Choice functions based multi-objective Bayesian optimisation

• URL: http://arxiv.org/abs/2110.08217v1
• Date: Fri, 15 Oct 2021 17:24:03 GMT
• Title: Choice functions based multi-objective Bayesian optimisation
• Authors: Alessio Benavoli and Dario Azzimonti and Dario Piga
• Abstract summary: We introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements. 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.
• Score: 1.0742675209112622
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $n_e$ 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.

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