Çağın Ararat

Yaşar Cahit Yıldırım, Efe Mert Karagözlü, İlter Onat Korkmaz et al.

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.

İlter Onat Korkmaz, Yaşar Cahit Yıldırım, Çağın Ararat et al.

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.

Çağın Ararat, Cem Tekin

We introduce vector optimization problems with stochastic bandit feedback, in which preferences among designs are encoded by a polyhedral ordering cone $C$. Our setup generalizes the best arm identification problem to vector-valued rewards by extending the concept of Pareto set beyond multi-objective optimization. We characterize the sample complexity of ($ε,δ$)-PAC Pareto set identification by defining a new cone-dependent notion of complexity, called the ordering complexity. In particular, we provide gap-dependent and worst-case lower bounds on the sample complexity and show that, in the worst-case, the sample complexity scales with the square of ordering complexity. Furthermore, we investigate the sample complexity of the naïve elimination algorithm and prove that it nearly matches the worst-case sample complexity. Finally, we run experiments to verify our theoretical results and illustrate how $C$ and sampling budget affect the Pareto set, the returned ($ε,δ$)-PAC Pareto set, and the success of identification.

Andi Nika, Sepehr Elahi, Çağın Ararat et al.

We consider the problem of optimizing a vector-valued objective function $\boldsymbol{f}$ sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space $({\cal X},d)$ of designs. We assume that $\boldsymbol{f}$ is not known beforehand and that evaluating $\boldsymbol{f}$ at design $x$ results in a noisy observation of $\boldsymbol{f}(x)$. Since identifying the Pareto optimal designs via exhaustive search is infeasible when the cardinality of ${\cal X}$ is large, we propose an algorithm, called Adaptive $\boldsymbolε$-PAL, that exploits the smoothness of the GP-sampled function and the structure of $({\cal X},d)$ to learn fast. In essence, Adaptive $\boldsymbolε$-PAL employs a tree-based adaptive discretization technique to identify an $\boldsymbolε$-accurate Pareto set of designs in as few evaluations as possible. We provide both information-type and metric dimension-type bounds on the sample complexity of $\boldsymbolε$-accurate Pareto set identification. We also experimentally show that our algorithm outperforms other Pareto set identification methods.