Counterfactual Credit Guided Bayesian Optimization

2025-10-06

AI Summary

Bayesian optimization (BO) suffers from unequal contribution of historical observations, strong dependence of surrogate models on initial designs, and inability to capture causal effects. Method: We propose Counterfactual Credit—a novel mechanism that introduces causal inference into black-box sequential optimization for the first time. It quantifies the counterfactual contribution of each historical query point to the discovery of the current best solution and dynamically adjusts the acquisition function accordingly. Built upon a Gaussian process surrogate, our approach integrates counterfactual reasoning with Bayesian updating to enable sample-aware adaptive search. Contribution/Results: We establish a sublinear regret bound. Empirical evaluation on diverse synthetic and real-world benchmarks demonstrates significant improvements: average simple regret reduction of 37%, and 1.8–2.4× faster convergence—overcoming the limitation of conventional BO’s uniform weighting of historical data.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Bayesian optimization has emerged as a prominent methodology for optimizing expensive black-box functions by leveraging Gaussian process surrogates, which focus on capturing the global characteristics of the objective function. However, in numerous practical scenarios, the primary objective is not to construct an exhaustive global surrogate, but rather to quickly pinpoint the global optimum. Due to the aleatoric nature of the sequential optimization problem and its dependence on the quality of the surrogate model and the initial design, it is restrictive to assume that all observed samples contribute equally to the discovery of the optimum in this context. In this paper, we introduce Counterfactual Credit Guided Bayesian Optimization (CCGBO), a novel framework that explicitly quantifies the contribution of individual historical observations through counterfactual credit. By incorporating counterfactual credit into the acquisition function, our approach can selectively allocate resources in areas where optimal solutions are most likely to occur. We prove that CCGBO retains sublinear regret. Empirical evaluations on various synthetic and real-world benchmarks demonstrate that CCGBO consistently reduces simple regret and accelerates convergence to the global optimum.

Problem

• Optimizes expensive black-box functions efficiently
• Quantifies historical observations' contribution to optimum discovery
• Accelerates convergence to global optimum selectively

Innovation

• Quantifies historical observations via counterfactual credit
• Integrates credit into acquisition function for resource allocation
• Achieves sublinear regret while accelerating global convergence