### 2021

Benavoli, Alessio; Azzimonti, Dario; Piga, Dario

Choice functions based multi-objective Bayesian optimisation Technical Report

2021.

Abstract | Links | BibTeX | Tags: bayesian nonparametric, bayesian optimisation, Gaussian Process

@techreport{Benavoli2021bb,

title = {Choice functions based multi-objective Bayesian optimisation},

author = {Benavoli , Alessio and Azzimonti, Dario and Piga, Dario },

url = {https://arxiv.org/pdf/2110.08217.pdf},

year = {2021},

date = {2021-10-18},

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 x1, x2, x3 among this set of five options x1, x2, . . . , x5”. The fact that the option x4 is rejected means that there is at least one option

among the selected ones x1, x2, x3 that I strictly prefer over x4 (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 ne, 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.},

keywords = {bayesian nonparametric, bayesian optimisation, Gaussian Process},

pubstate = {published},

tppubtype = {techreport}

}

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 x1, x2, x3 among this set of five options x1, x2, . . . , x5”. The fact that the option x4 is rejected means that there is at least one option

among the selected ones x1, x2, x3 that I strictly prefer over x4 (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 ne, 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.

among the selected ones x1, x2, x3 that I strictly prefer over x4 (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 ne, 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.