The Traveling Bandit: A Framework for Bayesian Optimization with Movement Costs

TL;DR

This paper presents a Bayesian Optimization framework that minimizes movement costs during input modifications, integrating Traveling Salesman Problem solutions to improve efficiency while maintaining performance.

Contribution

It introduces a plug-in framework for BO with movement costs, providing theoretical guarantees and empirical evidence of reduced costs without sacrificing regret.

Findings

Reduces average movement costs over time

Maintains comparable regret to standard BO methods

Applicable to broader bandit settings with movement costs

Abstract

This paper introduces a framework for Bayesian Optimization (BO) with metric movement costs, addressing a critical challenge in practical applications where input alterations incur varying costs. Our approach is a convenient plug-in that seamlessly integrates with the existing literature on batched algorithms, where designs within batches are observed following the solution of a Traveling Salesman Problem. The proposed method provides a theoretical guarantee of convergence in terms of movement costs for BO. Empirically, our method effectively reduces average movement costs over time while maintaining comparable regret performance to conventional BO methods. This framework also shows promise for broader applications in various bandit settings with movement costs.