Zachary Lipton, Alan Montgomery

Psychological research shows that enjoyment of many goods is subject to satiation, with short-term satisfaction declining after repeated exposures to the same item. Nevertheless, proposed algorithms for powering recommender systems seldom model these dynamics, instead proceeding as though user preferences were fixed in time. In this work, we introduce rebounding bandits, a multi-armed bandit setup, where satiation dynamics are modeled as time-invariant linear dynamical systems. Expected rewards for each arm decline monotonically with consecutive exposures and rebound towards the initial reward whenever that arm is not pulled. Unlike classical bandit algorithms, methods for tackling rebounding bandits must plan ahead and model-based methods rely on estimating the parameters of the satiation dynamics. We characterize the planning problem, showing that the greedy policy is optimal when the arms exhibit identical deterministic dynamics. To address stochastic satiation dynamics with unknown parameters, we propose Explore-Estimate-Plan, an algorithm that pulls arms methodically, estimates the system dynamics, and then plans accordingly.