Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?

2026-04-10

AI Summary

This work addresses the inefficiency of conventional multi-objective Bayesian optimization methods under extremely limited evaluation budgets, which often waste resources attempting to approximate the entire Pareto front despite decision-makers typically requiring only a single high-quality solution. To overcome this limitation, we propose the Single-Point-oriented Multi-objective Optimization (SPMO) framework, which abandons the full-coverage paradigm and instead introduces a novel single-point optimization strategy guided by final decision needs, accompanied by theoretical convergence guarantees. SPMO employs an Expected Single-Point Improvement (ESPI) acquisition function based on Sample Average Approximation (SAA), compatible with both noisy and noise-free settings, and amenable to gradient-based optimization. Empirical results demonstrate that SPMO significantly outperforms state-of-the-art methods across multiple benchmark and real-world problems, achieving superior solution quality with enhanced computational efficiency.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Many-objective optimisation, a subset of multi-objective optimisation, involves optimisation problems with more than three objectives. As the number of objectives increases, the number of solutions needed to adequately represent the entire Pareto front typically grows substantially. This makes it challenging, if not infeasible, to design a search algorithm capable of effectively exploring the entire Pareto front. This difficulty is particularly acute in the Bayesian optimisation paradigm, where sample efficiency is critical and only a limited number of solutions (often a few hundred) are evaluated. Moreover, after the optimisation process, the decision-maker eventually selects just one solution for deployment, regardless of how many high-quality, diverse solutions are available. In light of this, we argue an idea that under a very limited evaluation budget, it may be more useful to focus on finding a single solution of the highest possible quality for the decision-maker, rather than aiming to approximate the entire Pareto front as existing many-/multi-objective Bayesian optimisation methods typically do. Bearing this idea in mind, this paper proposes a \underline{s}ingle \underline{p}oint-based \underline{m}ulti-\underline{o}bjective search framework (SPMO) that aims to improve the quality of solutions along a direction that leads to a good tradeoff between objectives. Within SPMO, we present a simple acquisition function, called expected single-point improvement (ESPI), working under both noiseless and noisy scenarios. We show that ESPI can be optimised effectively with gradient-based methods via the sample average approximation (SAA) approach and theoretically prove its convergence guarantees under the SAA. We also empirically demonstrate that the proposed SPMO is computationally tractable and outperforms state-of-the-arts on a wide range of benchmark and real-world problems.

Problem

• many-objective optimisation
• Bayesian optimisation
• Pareto front
• sample efficiency
• decision-making

Innovation

• single-point optimization
• many-objective Bayesian optimisation
• expected single-point improvement (ESPI)
• sample average approximation (SAA)
• Pareto front approximation