Non-Myopic Multi-Objective Bayesian Optimization

2024-12-11

arXiv.org

AI Summary

This work addresses expensive black-box multi-objective optimization (MOO) under severe resource constraints, where conventional myopic Bayesian optimization (BO) fails due to its incompatibility with the Bellman optimality principle in MOO. Method: We propose the first non-myopic MOO framework, which employs hypervolume improvement (HVI) as the scalarization criterion and models finite-horizon lookahead decisions. We design three novel acquisition functions—Nested, Joint, and BINOM—and integrate batched expected HVI (EHVI) with lower-bound approximations of the Bellman equation. Contribution/Results: Evaluated on multiple real-world MOO benchmarks—including materials design—the framework significantly outperforms state-of-the-art myopic methods under limited evaluation budgets. It demonstrates superior effectiveness and robustness, establishing a scalable, non-myopic paradigm for resource-constrained experimental MOO.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• 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

We consider the problem of finite-horizon sequential experimental design to solve multi-objective optimization (MOO) of expensive black-box objective functions. This problem arises in many real-world applications, including materials design, where we have a small resource budget to make and evaluate candidate materials in the lab. We solve this problem using the framework of Bayesian optimization (BO) and propose the first set of non-myopic methods for MOO problems. Prior work on non-myopic BO for single-objective problems relies on the Bellman optimality principle to handle the lookahead reasoning process. However, this principle does not hold for most MOO problems because the reward function needs to satisfy some conditions: scalar variable, monotonicity, and additivity. We address this challenge by using hypervolume improvement (HVI) as our scalarization approach, which allows us to use a lower-bound on the Bellman equation to approximate the finite-horizon using a batch expected hypervolume improvement (EHVI) acquisition function (AF) for MOO. Our formulation naturally allows us to use other improvement-based scalarizations and compare their efficacy to HVI. We derive three non-myopic AFs for MOBO: 1) the Nested AF, which is based on the exact computation of the lower bound, 2) the Joint AF, which is a lower bound on the nested AF, and 3) the BINOM AF, which is a fast and approximate variant based on batch multi-objective acquisition functions. Our experiments on multiple diverse real-world MO problems demonstrate that our non-myopic AFs substantially improve performance over the existing myopic AFs for MOBO.

Problem

• Multi-objective optimization of expensive black-box functions
• Non-myopic methods for finite-horizon sequential experimental design
• Hypervolume improvement for Bellman equation approximation in MOO

Innovation

• Non-myopic Bayesian optimization for multi-objective problems
• Hypervolume improvement as scalarization approach
• Three novel acquisition functions for MOBO