Improving Pareto Set Learning for Expensive Multi-objective Optimization via Stein Variational Hypernetworks
This work addresses expensive multi-objective optimization problems, which are common in real-world scenarios with costly evaluations, by providing a novel method to enhance Pareto set learning, though it appears incremental as it builds on existing surrogate model and acquisition function approaches.
The paper tackles the problem of fragmented surrogate models and pseudo-local optima in expensive multi-objective optimization by proposing SVH-PSL, which integrates Stein Variational Gradient Descent with Hypernetworks to smooth the solution space and improve Pareto set learning, demonstrating significant improvements in quality across synthetic and real-world benchmarks.
Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.