Rising Rested MAB with Linear Drift
This addresses a specific challenge in online decision-making for scenarios with drifting rewards, representing an incremental theoretical advance.
The paper tackles the problem of non-stationary multi-armed bandits with linear drift in rewards, achieving a tight regret bound of θ̃(T^{4/5}K^{3/5}) and extending to instance-dependent bounds.
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 $\tildeΘ(T^{4/5}K^{3/5})$, 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.