VOPy: A Framework for Black-box Vector Optimization

We introduce VOPy, an open-source Python library designed to address black-box vector optimization, where multiple objectives must be optimized simultaneously with respect to a partial order induced by a convex cone. VOPy extends beyond traditional multi-objective optimization (MOO) tools by enabling flexible, cone-based ordering of solutions; with an application scope that includes environments with observation noise, discrete or continuous design spaces, limited budgets, and batch observations. VOPy provides a modular architecture, facilitating the integration of existing methods and the development of novel algorithms. We detail VOPy's architecture, usage, and potential to advance research and application in the field of vector optimization. The source code for VOPy is available at https://github.com/Bilkent-CYBORG/VOPy.

Vector Optimization with Gaussian Process Bandits

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 for dealing with multiple black-box objective functions, such as scalarization and identification of the Pareto set under the 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 either suffer from high sample complexity or lack theoretical guarantees. To address these issues, we propose Vector Optimization with Gaussian Process (VOGP), a probably approximately correct adaptive elimination algorithm that performs black-box vector optimization using Gaussian process bandits. 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 establish theoretical guarantees for VOGP and derive information gain-based and kernel-specific sample complexity bounds. We also conduct experiments on both real-world and synthetic datasets to compare VOGP with the state-of-the-art methods.