arXiv Machine Learning

Learned Pairwise Deep Dual-Optimal Inequalities for Stabilizing Column Generation

arXiv:2607. 13373v1 Announce Type: cross Abstract: Column generation (CG) is central to many large-scale optimization algorithms, including branch-price-and-cut methods for vehicle routing problems, but unstable dual solutions can substantially slow its convergence.

arXiv AI
Aug 28

CG4AI: A Column Generation Framework for Training AI Models Under Constraints

CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.

By Youcef Magnouche, Abderrahmane Driouch, S\'ebastien Martin, Pierre Bauguion
Hugging Face Trending Papers
Aug 20

Learning Early-to-Final Solution Consistency for MILP Acceleration

Mixed-Integer Linear Programming (MILP) is a fundamental problem class in operations research and combinatorial optimization, with broad applications to industrial decision-making. Owing to their NP-hardness, however, modern solvers may struggle to find high-quality solutions for challenging MILP instances within practical time limits.

arXiv Machine Learning
Aug 27

StoSignSGD: Unbiased Structural Stochasticity Fixes SignSGD for Training Large Language Models

StoSignSGD is a new sign‑based optimization algorithm that injects structural stochasticity into the sign operator, ensuring unbiased updates. It resolves the divergence issues of traditional SignSGD on non‑smooth objectives, achieving optimal convergence rates in convex settings and improved complexity bounds in non‑convex, non‑smooth problems. Empirical results show that StoSignSGD is stable and efficient across large language model training, outperforming AdamW and SignSGD in low‑precision regimes (FP8 and FP4) and delivering speedups and accuracy gains on models ranging from OLMo2‑370M to 7B LLMs.

By Dingzhi Yu, Rui Pan, Yuxing Liu, Difan Zou, Tong Zhang
arXiv Machine Learning
Sep 7

GNN-Guided Graph Coarsening and Adaptive QUBO Penalties for the Capacitated Vehicle Routing Problem with Time Windows on a Quantum Annealer

The paper presents a method for reducing the size of Quadratic Unconstrained Binary Optimization (QUBO) models used to solve the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) on quantum annealers. It introduces adaptive penalty calibration to improve constraint satisfaction and replaces hand‑tuned merge heuristics with a graph neural network (GNN) that consistently achieves higher feasibility across Solomon benchmark families. Experiments on simulated annealing and a D‑Wave Advantage2 processor show significant reductions in constraint violations and improved feasibility rates, with the QUBO size remaining 5–6 times smaller.

By Youssef Kamel Rezk, Pawe{\l} Gora