Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics

• URL: http://arxiv.org/abs/2606.16564v1
• Date: Mon, 15 Jun 2026 11:06:22 GMT
• Title: Elastic ODYN: Differentiable Optimization for Infeasible Control and Learning in Robotics
• Abstract summary: Elastic ODYN is a primal-dual non-interior-point QP solver that handles infeasibility through smooth squared-$ell$ elastic relaxations.<n>Building on this framework, we develop Elastic OdynLayer, a differentiable QP layer with stable gradients under infeasibility, and Elastic OdynSQP, an infeasibility-aware SQP method.
• Score: 6.783137696981211
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Robotic systems routinely encounter conflicting objectives, modeling errors, and degenerate contact conditions that render quadratic programs (QPs) infeasible. Yet most optimization solvers and differentiable QP layers assume feasibility, leading to numerical failures, unstable gradients, or solver breakdown when constraints cannot be simultaneously satisfied. We present Elastic ODYN, a primal--dual non-interior-point QP solver that handles infeasibility through smooth squared-$\ell_2$ elastic relaxations. The resulting formulation remains well posed under ill-conditioning and degeneracy, supports warm starting, and converges to closest-to-feasible solutions when no feasible point exists. A lightweight refinement stage recovers physically meaningful dual variables from the elastic solution. Building on this framework, we develop Elastic OdynLayer, a differentiable QP layer with stable gradients under infeasibility, and Elastic OdynSQP, an infeasibility-aware SQP method that resolves inconsistent subproblems and intrinsically infeasible optimal control tasks through selective constraint relaxation. We evaluate the framework on benchmark QPs, singular contact mechanics, differentiable parameter identification, and quadrupedal and humanoid trajectory optimization. Across all settings, Elastic ODYN consistently outperforms state-of-the-art elastic QP solvers in robustness, warm-start performance, and convergence reliability, enabling optimization, simulation, control, and learning beyond the feasibility assumptions of existing methods.

Related papers

• Q-Flow: Stable and Expressive Reinforcement Learning with Flow-Based Policy [51.31164293751206]
  We introduce Q-Flow, a framework that leverages the deterministic nature of flow dynamics to explicitly propagate latent states along policy-induced flow.<n>We evaluate Q-Flow in the offline learning setting on the challenging OGBench suite, where it consistently outperforms state-of-the-art baselines by an average of 10.6 percentage points.
  arXiv  Detail & Related papers  (2026-05-13T12:31:02Z)
• Adaptive Smooth Tchebycheff Attention for Multi-Objective Policy Optimization [55.338784037660474]
  Multi- curvature reinforcement learning in domains requires balancing complex, non-fragile interference trade-offs between conflicting objectives.<n>In this paper we introduce a novel based real-time based real-time optimization on a robotic visual -- a proxy for monitoring ecosystems.
  arXiv  Detail & Related papers  (2026-05-12T21:32:57Z)
• AdamFLIP: Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN Training [9.082213877961541]
  Physics-informed neural networks (PINNs) provide a flexible framework for solving forward and inverse problems governed by partial differential equations (PDEs)<n>Standard PINN training typically relies on soft penalty formulations that combine PDE residuals, data mismatch, and initial/boundary conditions using manually chosen weights.<n>In this work, we reformulate PINN training as an equality-constrained optimization problem and propose a novel Adaptive Momentum Feedback Linearization Optimization for Hard Constrained PINN (AdamFLIP)
  arXiv  Detail & Related papers  (2026-05-08T19:13:15Z)
• Not All Preferences Are Created Equal: Stability-Aware and Gradient-Efficient Alignment for Reasoning Models [52.48582333951919]
  We propose a dynamic framework designed to enhance alignment reliability by maximizing the Signal-to-Noise Ratio of policy updates.<n>SAGE (Stability-Aware Gradient Efficiency) integrates a coarse-grained curriculum mechanism that refreshes candidate pools based on model competence.<n> Experiments on multiple mathematical reasoning benchmarks demonstrate that SAGE significantly accelerates convergence and outperforms static baselines.
  arXiv  Detail & Related papers  (2026-02-01T12:56:10Z)
• Adaptive Dual-Weighting Framework for Federated Learning via Out-of-Distribution Detection [53.45696787935487]
  Federated Learning (FL) enables collaborative model training across large-scale distributed service nodes.<n>In real-world service-oriented deployments, data generated by heterogeneous users, devices, and application scenarios are inherently non-IID.<n>We propose FLood, a novel FL framework inspired by out-of-distribution (OOD) detection.
  arXiv  Detail & Related papers  (2026-02-01T05:54:59Z)
• Stationary Reweighting Yields Local Convergence of Soft Fitted Q-Iteration [40.322273308230606]
  We show that fitted Q-iteration and its entropy-regularized variant, soft FQI, behave poorly under function approximation and distribution shift.<n>We introduce stationary-reweighted soft FQI, which reweights each regression update using the stationary distribution of the current policy.<n>Our analysis suggests that global convergence may be recovered by gradually reducing the softmax temperature.
  arXiv  Detail & Related papers  (2025-12-30T00:58:35Z)
• Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding [16.300563027214555]
  We propose an always-feasible quadratic programming (QP) solver, FlexQP, based on an exact relaxation of the QP constraints.<n>If the original constraints are feasible, then the solver finds the optimal solution to the original QP.<n>If the constraints are infeasible, then the solution minimizes the constraint violation in a sparse manner.
  arXiv  Detail & Related papers  (2025-12-01T11:38:45Z)
• A General and Streamlined Differentiable Optimization Framework [10.851559133306196]
  This paper presents the DiffOptl interface for Julia optimization framework.<n>A first-class JuMP-native API allows users to obtain named parameters derivatives directly with respect to them.<n>Results demonstrate that differentiing a routine can be as a training tool for experimentation, learning, and design-without deviating from standard JuMP modeling practices.
  arXiv  Detail & Related papers  (2025-10-29T21:42:36Z)
• Differentiation Through Black-Box Quadratic Programming Solvers [21.717766458737426]
  Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP)<n>We introduce dQP, a modular and solver-agnostic framework for plug-and-play differentiation of virtually any QP solver.<n>Building on this result, we provide a minimal-overhead, open-source implementation that seamlessly integrates with over 15 state-of-the-art solvers.
  arXiv  Detail & Related papers  (2024-10-08T20:01:39Z)
• Scaling physics-informed hard constraints with mixture-of-experts [0.0]
  We develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE) MoE imposes the constraint over smaller domains, each of which is solved by an "expert" through differentiable optimization. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy in the neural PDE solver setting.
  arXiv  Detail & Related papers  (2024-02-20T22:45:00Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• Adaptivity and Non-stationarity: Problem-dependent Dynamic Regret for Online Convex Optimization [70.4342220499858]
  We introduce novel online algorithms that can exploit smoothness and replace the dependence on $T$ in dynamic regret with problem-dependent quantities. Our results are adaptive to the intrinsic difficulty of the problem, since the bounds are tighter than existing results for easy problems and safeguard the same rate in the worst case.
  arXiv  Detail & Related papers  (2021-12-29T02:42:59Z)

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.