# Predictive Dual Smoothing for Column Generation

arXiv: https://arxiv.org/abs/2609.34740 · HTML: https://mlsanity.com/paper/2609.34740/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 25 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [A Deep Reinforcement Learning Framework For Column Generation](https://mlsanity.com/paper/2206.02568/) (2022)
- [Machine-learning-based arc selection for constrained shortest path problems in column generation](https://mlsanity.com/paper/2201.02535/) (2022)
- [Enhancing Column Generation by a Machine-Learning-Based Pricing Heuristic for Graph Coloring](https://mlsanity.com/paper/2112.04906/) (2021)
- [A Reinforcement-Learning-Based Multiple-Column Selection Strategy for Column Generation](https://mlsanity.com/paper/2312.14213/) (2023)
- [Adaptive Stabilization Based on Machine Learning for Column Generation](https://mlsanity.com/paper/2405.11198/) (2024)
- [FFCG: Effective and Fast Family Column Generation for Solving Large-Scale Linear Program](https://mlsanity.com/paper/2412.19066/) (2024)

## Abstract (arXiv)

Solving large-scale linear programs efficiently is an important challenge in many optimization settings. A key technique is column generation, which alternates between solving the master problem over a restricted subset of the variables, and using a pricing subproblem to identify new variables to add. The pricing subproblem is guided by the dual solution of the current restricted master problem, but oscillations in these dual solutions can substantially slow convergence. Dual stabilization methods address this issue. Dual smoothing is a common stabilization method, which guides the pricing subproblem using a combination of the current dual solution and duals from previous iterations. However, while past dual solutions can stabilize the dual trajectory, they do not necessarily guide pricing towards useful new variables. We therefore introduce predictive dual smoothing, which instead combines the current dual solution with a learned prediction of future duals to steer pricing towards variables that are more useful in subsequent iterations. The predictor is trained offline using supervision extracted from standard column generation trajectories and is used only to modify the pricing subproblem's objective function, while exact reduced-cost checks and fallback pricing with the unsmoothed duals preserve correctness. Experiments on cutting stock and generalized assignment problems show that predictive dual smoothing substantially reduces generated columns and wall-clock time relative to standard column generation and existing classical and learned stabilization methods. These gains extend to out-of-distribution instance sizes, and predictive smoothing provides further improvements when combined with strong classical stabilization.