Achievable Goals in Bayesian Multi-Objective Optimization

International audienceWe consider multi-objective optimization problems, min x∈Rd(f1(x), . . . , fm(x)), where the functionsare expensive to evaluate. In such a context, Bayesian methods relying on Gaussian Processes(GP) [1], adapted to multi-objective problems [2] have allowed to approximate Pareto fronts ina limited number of iterations.In the current work, we assume that the Pareto front center has already been attained (typicallywith the approach described in [3]) and that a computational budget remains. The goal is touncover of a broader central part of the Pareto front: the intersection of it with some regionto target, IR(see Fig. 1). IRhas however to be defined carefully: choosing it too wide, i.e.too ambitious with regard to the remaining budget, will lead to a non converged approximationfront. Conversely, a suboptimal diversity of Pareto optimal solutions will be obtained if choosinga too narrow area.The GPs allow to forecast the future behavior of the algorithm: they are used in lieu of thetrue functions to anticipate which inputs/outputs will be obtained when targeting growingparts of the Pareto front. Virtual final Pareto fronts corresponding to a possible version of theapproximation front at the depletion of the budget are produced for each IR. A measure ofuncertainty is defined and applied to all of them to determine the optimal improvement region IR∗, balancing the size of the approximation front and the convergence to the Pareto front