A Last Switch Dependent Analysis of Satiation and Seasonality in Bandits

Motivated by the fact that humans like some level of unpredictability or novelty, and might therefore get quickly bored when interacting with a stationary policy, we introduce a novel non-stationary bandit problem, where the expected reward of an arm is fully determined by the time elapsed since the arm last took part in a switch of actions. Our model generalizes previous notions of delay-dependent rewards, and also relaxes most assumptions on the reward function. This enables the modeling of phenomena such as progressive satiation and periodic behaviours. Building upon the Combinatorial Semi-Bandits (CSB) framework, we design an algorithm and prove a bound on its regret with respect to the optimal non-stationary policy (which is NP-hard to compute). Similarly to previous works, our regret analysis is based on defining and solving an appropriate trade-off between approximation and estimation. Preliminary experiments confirm the superiority of our algorithm over both the oracle greedy approach and a vanilla CSB solver.