2021/10/15 by Alessio Benavoli, Benavoli, Alessio, Dario Azzimonti +3
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.2110.08217
openalex publication_date 2021/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as ``I pick options A,B,C among this set of five options A,B,C,D,E''. The fact that the option D is rejected means that there is at least one option among the selected ones A,B,C that I strictly prefer over D (but I do not have to specify which one). We assume that there is a latent vector function f for some dimension ne which embeds the options into the real vector space of dimension n, so that the choice set can be represented through a Pareto set of non-dominated options. By placing a Gaussian process prior on f and deriving a novel likelihood model for choice data, we propose a Bayesian framework for choice functions learning. We then apply this surrogate model to solve a novel multi-objective Bayesian optimisation from choice data problem.