# Optimality and Suboptimality of MPPI Control in Stochastic and Deterministic Settings

arXiv: https://arxiv.org/abs/2502.20953 · HTML: https://mlsanity.com/paper/2502.20953/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for autonomous driving and traffic, one of 15 directions in Deep reinforcement learning methods.
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Placed in

- Deep reinforcement learning methods / [RL for autonomous driving and traffic](https://mlsanity.com/deeprl/rl-for-autonomous-driving-and-traffic/)

## Builds on (most cited first, 7 of 7)

- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Recent Advances in Path Integral Control for Trajectory Optimization: An Overview in Theoretical and Algorithmic Perspectives](https://mlsanity.com/paper/2309.12566/) (2023)
- [CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design](https://mlsanity.com/paper/2401.07369/) (2024)
- [Multi-Modal MPPI and Active Inference for Reactive Task and Motion Planning](https://mlsanity.com/paper/2312.02328/) (2023)
- [Sampling Complexity of Path Integral Methods for Trajectory Optimization](https://mlsanity.com/paper/2203.10067/) (2022)
- [Fourth-order suboptimality of nominal model predictive control in the presence of uncertainty](https://mlsanity.com/paper/2403.04559/) (2024)
- [Output-Sampled Model Predictive Path Integral Control (o-MPPI) for Increased Efficiency](https://mlsanity.com/paper/2309.13201/) (2023)

## Built on by (most cited first, 1 of 1)

- [Soft MPCritic: Value-Based Reinforcement Learning for Non-Differentiable Predictive Control](https://mlsanity.com/paper/2604.01477/) (2026)

## Abstract (arXiv)

Model predictive path integral (MPPI) control has recently received a lot of attention, especially in the robotics and reinforcement learning communities. This letter aims to make the MPPI control framework more accessible to the optimal control community. We present three classes of optimal control problems and their solutions by MPPI. Further, we investigate the suboptimality of MPPI to general deterministic nonlinear discrete-time systems. Here, suboptimality is defined as the deviation between the control provided by MPPI and the optimal solution to the deterministic optimal control problem. Our findings are that in a smooth and unconstrained setting, the growth of suboptimality in the control input trajectory is second-order with the scaling of uncertainty. The results indicate that the suboptimality of the MPPI solution can be modulated by appropriately tuning the hyperparameters. We illustrate our findings using numerical examples.