Topological Feasibility Guarantees for Differentiable Predictive Control

• URL: http://arxiv.org/abs/2608.10332v1
• Date: Tue, 11 Aug 2026 00:27:50 GMT
• Title: Topological Feasibility Guarantees for Differentiable Predictive Control
• Abstract summary: Differentiable predictive control (DPC) is a self-supervised learning approach for approximating explicit model predictive control (MPC) policies.<n> feasibility guarantees, a core requirement for safe control, are currently provided either probabilistically or via online safety filters.<n>This paper establishes deterministic feasibility guarantees for DPC using a novel topological analysis of the induced reachable safe set.
• Score: 0.8880611506199766
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Differentiable predictive control (DPC), a self-supervised learning approach for approximating explicit model predictive control (MPC) policies, offers significant computational advantages over online optimization-based MPC. However, feasibility guarantees, a core requirement for safe control, are currently provided either probabilistically or via online safety filters. The lack of rigorous feasibility guarantees for offline policy optimization remains an open problem. This paper establishes deterministic feasibility guarantees for DPC using a novel topological analysis of the induced reachable safe set, without requiring online safety filters. By exploiting the inherent model-based nature of DPC, in which differentiable system dynamics are embedded directly into the computational graph, we analyze the properties of the learned control policies and the corresponding system states from topological and geometric perspectives. Inspired by our theoretical analysis, we propose a novel self-supervised offline policy learning strategy that utilizes a proxy loss with Control Barrier Functions (CBFs). Crucially, these properties not only significantly improve policy training but also enable the derivation of strict, deterministic feasibility guarantees from a finite number of training samples. Extensive closed-loop simulations validate our theoretical findings, demonstrating that the empirical constraint violations monotonically decrease to zero as the training sample size increases. Ultimately, this work illustrates that DPC policy optimization yields formal safety certificates that are structurally unattainable with conventional black-box methods, e.g., reinforcement learning (RL) or supervised learning-based approximate MPC, thereby providing a new perspective on feasibility guarantees in learning-based control.

Related papers

• Test-Time Gradient Guidance of Flow Policies in Reinforcement Learning [50.738952715864116]
  Expressive continuous control policies form the backbone of advances in scaling imitation learning for simulated and real robot control.<n>We propose QGF (Q-Guided Flow), an RL algorithm that performs policy optimization entirely at test time.<n> Empirically, QGF outperforms prior test-time RL methods on single-task and goal-conditioned offline RL benchmarks.
  arXiv  Detail & Related papers  (2026-06-09T16:45:57Z)
• Learning Predictive Control with Deep Koopman Operators for Autonomous Vehicle Motion Planning [11.149068950974113]
  Model Predictive Control (MPC) is widely used for autonomous-vehicle (AV) motion planning, but its real-time applicability is often limited.<n>Actor-critic offers an online solution for nonlinear learning problems in dynamic road environments.<n>This article proposes a framework with deep Koopman operators for efficient real-time motion control.
  arXiv  Detail & Related papers  (2026-06-06T12:26:21Z)
• OGPO: Sample Efficient Full-Finetuning of Generative Control Policies [53.42266064673132]
  Generative control policies (GCPs) have emerged as effective parameterizations for robot learning.<n>This work introduces Off-policy Generative Policy Optimization (OGPO), a sample-efficient for finetuning GCPs.<n>OGPO achieves state-of-the-art performance on manipulation tasks spanning multi-task settings, high-precision insertion, and dexterous control.
  arXiv  Detail & Related papers  (2026-05-04T18:36:40Z)
• Stabilizing Policy Gradients for Sample-Efficient Reinforcement Learning in LLM Reasoning [77.92320830700797]
  Reinforcement Learning has played a central role in enabling reasoning capabilities of Large Language Models.<n>We propose a tractable computational framework that tracks and leverages curvature information during policy updates.<n>The algorithm, Curvature-Aware Policy Optimization (CAPO), identifies samples that contribute to unstable updates and masks them out.
  arXiv  Detail & Related papers  (2025-10-01T12:29:32Z)
• Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach [3.617866023850784]
  We develop a novel form of differentiable predictive control (DPC) with safety and robustness guarantees. DPC is an unsupervised learning-based method for obtaining approximate solutions to explicit model predictive control (MPC) problems.
  arXiv  Detail & Related papers  (2022-08-03T19:24:44Z)
• Supported Policy Optimization for Offline Reinforcement Learning [74.1011309005488]
  Policy constraint methods to offline reinforcement learning (RL) typically utilize parameterization or regularization. Regularization methods reduce the divergence between the learned policy and the behavior policy. This paper presents Supported Policy OpTimization (SPOT), which is directly derived from the theoretical formalization of the density-based support constraint.
  arXiv  Detail & Related papers  (2022-02-13T07:38:36Z)
• Closing the Closed-Loop Distribution Shift in Safe Imitation Learning [80.05727171757454]
  We treat safe optimization-based control strategies as experts in an imitation learning problem. We train a learned policy that can be cheaply evaluated at run-time and that provably satisfies the same safety guarantees as the expert.
  arXiv  Detail & Related papers  (2021-02-18T05:11:41Z)
• COMBO: Conservative Offline Model-Based Policy Optimization [120.55713363569845]
  Uncertainty estimation with complex models, such as deep neural networks, can be difficult and unreliable. We develop a new model-based offline RL algorithm, COMBO, that regularizes the value function on out-of-support state-actions. We find that COMBO consistently performs as well or better as compared to prior offline model-free and model-based methods.
  arXiv  Detail & Related papers  (2021-02-16T18:50:32Z)
• Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees [1.1086440815804224]
  We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems. We employ automatic differentiation to obtain direct policy gradients by backpropagating the model predictive control (MPC) loss function and constraints penalties through a differentiable closed-loop system dynamics model.
  arXiv  Detail & Related papers  (2020-04-23T14:24:44Z)
• Neural Lyapunov Model Predictive Control: Learning Safe Global Controllers from Sub-optimal Examples [4.777323087050061]
  In many real-world and industrial applications, it is typical to have an existing control strategy, for instance, execution from a human operator. The objective of this work is to improve upon this unknown, safe but suboptimal policy by learning a new controller that retains safety and stability. The proposed algorithm alternatively learns the terminal cost and updates the MPC parameters according to a stability metric.
  arXiv  Detail & Related papers  (2020-02-21T16:57:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.