# The Kalai-Smorodinski solution for many-objective Bayesian optimization

arXiv: https://arxiv.org/abs/1902.06565 · HTML: https://mlsanity.com/paper/1902.06565/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2019.

## Built on by (most cited first, 13 of 13)

- [Multi-Task Learning as a Bargaining Game](https://mlsanity.com/paper/2202.01017/) (2022)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Multi-objective Asynchronous Successive Halving](https://mlsanity.com/paper/2106.12639/) (2021)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [A portfolio approach to massively parallel Bayesian optimization](https://mlsanity.com/paper/2110.09334/) (2021)
- [Multi-Objective Model Selection for Time Series Forecasting](https://mlsanity.com/paper/2202.08485/) (2022)
- [Fairness-Aware Meta-Learning via Nash Bargaining](https://mlsanity.com/paper/2406.07029/) (2024)
- [Many Objective Bayesian Optimization](https://mlsanity.com/paper/2107.04126/) (2021)
- [Multi-objective optimisation via the R2 utilities](https://mlsanity.com/paper/2305.11774/) (2023)
- [Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?](https://mlsanity.com/paper/2604.09417/) (2026)
- [Transforming Vision Transformer: Towards Efficient Multi-Task Asynchronous Learning](https://mlsanity.com/paper/2501.06884/) (2025)
- [Active Preference Learning over Latent Preference Archetypes for Many-Objective Bayesian Optimization](https://mlsanity.com/paper/2603.28410/) (2026)
- [Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation](https://mlsanity.com/paper/2609.13396/) (2026)

## Abstract (arXiv)

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame.