# A Stochastic Derivative Free Optimization Method with Momentum

arXiv: https://arxiv.org/abs/1905.13278 · HTML: https://mlsanity.com/paper/1905.13278/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 9 of 9)

- [Derivative-Free Reinforcement Learning: A Review](https://mlsanity.com/paper/2102.05710/) (2021)
- [Curvature-Aware Derivative-Free Optimization](https://mlsanity.com/paper/2109.13391/) (2021)
- [Minibatch Stochastic Three Points Method for Unconstrained Smooth Minimization](https://mlsanity.com/paper/2209.07883/) (2022)
- [Towards a Better Theoretical Understanding of Independent Subnetwork Training](https://mlsanity.com/paper/2306.16484/) (2023)
- [Variance Reduction is an Antidote to Byzantines: Better Rates, Weaker Assumptions and Communication Compression as a Cherry on the Top](https://mlsanity.com/paper/2206.00529/) (2022)
- [Stochastic Optimization with Random Search](https://mlsanity.com/paper/2510.15610/) (2025)
- [Finding Stationary Points by Comparisons](https://mlsanity.com/paper/2606.27082/) (2026)
- [Trust the Direction, Search the Step: Zero-and-First-Order Methods for LLM Fine-Tuning](https://mlsanity.com/paper/2610.02190/) (2026)
- [TACO: Ternary Absolute-max Column-wise One-sparse Optimizer for LLM Fine-Tuning](https://mlsanity.com/paper/2610.02199/) (2026)

## Abstract (arXiv)

We consider the problem of unconstrained minimization of a smooth objective function in ℝd in setting where only function evaluations are possible. We propose and analyze stochastic zeroth-order method with heavy ball momentum. In particular, we propose, SMTP, a momentum version of the stochastic three-point method (STP) citeBergou2018. We show new complexity results for non-convex, convex and strongly convex functions. We test our method on a collection of learning to continuous control tasks on several MuJoCo citeTodorov2012 environments with varying difficulty and compare against STP, other state-of-the-art derivative-free optimization algorithms and against policy gradient methods. SMTP significantly outperforms STP and all other methods that we considered in our numerical experiments. Our second contribution is SMTP with importance sampling which we call SMTPIS. We provide convergence analysis of this method for non-convex, convex and strongly convex objectives.