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