Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?
Summary: arXiv:2604.09417v1 Announce Type: new
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.
Proposed Framework: SPMO
Bearing this idea in mind, this paper proposes a single point-based multi-objective search framework (SPMO) that aims to improve the quality of solutions along a direction that leads to a good tradeoff between objectives. Within the SPMO framework, we present a simple acquisition function, called expected single-point improvement (ESPI), which operates under both noiseless and noisy scenarios.
Key Features of SPMO
- Acquisition Function: The ESPI function is designed for effective optimisation, allowing practitioners to focus on a single high-quality solution.
- Gradient-Based Optimisation: ESPI can be optimised effectively using gradient-based methods through the sample average approximation (SAA) approach.
- Theoretical Guarantees: The paper provides theoretical proofs for the convergence of the ESPI under the SAA framework.
- Empirical Validation: Results demonstrate that SPMO is computationally tractable and outperforms state-of-the-art methods on a variety of benchmark and real-world problems.
Conclusion
As the field of many-objective optimisation continues to evolve, it is crucial to reassess the objectives and methodologies employed. The proposed SPMO framework, with its focus on high-quality single solutions rather than the entire Pareto front, offers a promising direction for future research and practical applications. By prioritising quality over quantity, decision-makers can achieve optimal solutions even within stringent evaluation budgets.
In conclusion, while exploring the full Pareto front may seem ideal, the limitations of current methodologies and the practical needs of decision-makers suggest that a shift towards single-point optimisation could be more beneficial in many contexts.