Generalizing Gaussian Smoothing for Random Search
This work provides an incremental improvement for derivative-free optimization, benefiting researchers and practitioners in fields like reinforcement learning and non-convex optimization.
The authors tackled the problem of improving gradient estimation in derivative-free optimization by generalizing Gaussian smoothing to a family of distributions that minimize mean squared error, resulting in three new distributions that outperform Gaussian smoothing and often compete with more expensive methods.
Gaussian smoothing (GS) is a derivative-free optimization (DFO) algorithm that estimates the gradient of an objective using perturbations of the current parameters sampled from a standard normal distribution. We generalize it to sampling perturbations from a larger family of distributions. Based on an analysis of DFO for non-convex functions, we propose to choose a distribution for perturbations that minimizes the mean squared error (MSE) of the gradient estimate. We derive three such distributions with provably smaller MSE than Gaussian smoothing. We conduct evaluations of the three sampling distributions on linear regression, reinforcement learning, and DFO benchmarks in order to validate our claims. Our proposal improves on GS with the same computational complexity, and are usually competitive with and often outperform Guided ES and Orthogonal ES, two computationally more expensive algorithms that adapt the covariance matrix of normally distributed perturbations.