Non-Stationary Bandits under Recharging Payoffs: Improved Planning with Sublinear Regret
This work addresses a critical challenge in recommendation and ad systems by improving algorithmic guarantees for handling user behavior dynamics, though it is incremental as it builds on prior approximations.
The paper tackles the NP-hard planning problem in non-stationary bandits with recharging payoffs, where mean payoffs increase after an arm is not played, by developing a polynomial-time (1-1/e)-approximation algorithm for known functions and extending it to achieve sublinear regret when functions are unknown.
The stochastic multi-armed bandit setting has been recently studied in the non-stationary regime, where the mean payoff of each action is a non-decreasing function of the number of rounds passed since it was last played. This model captures natural behavioral aspects of the users which crucially determine the performance of recommendation platforms, ad placement systems, and more. Even assuming prior knowledge of the mean payoff functions, computing an optimal planning in the above model is NP-hard, while the state-of-the-art is a $1/4$-approximation algorithm for the case where at most one arm can be played per round. We first focus on the setting where the mean payoff functions are known. In this setting, we significantly improve the best-known guarantees for the planning problem by developing a polynomial-time $(1-{1}/{e})$-approximation algorithm (asymptotically and in expectation), based on a novel combination of randomized LP rounding and a time-correlated (interleaved) scheduling method. Furthermore, our algorithm achieves improved guarantees -- compared to prior work -- for the case where more than one arm can be played at each round. Moving to the bandit setting, when the mean payoff functions are initially unknown, we show how our algorithm can be transformed into a bandit algorithm with sublinear regret.