Emergent Mind

Weighted Gaussian Process Bandits for Non-stationary Environments

(2107.02371)
Published Jul 6, 2021 in cs.LG and cs.AI

Abstract

In this paper, we consider the Gaussian process (GP) bandit optimization problem in a non-stationary environment. To capture external changes, the black-box function is allowed to be time-varying within a reproducing kernel Hilbert space (RKHS). To this end, we develop WGP-UCB, a novel UCB-type algorithm based on weighted Gaussian process regression. A key challenge is how to cope with infinite-dimensional feature maps. To that end, we leverage kernel approximation techniques to prove a sublinear regret bound, which is the first (frequentist) sublinear regret guarantee on weighted time-varying bandits with general nonlinear rewards. This result generalizes both non-stationary linear bandits and standard GP-UCB algorithms. Further, a novel concentration inequality is achieved for weighted Gaussian process regression with general weights. We also provide universal upper bounds and weight-dependent upper bounds for weighted maximum information gains. These results are of independent interest for applications such as news ranking and adaptive pricing, where weights can be adopted to capture the importance or quality of data. Finally, we conduct experiments to highlight the favorable gains of the proposed algorithm in many cases when compared to existing methods.

We're not able to analyze this paper right now due to high demand.

Please check back later (sorry!).

Generate a summary of this paper on our Pro plan:

We ran into a problem analyzing this paper.

Newsletter

Get summaries of trending comp sci papers delivered straight to your inbox:

Unsubscribe anytime.