Choice functions based multi-objective Bayesian optimisation
This addresses the challenge of optimizing multi-objective functions without direct access to objective values, which is incremental as it extends Bayesian optimization to choice-based settings.
The paper tackles the problem of multi-objective Bayesian optimization when only choice judgments (e.g., selecting preferred options from a set) are available, by introducing a Gaussian process-based framework with a novel likelihood model for choice data, and applies it to solve this optimization problem.
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.