# Leveraging Randomized Smoothing for Optimal Control of Nonsmooth Dynamical Systems

arXiv: https://arxiv.org/abs/2203.03986 · HTML: https://mlsanity.com/paper/2203.03986/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2022.

## Built on by (most cited first, 3 of 3)

- [Smoothed Online Learning for Prediction in Piecewise Affine Systems](https://mlsanity.com/paper/2301.11187/) (2023)
- [Generative Predictive Control: Flow Matching Policies for Dynamic and Difficult-to-Demonstrate Tasks](https://mlsanity.com/paper/2502.13406/) (2025)
- [Combined Constrained Sampling and Reinforcement Learning for Robotic Manipulation](https://mlsanity.com/paper/2602.08557/) (2026)

## Abstract (arXiv)

Optimal control (OC) algorithms such as Differential Dynamic Programming (DDP) take advantage of the derivatives of the dynamics to efficiently control physical systems. Yet, in the presence of nonsmooth dynamical systems, such class of algorithms are likely to fail due, for instance, to the presence of discontinuities in the dynamics derivatives or because of non-informative gradient. On the contrary, reinforcement learning (RL) algorithms have shown better empirical results in scenarios exhibiting non-smooth effects (contacts, frictions, etc). Our approach leverages recent works on randomized smoothing (RS) to tackle non-smoothness issues commonly encountered in optimal control, and provides key insights on the interplay between RL and OC through the prism of RS methods. This naturally leads us to introduce the randomized Differential Dynamic Programming (R-DDP) algorithm accounting for deterministic but non-smooth dynamics in a very sample-efficient way. The experiments demonstrate that our method is able to solve classic robotic problems with dry friction and frictional contacts, where classical OC algorithms are likely to fail and RL algorithms require in practice a prohibitive number of samples to find an optimal solution.