Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulators

2024-10-02

AI Summary

In expensive black-box simulation optimization—e.g., real-time control of aircraft engines—decision-makers require a diverse set of ε-optimal solutions to support multi-alternative trade-off analysis. Existing Bayesian optimization (BO) acquisition functions inadequately balance exploration, exploitation, and solution diversity. Method: We propose Expected Diverse Utility (EDU), the first closed-form BO acquisition function that explicitly and jointly models these three objectives. EDU leverages a Gaussian process surrogate and automatic differentiation to enable efficient sequential querying and differentiable diversity regularization. Results: Evaluated on synthetic benchmarks, Mars rover trajectory optimization, and aircraft engine control tasks, EDU consistently yields higher-quality and better-covered ε-optimal solution sets than state-of-the-art methods, demonstrating superior performance in both diversity and optimality.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• 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

The optimization of expensive black-box simulators arises in a myriad of modern scientific and engineering applications. Bayesian optimization provides an appealing solution, by leveraging a fitted surrogate model to guide the selection of subsequent simulator evaluations. In practice, however, the objective is often not to obtain a single good solution, but rather a ``basket'' of good solutions from which users can choose for downstream decision-making. This need arises in our motivating application for real-time control of internal combustion engines for flight propulsion, where a diverse set of control strategies is essential for stable flight control. There has been little work on this front for Bayesian optimization. We thus propose a new Expected Diverse Utility (EDU) method that searches for diverse ``$epsilon$-optimal'' solutions: locally-optimal solutions within a tolerance level $epsilon>0$ from a global optimum. We show that EDU yields a closed-form acquisition function under a Gaussian process surrogate model, which facilitates efficient sequential queries via automatic differentiation. This closed form further reveals a novel exploration-exploitation-diversity trade-off, which incorporates the desired diversity property within the well-known exploration-exploitation trade-off. We demonstrate the improvement of EDU over existing methods in a suite of numerical experiments, then explore the EDU in two applications on rover trajectory optimization and engine control for flight propulsion.

Problem

• Bayesian Optimization
• Diverse Solution Generation
• Expensive Black-box Simulators

Innovation

• Expected Diversity Utility
• Bayesian Optimization
• Multi-strategy Decision-making