# CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design

arXiv: https://arxiv.org/abs/2401.07369 · HTML: https://mlsanity.com/paper/2401.07369/

## Key facts

- Cited by 4 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 24 of its 46 references that are in the map.
- First posted on arXiv 14 Jan 2024.

## 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, 24 of 24)

- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Model-Based Reinforcement Learning for Atari](https://mlsanity.com/paper/1903.00374/) (2019)
- [Temporal Difference Learning for Model Predictive Control](https://mlsanity.com/paper/2203.04955/) (2022)
- [Visual Foresight: Model-Based Deep Reinforcement Learning for Vision-Based Robotic Control](https://mlsanity.com/paper/1812.00568/) (2018)
- [Model-Based Offline Planning](https://mlsanity.com/paper/2008.05556/) (2020)
- [Plan Online, Learn Offline: Efficient Learning and Exploration via Model-Based Control](https://mlsanity.com/paper/1811.01848/) (2018)
- [Reaching the Limit in Autonomous Racing: Optimal Control versus Reinforcement Learning](https://mlsanity.com/paper/2310.10943/) (2023)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Temporal Predictive Coding For Model-Based Planning In Latent Space](https://mlsanity.com/paper/2106.07156/) (2021)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [An Online Learning Approach to Model Predictive Control](https://mlsanity.com/paper/1902.08967/) (2019)
- [Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems](https://mlsanity.com/paper/2106.10497/) (2021)
- [Regularized Newton Method with Global O(1/k2) Convergence](https://mlsanity.com/paper/2112.02089/) (2021)
- [Neural-Swarm2: Planning and Control of Heterogeneous Multirotor Swarms using Learned Interactions](https://mlsanity.com/paper/2012.05457/) (2020)
- [Information Theoretic Model Predictive Q-Learning](https://mlsanity.com/paper/2001.02153/) (2019)
- [Robust Model Predictive Path Integral Control: Analysis and Performance Guarantees](https://mlsanity.com/paper/2102.09027/) (2021)
- [DATT: Deep Adaptive Trajectory Tracking for Quadrotor Control](https://mlsanity.com/paper/2310.09053/) (2023)
- [L1-Adaptive MPPI Architecture for Robust and Agile Control of Multirotors](https://mlsanity.com/paper/2004.00152/) (2020)
- [Variational Inference MPC using Tsallis Divergence](https://mlsanity.com/paper/2104.00241/) (2021)
- [Vision-Based High Speed Driving with a Deep Dynamic Observer](https://mlsanity.com/paper/1812.02071/) (2018)
- [Constrained Covariance Steering Based Tube-MPPI](https://mlsanity.com/paper/2110.07744/) (2021)

## Built on by (most cited first, 4 of 4)

- [Model-Based Diffusion for Trajectory Optimization](https://mlsanity.com/paper/2407.01573/) (2024)
- [Optimality and Suboptimality of MPPI Control in Stochastic and Deterministic Settings](https://mlsanity.com/paper/2502.20953/) (2025)
- [Model Tensor Planning](https://mlsanity.com/paper/2505.01059/) (2025)
- [PegasusFlow: Parallel Rolling-Denoising Score Sampling for Robot Diffusion Planner Flow Matching](https://mlsanity.com/paper/2509.08435/) (2025)

## Abstract (arXiv)

Sampling-based Model Predictive Control (MPC) has been a practical and effective approach in many domains, notably model-based reinforcement learning, thanks to its flexibility and parallelizability. Despite its appealing empirical performance, the theoretical understanding, particularly in terms of convergence analysis and hyperparameter tuning, remains absent. In this paper, we characterize the convergence property of a widely used sampling-based MPC method, Model Predictive Path Integral Control (MPPI). We show that MPPI enjoys at least linear convergence rates when the optimization is quadratic, which covers time-varying LQR systems. We then extend to more general nonlinear systems. Our theoretical analysis directly leads to a novel sampling-based MPC algorithm, CoVariance-Optimal MPC (CoVo-MPC) that optimally schedules the sampling covariance to optimize the convergence rate. Empirically, CoVo-MPC significantly outperforms standard MPPI by 43-54% in both simulations and real-world quadrotor agile control tasks. Videos and Appendices are available at urlhttps://lecar-lab.github.io/CoVO-MPC/.