# An Online Learning Approach to Model Predictive Control

arXiv: https://arxiv.org/abs/1902.08967 · HTML: https://mlsanity.com/paper/1902.08967/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2019.

## Built on by (most cited first, 30 of 30)

- [Autonomous Vehicles on the Edge: A Survey on Autonomous Vehicle Racing](https://mlsanity.com/paper/2202.07008/) (2022)
- [A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/2209.15634/) (2022)
- [Efficient Exploration in Continuous-time Model-based Reinforcement Learning](https://mlsanity.com/paper/2310.19848/) (2023)
- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Learning to Optimize in Model Predictive Control](https://mlsanity.com/paper/2212.02603/) (2022)
- [Dual Online Stein Variational Inference for Control and Dynamics](https://mlsanity.com/paper/2103.12890/) (2021)
- [Inferring Smooth Control: Monte Carlo Posterior Policy Iteration with Gaussian Processes](https://mlsanity.com/paper/2210.03512/) (2022)
- [Learning Sampling Distributions for Model Predictive Control](https://mlsanity.com/paper/2212.02587/) (2022)
- [A Regret Minimization Approach to Iterative Learning Control](https://mlsanity.com/paper/2102.13478/) (2021)
- [The Value of Planning for Infinite-Horizon Model Predictive Control](https://mlsanity.com/paper/2104.02863/) (2021)
- [Deep Model Predictive Optimization](https://mlsanity.com/paper/2310.04590/) (2023)
- [Adaptive Composite Online Optimization: Predictions in Static and Dynamic Environments](https://mlsanity.com/paper/2205.00446/) (2022)
- [Autonomous Driving Small-Scale Cars: A Survey of Recent Development](https://mlsanity.com/paper/2404.06229/) (2024)
- [Exponential Family Model-Based Reinforcement Learning via Score Matching](https://mlsanity.com/paper/2112.14195/) (2021)
- [CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design](https://mlsanity.com/paper/2401.07369/) (2024)
- [Efficient Stochastic Optimal Control through Approximate Bayesian Input Inference](https://mlsanity.com/paper/2105.07693/) (2021)
- [Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions](https://mlsanity.com/paper/2207.14419/) (2022)
- [AdaReP:Adaptive Re-Planning under Model Mismatch for Neural World-Model Predictive Control](https://mlsanity.com/paper/2606.23079/) (2026)
- [Improving Model-Based Reinforcement Learning with Internal State Representations through Self-Supervision](https://mlsanity.com/paper/2102.05599/) (2021)
- [DiSProD: Differentiable Symbolic Propagation of Distributions for Planning](https://mlsanity.com/paper/2302.01491/) (2023)
- [Double Duality: Variational Primal-Dual Policy Optimization for Constrained Reinforcement Learning](https://mlsanity.com/paper/2402.10810/) (2024)
- [Model Predictive Adversarial Imitation Learning for Planning from Observation](https://mlsanity.com/paper/2507.21533/) (2025)
- [Optimisation of Structured Neural Controller Based on Continuous-Time Policy Gradient](https://mlsanity.com/paper/2201.06262/) (2022)
- [Bayesian Learning Approach to Model Predictive Control](https://mlsanity.com/paper/2203.02720/) (2022)
- [Regret Analysis of Distributed Online Control for LTI Systems with Adversarial Disturbances](https://mlsanity.com/paper/2310.03206/) (2023)
- [Policy Search using Dynamic Mirror Descent MPC for Model Free Off Policy RL](https://mlsanity.com/paper/2110.12239/) (2021)
- [Enhancing AUV Autonomy With Model Predictive Path Integral Control](https://mlsanity.com/paper/2308.05547/) (2023)
- [Safe and Efficient Online Convex Optimization with Linear Budget Constraints and Partial Feedback](https://mlsanity.com/paper/2412.03983/) (2024)
- [Shield-Loco: Shielding Locomotion Policies with Predictive Safety Filtering](https://mlsanity.com/paper/2606.07193/) (2026)
- [BOBA: Dynamic Bayesian Optimization through Bayesian Active Inference](https://mlsanity.com/paper/2609.26021/) (2026)

## Abstract (arXiv)

Model predictive control (MPC) is a powerful technique for solving dynamic control tasks. In this paper, we show that there exists a close connection between MPC and online learning, an abstract theoretical framework for analyzing online decision making in the optimization literature. This new perspective provides a foundation for leveraging powerful online learning algorithms to design MPC algorithms. Specifically, we propose a new algorithm based on dynamic mirror descent (DMD), an online learning algorithm that is designed for non-stationary setups. Our algorithm, Dynamic Mirror Descent Model Predictive Control (DMD-MPC), represents a general family of MPC algorithms that includes many existing techniques as special instances. DMD-MPC also provides a fresh perspective on previous heuristics used in MPC and suggests a principled way to design new MPC algorithms. In the experimental section of this paper, we demonstrate the flexibility of DMD-MPC, presenting a set of new MPC algorithms on a simple simulated cartpole and a simulated and real-world aggressive driving task. Videos of the real-world experiments can be found at https://youtu.be/vZST3v0_S9w and https://youtu.be/MhuqiHo2t98.