Deterministic Langevin Unconstrained Optimization with Normalizing Flows
James M. Sullivan Uros Seljak
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.