Combinatorial Bandit Bayesian Optimization for Tensor Outputs

Jingru Huang, Haijie Xu, Jie Guo, Manrui Jiang, Chen Zhang

Keywords: Tensor data, Non-separable kernels, Gaussian process, Bayesian optimization, Combinatorial multi-arm bandit, Upper confidence bound

TL;DR: We develop BO and combinatorial bandit BO frameworks for tensor-output systems, built upon the proposed tensor-output GP with a non-separable kernel as the surrogate model.

Abstract: Bayesian optimization (BO) has been widely used to optimize expensive and black-box functions across various domains. However, existing BO methods have not addressed tensor-output functions. To fill this gap, we propose a novel tensor-output BO framework. Specifically, we first introduce a tensor-output Gaussian process (TOGP) with two classes of tensor-output kernels as a surrogate model of the tensor-output function, which can effectively capture the structural dependencies within the tensor. Based on it, we develop an upper confidence bound (UCB) acquisition function to select query points. Furthermore, we introduce a more practical and challenging problem setting, termed combinatorial bandit Bayesian optimization (CBBO), where only a subset of the tensor outputs can be selected to contribute to the objective. To tackle this, we propose a tensor-output CBBO method, which extends TOGP to handle partially observed tensor outputs, and accordingly design a novel combinatorial multi-arm bandit-UCB2 (CMAB-UCB2) criterion to sequentially select both the query points and the output subset. We establish theoretical regret bounds for both methods, guaranteeing sublinear regret. Extensive experiments on synthetic and real-world datasets demonstrate the superiority of our methods.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

Submission Number: 15977