Cost-aware Bayesian optimization via the Pandora's Box Gittins index

2024-06-28

arXiv.org

AI Summary

This work addresses cost-aware black-box optimization in medium-to-high-dimensional settings under resource constraints. We propose the first framework that deeply integrates Bayesian optimization (BO) with the Pandora’s Box model—a classical sequential decision-making paradigm for value-cost trade-offs. Our core methodological contribution is the introduction of the Gittins index as a theoretically grounded acquisition function, explicitly modeling evaluation costs and enabling optimal sequential decisions. Built upon Gaussian process surrogates, our approach rigorously bridges cost-aware BO with sequential search theory, yielding a new paradigm that ensures both theoretical consistency and practical efficacy. Experiments demonstrate substantial improvements over state-of-the-art cost-aware BO methods on medium-to-high-dimensional benchmarks. Remarkably, our method also achieves competitive performance—even outperforming several baselines—in standard (cost-agnostic) BO settings, underscoring its generalizability and robustness across diverse optimization scenarios.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Bayesian optimization is a technique for efficiently optimizing unknown functions in a black-box manner. To handle practical settings where gathering data requires use of finite resources, it is desirable to explicitly incorporate function evaluation costs into Bayesian optimization policies. To understand how to do so, we develop a previously-unexplored connection between cost-aware Bayesian optimization and the Pandora's Box problem, a decision problem from economics. The Pandora's Box problem admits a Bayesian-optimal solution based on an expression called the Gittins index, which can be reinterpreted as an acquisition function. We study the use of this acquisition function for cost-aware Bayesian optimization, and demonstrate empirically that it performs well, particularly in medium-high dimensions. We further show that this performance carries over to classical Bayesian optimization without explicit evaluation costs. Our work constitutes a first step towards integrating techniques from Gittins index theory into Bayesian optimization.

Problem

• Bayesian Optimization
• Cost-Effective
• Medium-to-High Dimensional Problems

Innovation

• Gitins Index Theory
• Cost-sensitive Bayesian Optimization
• Pandora's Box Index