Bayesian Vector Optimization with Gaussian Processes

İlter Onat Korkmaz, Cagin Ararat, Cem Tekin

Primary Area: reinforcement learning

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Keywords: Vector Optimization, Bayesian Optimization, Gaussian Processes, Ordering Cones

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Abstract: Learning problems in which multiple conflicting objectives must be considered simultaneously often arise in various fields, including engineering, drug design, and environmental management. Traditional methods of multi-objective optimization, such as scalarization and identification of the Pareto set under componentwise order, have limitations in incorporating objective preferences and exploring the solution space accordingly. While vector optimization offers improved flexibility and adaptability via specifying partial orders based on ordering cones, current techniques designed for sequential experiments suffer from high sample complexity, which makes them unfit for large-scale learning problems. To address this issue, we propose VOGP, an ($\epsilon,\delta$)-PAC adaptive elimination algorithm that performs vector optimization using Gaussian processes. VOGP allows users to convey objective preferences through ordering cones while performing efficient sampling by exploiting the smoothness of the objective function, resulting in a more effective optimization process that requires fewer evaluations. We first establish provable theoretical guarantees for VOGP, and then derive information gain based and kernel specific sample complexity bounds. VOGP demonstrates strong empirical results on both real-world and synthetic datasets, outperforming previous work in sequential vector optimization and its special case multi-objective optimization. This work highlights the potential of VOGP as a powerful preference-driven method for addressing complex sequential vector optimization problems.

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Submission Number: 9167