# A Stochastic Derivative-Free Optimization Method with Importance Sampling: Theory and Learning to Control

## TL;DR

This paper introduces a novel derivative-free optimization method that incorporates importance sampling, providing theoretical complexity improvements and demonstrating practical effectiveness in high-dimensional control tasks.

## Contribution

It is the first to combine importance sampling with derivative-free optimization and offers new theoretical complexity bounds for non-convex, convex, and strongly convex functions.

## Key findings

- The method achieves improved complexity bounds.
- Experiments confirm theoretical predictions on synthetic and real datasets.
- Significant sample complexity reduction in high-dimensional control problems.

## Abstract

We consider the problem of unconstrained minimization of a smooth objective function in $\R^n$ in a setting where only function evaluations are possible. While importance sampling is one of the most popular techniques used by machine learning practitioners to accelerate the convergence of their models when applicable, there is not much existing theory for this acceleration in the derivative-free setting. In this paper, we propose the first derivative free optimization method with importance sampling and derive new improved complexity results on non-convex, convex and strongly convex functions. We conduct extensive experiments on various synthetic and real LIBSVM datasets confirming our theoretical results. We further test our method on a collection of continuous control tasks on MuJoCo environments with varying difficulty. Experiments suggest that our algorithm is practical for high dimensional continuous control problems where importance sampling results in a significant sample complexity improvement.