Deterministic Langevin Unconstrained Optimization with Normalizing Flows

TL;DR

This paper presents Deterministic Langevin Optimization (DLO), a gradient-free surrogate method using normalizing flows for global optimization of expensive black-box functions, balancing exploration and exploitation.

Contribution

The paper introduces DLO, a novel gradient-free optimization approach leveraging normalizing flows and Langevin dynamics, differing from Bayesian optimization by its active learning strategy.

Findings

DLO outperforms or matches existing methods on synthetic test functions.

DLO is effective on non-convex, multi-modal, and real-world problems.

DLO is competitive with state-of-the-art hyperparameter optimization techniques.

Abstract

We introduce a global, gradient-free surrogate optimization strategy for expensive black-box functions inspired by the Fokker-Planck and Langevin equations. These can be written as an optimization problem where the objective is the target function to maximize minus the logarithm of the current density of evaluated samples. This objective balances exploitation of the target objective with exploration of low-density regions. The method, Deterministic Langevin Optimization (DLO), relies on a Normalizing Flow density estimate to perform active learning and select proposal points for evaluation. This strategy differs qualitatively from the widely-used acquisition functions employed by Bayesian Optimization methods, and can accommodate a range of surrogate choices. We demonstrate superior or competitive progress toward objective optima on standard synthetic test functions, as well as on non-convex and multi-modal posteriors of moderate dimension. On real-world objectives, such as scientific and neural network hyperparameter optimization, DLO is competitive with state-of-the-art baselines.