Rising Rested MAB with Linear Drift

TL;DR

This paper analyzes a non-stationary multi-armed bandit problem where rewards follow a linear drift, providing tight regret bounds and extending results to instance-dependent cases.

Contribution

It introduces tight regret bounds for a linear drift MAB model and extends to instance-dependent regret analysis, advancing understanding of non-stationary bandit problems.

Findings

Tight regret bounds of rac{4}{5}T^{4/5}K^{3/5} established

Extension to instance-dependent regret bounds based on unknown parameters

Provides both upper and lower bounds for the regret in linear drift MABs

Abstract

We consider non-stationary multi-arm bandit (MAB) where the expected reward of each action follows a linear function of the number of times we executed the action. Our main result is a tight regret bound of $\tilde{\Theta}(T^{4/5}K^{3/5})$, by providing both upper and lower bounds. We extend our results to derive instance dependent regret bounds, which depend on the unknown parametrization of the linear drift of the rewards.