Indirect Query Bayesian Optimization with Integrated Feedback

TL;DR

This paper introduces Indirect Query Bayesian Optimization (IQBO), a framework for optimizing functions using integrated feedback via conditional expectations, applicable in privacy-sensitive or constrained environments.

Contribution

The paper proposes the IQBO framework, a new class of Bayesian optimization that handles indirect feedback through conditional expectations, along with the CMES acquisition function and hierarchical search algorithm.

Findings

Regret bounds established for the proposed methods.

Effective optimization demonstrated on simulated tasks.

Hierarchical search improves computational efficiency.

Abstract

We develop the framework of Indirect Query Bayesian Optimization (IQBO), a new class of Bayesian optimization problems where the integrated feedback is given via a conditional expectation of the unknown function $f$ to be optimized. The underlying conditional distribution can be unknown and learned from data. The goal is to find the global optimum of $f$ by adaptively querying and observing in the space transformed by the conditional distribution. This is motivated by real-world applications where one cannot access direct feedback due to privacy, hardware or computational constraints. We propose the Conditional Max-Value Entropy Search (CMES) acquisition function to address this novel setting, and propose a hierarchical search algorithm with multi-resolution feedback to improve computational efficiency. We show regret bounds for our proposed methods and demonstrate the effectiveness of our approaches on simulated optimization tasks.