Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimization

Understand

Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$.

• In this paper, we consider multi-objective optimization, where $f(x)$ outputs a vector of possibly competing objectives and the goal is to converge to the Pareto frontier.
• Quantitatively, we wish to maximize the standard hypervolume indicator metric, which measures the dominated hypervolume of the entire set of chosen inputs.
• In this paper, we introduce a novel scalarization function, which we term the hypervolume scalarization, and show that drawing random scalarizations from an appropriately chosen distribution can be used to efficiently approximate the hypervolume indicator metric.