Convex‑SKM‑Net is a neural layer that enforces convex constraints by constructing linearization halfspaces from residual and gradient oracles, avoiding constraint‑specific projections. It uses fixed‑depth dual projected‑gradient descent on GPU‑friendly matrix operations to solve minimum‑displacement block problems, jointly learning a predictor and a positive‑definite mobility matrix to shape corrections. The method converges theoretically, achieves sub‑$10^{-3}$ feasibility on SOC‑MPC and power‑system relaxations, and outperforms state‑of‑the‑art constraint‑satisfaction techniques with up to 144× speedups and near‑optimal objective gaps.
By Haoyu Zhu, Xiaochen Zhang, Qingchun Hou
The paper introduces Policy Gradient Penalty (PGP), a single‑loop policy‑space method that enforces convex occupancy‑measure constraints via quadratic‑penalty regularization. PGP constructs pseudo‑rewards to estimate gradients of the penalized objective and uses the classical Policy Gradient Theorem, establishing smoothness and global last‑iterate convergence guarantees for an ε‑optimal constrained entropy value with ε‑bounded constraint violation. The authors validate PGP with ablations on a grid‑world benchmark and demonstrate scalability on two challenging continuous‑control tasks.
By Florian Wolf, Ilyas Fatkhullin, Niao He
The paper introduces D$^3$Opt, a derivative‑free diffusion‑based framework that separates constraint modeling from objective optimization in chance‑constrained programs. It learns a risk‑conditioned diffusion model once on constraint‑filtered decisions, then uses an annealed, particle‑based Feynman–Kac correction to optimize any post‑specified objective without retraining. The method is proven to preserve feasibility and provides an error bound, and experiments show effective optimization across smooth, non‑smooth, and non‑convex objectives, including objective transfer tasks.
By Ziwen Liu, Yan Liu, Congying Han, Tiande Guo, Yao Yan, Weichen Zhao
arXiv:2508. 00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems.
By Andrea Martin, Ian R. Manchester, Luca Furieri
arXiv:2608. 13079v1 Announce Type: new Abstract: This paper proposes a novel learning-based approach to approximately solve instances of mixed-integer optimization problems.
By Vincenzo Di Vito, Mehdi Taghizadeh, Deepjyoti Deka, Kaarthik Sundar, Ferdinando Fioretto
arXiv:2609. 30501v1 Announce Type: new Abstract: Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.
By Zhiyao Zhang, Menglu Yu, Alvaro Velasquez, Nathaniel D. Bastian, Jia Liu
The paper introduces Network Feasibility Geometry Reinforcement Learning (NFG‑RL), a method that enforces multi‑layer network constraints—such as interference, power‑rate coupling, flow conservation, service chains, capacity, latency, and reliability—by transporting a proto‑policy through a differentiable feasibility map. By compiling heterogeneous constraints into typed residual blocks and using a variational transport operator, NFG‑RL ensures almost‑sure feasible execution and shapes exploration and gradients to respect active constraints. Experiments on two wireless‑edge surrogate environments show that NFG‑RL boosts feasible utility by 37.5–41.5 %, cuts raw‑action violations by 48.5–60.8 %, and reduces P99 delay by 57.0–75.5 % compared to leading baselines.
By Zuyuan Zhang, Zeyu Fang, Mahdi Imani, Nathaniel D. Bastian, Tian Lan
arXiv:2605. 30456v2 Announce Type: replace Abstract: Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches.
By Shraman Pal, Can Li
The paper introduces Convex-Concave Reinforcement Learning (CCRL), showing that the exact per‑iteration objective in policy learning can be expressed as a difference‑of‑convex (DC) program in log‑density‑ratio coordinates. This formulation unifies existing methods such as CPI, NPG, TRPO, and AWR as special cases and enables a multi‑step axis that couples consecutive decisions. Using sequential convex programming, the authors provide convergence guarantees and demonstrate that CCRL outperforms or matches PPO on diagnostic MDPs, classic control tasks, and a stochastic mid‑horizon healthcare domain, achieving faster convergence and higher training‑curve area.
By Shripad V. Deshmukh, Yaswanth Chittepu, Dhawal Gupta, Philip Thomas, Scott Niekum
arXiv:2508. 20330v5 Announce Type: replace Abstract: Combinatorial optimization problems are ubiquitous in science and engineering.
By Zohair Shafi, Serdar Kadioglu
The paper introduces REP-PD-TEG, a representation‑learning algorithm for low‑rank continuous‑state constrained Markov Decision Processes (CMDPs) that achieves optimal ≥O(√K) regret in the soft cumulative‑violation setting while maintaining a ≥O(K^{3/4}) sample bound when exploratory actions are penalised. For the stricter hard cumulative‑violation scenario, REP-PD-H-TEG is proposed, which uses a bonus‑corrected lower‑confidence utility certificate and a stabilized dual search to guarantee both regret and hard‑violation bounds. Together, these methods provide the first theoretically guaranteed representation‑learning framework for low‑rank continuous‑state CMDPs with both soft and hard violation controls.
By Chenhao Zhou, Chao Zhang, Wensong Bai, Hanbin Zhao, Hui Qian
arXiv:2610. 12328v1 Announce Type: new Abstract: We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks.
By Mingyi Li, Taira Tsuchiya, Kenji Yamanishi