Bayesian Optimization For Choice Data

Benavoli, Alessio and Azzimonti, Dario Filippo and Piga, Dario (2023) Bayesian Optimization For Choice Data. In: Proceedings of the Companion Conference on Genetic and Evolutionary Computation UNSPECIFIED.

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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 u for some dimension d which embeds the options into the real vector space of dimension d, so that the choice set can be represented through a Pareto set of non-dominated options. By placing a Gaussian process prior on u and by using a novel likelihood model for choice data, we derive a surrogate model for the latent vector function. We then propose two novel acquisition functions to solve the multi-objective Bayesian optimisation from choice data.

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