Deterministic Langevin Unconstrained Optimization with Normalizing Flows
This method addresses optimization challenges in fields like scientific computing and machine learning, offering a novel alternative to Bayesian Optimization, though it appears incremental as it builds on existing concepts like Langevin dynamics and Normalizing Flows.
The paper tackled the problem of optimizing expensive black-box functions by introducing Deterministic Langevin Optimization (DLO), a gradient-free method that balances exploitation and exploration using a Normalizing Flow density estimate, resulting in superior or competitive performance on synthetic test functions and real-world objectives like hyperparameter optimization.
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.