2025/05/30 by Everett, Derek, Lu, Fred, Raff, Edward +2
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · doi:10.48550/arxiv.2505.24692
Canonical algorithms for multi-armed bandits typically assume a stationary reward environment where the size of the action space (number of arms) is small. More recently developed methods typically relax only one of these assumptions: existing non-stationary bandit policies are designed for a small number of arms, while Lipschitz, linear, and Gaussian process bandit policies are designed to handle a large (or infinite) number of arms in stationary reward environments under constraints on the reward function. In this manuscript, we propose a novel policy to learn reward environments over a continuous space using Gaussian interpolation. We show that our method efficiently learns continuous Lipschitz reward functions with O^*(√(T)) cumulative regret. Furthermore, our method naturally extends to non-stationary problems with a simple modification. We finally demonstrate that our method is computationally favorable (100-10000x faster) and experimentally outperforms sliding Gaussian process policies on datasets with non-stationarity and an extremely large number of arms.