mlsanityData to 14 Oct 2026

Optimality and Suboptimality of MPPI Control in Stochastic and Deterministic Settings

arXiv 2502.20953 ↗First posted 28 Feb 2025eess.SY cs.SYcited by 1

On the map: Deep reinforcement learning methods → RL for autonomous driving and traffic

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.

Key facts. Cited by 1 paper 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.

Builds on

7 of 30 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design14 Jan

Other references · 6

  1. 2017Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Drivingcited by 90
  2. 2023Recent Advances in Path Integral Control for Trajectory Optimization: An Overview in Theoretical and Algorithmic Perspectivescited by 5
  3. 2023Multi-Modal MPPI and Active Inference for Reactive Task and Motion Planningcited by 3
  4. 2022Sampling Complexity of Path Integral Methods for Trajectory Optimizationcited by 2
  5. 2024Fourth-order suboptimality of nominal model predictive control in the presence of uncertaintycited by 2
  6. 2023Output-Sampled Model Predictive Path Integral Control (o-MPPI) for Increased Efficiencycited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Soft MPCritic: Value-Based Reinforcement Learning for Non-Differentiable Predictive Controlcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Gauss-Newton accelerated MPPI Control ↗
  2. 2025Unifying Model Predictive Path Integral Control, Reinforcement Learning, and Diffusion Models for Optimal Control and Planning
  3. 2026HOLO-MPPI: Multi-Scenario Motion Planning via Hierarchical Policy Optimization
  4. 2025CoRL-MPPI: Enhancing MPPI With Learnable Behaviours For Efficient And Provably-Safe Multi-Robot Collision Avoidance
  5. 2026A Decade of Bayesian Optimization for Controller Tuning and Robot Learning: Tutorial, Review, and Future Prospects
  6. 2025Equivalence of stochastic and deterministic policy gradients
  7. 2025Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification
  8. 2026Solving Markov Decision Processes with Future Information via MPC