🤖 AI Summary
This study addresses the low sample efficiency caused by coupled evaluations in multi-objective Bayesian optimization by proposing a correlation-based decoupled evaluation strategy. Methodologically, it jointly models a multi-task Gaussian process and designs a total correlation metric to dynamically select optimal evaluation subsets, exploiting intrinsic correlations between objectives and constraints to enable decoupled evaluations. Theoretically, the asymptotic consistency of this strategy is established, along with its advantage in maximizing posterior entropy reduction for unevaluated tasks. Experimental results demonstrate that the proposed method significantly outperforms existing coupled and decoupled baselines, effectively enhancing optimization performance, sample efficiency, and convergence speed while reducing computational costs.
📝 Abstract
Multiobjective Bayesian optimization (MOBO) with Gaussian process (GP) surrogates is a sample efficient approach to solving multiobjective optimization problems. In MOBO, a Bayesian decision theoretic acquisition function guides the adaptive selection of new candidate inputs, on which objectives and constraints are evaluated to update the surrogate model sequentially. Existing approaches maintain independent GP models for the objectives and constraints, with new observations evaluating all objectives and constraints in a coupled fashion. However, the objectives and constraints often contain inherent correlations which, if exploited, can enable ${decoupled}$ evaluations where only a subset of them are evaluated at each round. We present a new approach that leverages a multitask GP model to jointly learn all objectives and constraints, and propose a total correlation metric that enables identifying an ${optimal}$ subset of objectives and constraints to be evaluated at every round, even under uniform evaluation costs. Theoretically, we show that our acquisition policy is asymptotically consistent despite decoupling and that our proposed decoupled subset selection rule maximizes the expected posterior entropy reduction about unevaluated tasks under mild conditions. Empirically, we show that our approach outperforms coupled and decoupled baselines in the state of the art.