Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?
2026-04-10 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors explore optimisation problems with many goals, where usually a broad set of solutions is found, but this is hard when you can only test a few options. Instead of finding many possible solutions, they suggest focusing on finding one really good solution that balances all goals well. They introduce a method called SPMO with a tool named ESPI to efficiently guide this search, even when results are noisy. They prove their approach works theoretically and show it performs better than existing methods on tests.
many-objective optimisationmulti-objective optimisationPareto frontBayesian optimisationsample efficiencyacquisition functionexpected single-point improvement (ESPI)gradient-based methodssample average approximation (SAA)convergence guarantees
Authors
Chao Jiang, Jingyu Huang, Miqing Li
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.