Indirect Query Bayesian Optimization with Integrated Feedback

2024-12-18

arXiv.org

AI Summary

We address the optimization of a black-box function $f$ under privacy- or hardware-constrained settings where direct evaluations are infeasible and only conditional expectation feedback is accessible. To this end, we propose Indirect Query Bayesian Optimization (IQBO), the first formal framework for indirect query optimization. Our method introduces the Conditional Maximum Entropy Search (CMES) acquisition function, which maximizes information gain about the optimal value by reducing uncertainty in the conditional distribution of $f$’s maximum. We further design a multi-resolution hierarchical search algorithm and provide a theoretical guarantee on its cumulative regret: $O(sqrt{Tgamma_T})$, where $gamma_T$ denotes the maximum information gain. Extensive experiments on diverse synthetic benchmarks demonstrate that IQBO significantly outperforms existing Bayesian optimization and surrogate-based approaches, confirming its efficacy and robustness in settings with indirect, expectation-based observations.

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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 to address the multi-resolution setting and improve the computational efficiency. We show regret bounds for our proposed methods and demonstrate the effectiveness of our approaches on simulated optimization tasks.

Problem

• Optimize unknown function f via conditional expectation feedback
• Learn conditional distribution from data for indirect queries
• Address privacy and hardware constraints in optimization tasks

Innovation

• Indirect Query Bayesian Optimization framework
• Conditional Max-Value Entropy Search acquisition
• Hierarchical search with multi-resolution feedback