The paper presents a finite‑sample learning‑to‑control framework for geometrically supervised latent models of nonlinear deterministic systems. It introduces an encoder‑only local–global metric hinge that ensures directional resolution and state discrimination, and proves that any approximate empirical minimizer is pointwise co‑Lipschitz and uniformly approximately semiconjugate to the true dynamics under regularity assumptions. The results provide explicit bounds on approximation, sampling, and optimization errors, and demonstrate through controlled experiments that restoring metric resolution improves control performance.
By Alain Bensoussan, Minh-Nhat Phung, Minh-Binh Tran
The paper introduces AutoConvexRelax, a learning-based framework that automates the design of convex relaxations for nonconvex optimization problems. By representing a problem as a tripartite graph of variables, symbolic terms, and objective/constraint positions, the method learns a policy to compose symbolic rewrites that generate valid relaxation trajectories. Experiments on quadratic and fractional problems show that the learned policy improves McCormick lower bounds by 13.52% and achieves near‑semidefinite bounds while using smaller formulations.
By Jinrun Liu, Bai Yan, Tengfei Liu, Qunfeng Liu, Jian Yang, Shi Cheng, Yuhui Shi, Qi Zhao
arXiv:2607. 20235v1 Announce Type: cross Abstract: Classical regularization removes the binary-collision singularity from the Kepler problem, but its value as a representation for learned Hamiltonian dynamics has not been systematically isolated.
By Abhishek Shankar
The paper introduces SD‑DPC, a method that learns sparse, interpretable feedback policies for nonlinear systems using data. It first identifies a prediction model via rollout‑based sparse identification of nonlinear dynamics (SINDy), then parameterizes the policy as a sparse combination of dictionary functions and trains it by differentiating a constrained finite‑horizon predictive‑control objective. The resulting explicit feedback law contains only a few terms, satisfies constraints across three benchmark problems, outperforms a distilled policy by up to an order of magnitude, and requires far less memory and online computation than an optimization benchmark while providing explicit sensitivity bounds.
By Ali Reza Daneshvar Garmroodi, Jan Drgo\v{n}a
arXiv:2606. 17317v1 Announce Type: cross Abstract: Real-time trajectory generation for on-orbit robotic servicing is challenging due to the nonlinear coupling between spacecraft bus motion, manipulator dynamics, visibility cone, and trajectory-level safety constraints.
By Yuji Takubo, Maximilian Adang, Mac Schwager, Simone D'Amico
The paper introduces Reachability Analysis-Informed Reinforcement Learning (RARL) for designing deterministic multi‑impulse interplanetary transfers. RARL uses local first‑order reachability maps to bound velocity perturbations and selects intermediate waypoints, which are then translated into maneuvers via Lambert reconstruction and a terminal two‑impulse solution. Numerical experiments on an Earth‑Mars benchmark show that RARL achieves a mean maneuver cost only 1.72% above a validated convex programming reference and can be trained once to handle a wide range of departure states, achieving 100% feasibility on 10,000 held‑out Monte Carlo departures.
By Yashdeep Chaudhary, Roberto Armellin, Harry Holt
Joint-embedding predictive architectures (JEPAs) learn latent dynamics for planning and avoid representation collapse by matching features to maximum-entropy distributions such as isotropic Gaussians,...
The paper introduces Sparse Sum-of-Squares (SOS) Layers, a new type of differentiable layer that reuses the sparse structure of forward semidefinite programming (SDP) solves during backpropagation. By avoiding dense certificate construction, the method achieves up to 2.7× faster warm‑call times and reduces memory usage from 160 GiB to 1.7 GiB on large problems. Experiments demonstrate its effectiveness across sparse polynomial certification, control, combinatorial relaxations, robotics, oscillator chains, and pose‑graph synchronization, achieving zero certified violations on unseen instances with far fewer optimization solves than finite‑difference approaches.
By Ege Gursoy, Nicolas Mansard
arXiv:2610.35428v1 Announce Type: new
Abstract: Structured sparse learning is a leading paradigm for high-dimensional data modeling, as it enables rigorous integration of domain-validated structural...
By Wanling Xie, Hu Yang
The paper tackles learning structured linear dynamical systems when only a few observations are available at each time step. It proposes an estimator that minimizes a bias‑corrected, potentially non‑convex objective and derives non‑asymptotic error bounds that depend on the local complexity of the constraint set, the trajectory length, and the sub‑sampling probability. The authors also prove convergence of projected gradient descent and demonstrate the theory for three specific constraint sets, showing that accurate recovery of the transition matrix is achievable with much shorter trajectories and very low observation rates.
By Aravinda Kanchana Ruwanpathirana, Hemant Tyagi, Sunny G. W. Wang
Structured sparse learning is a leading paradigm for high-dimensional data modeling, as it enables rigorous integration of domain-validated structural priors into the learning process. Among these pri...
arXiv:2607. 15077v1 Announce Type: new Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known.
By Yao Cheng Li, Ana Larra\~naga, Steven L. Brunton, Urban Fasel