## 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. |

# Publications

## 2021 |

Choice functions based multi-objective Bayesian optimisation Technical Report 2021. |