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Principled Data Augmentation for Learning to Solve Quadratic Programming Problems

NeurIPS 2025 · Label-efficient and robust learning › Self-supervised and contrastive · approach: Representation evaluation and trade-offs · 0 citations (OpenAlex)

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Proposes principled, optimality-preserving data augmentations for LP/QP instances derived from affine transformations of the KKT system, used for supervised training and contrastive pretraining of MPNNs for L2O.

Problem

Learning-to-optimize MPNNs for linear and quadratic programs suffer from scarce labeled data; standard graph augmentations ignore optimization structure and can break optimality.

Approach

Construct augmentations as affine transformations of the KKT system (variable/constraint add, remove, scale) whose new optimal primal-dual solutions are recoverable in linear time without a solver, and use them for supervised training and NT-Xent contrastive pretraining of MPNNs.

Key results

• Combined augmentations reduce LP objective error at 20% data from 6.149% to 2.300% (up to 62.6% improvement).
• Contrastive pretraining reduces objective gap by 59.4% on LP and 54.1% on QP with 10% labeled data, outperforming GraphCL, GCC, IGSD, MVGRL, InfoGraph, DGI, and GAE.
• Per-epoch overhead of augmentation is negligible (LP 10%: 0.975 s vs 1.005 s without augmentation).

Measured effects reported in the paper

Surprising findings

• Graph augmentations from GraphCL-style node dropping, edge flipping, and feature masking often hurt supervised performance compared with no augmentation.
• Several generic graph contrastive baselines (IGSD, MVGRL, DGI, InfoGraph) degrade performance relative to training from scratch.

Limitations

• Some transformations require access to the optimal primal-dual solution, limiting use in unsupervised settings.
• Assumes convex, feasible QPs with positive definite Q; non-convex and infeasible cases are not covered.
• Evaluated only on synthetic LP/QP instances rather than real benchmarks such as MIPLIB or QPLIB.

Experimental setup

Datasets: synthetic LP instances (100 vars, 100 constraints) synthetic QP instances (100 vars, 100 constraints) OOD LP families SC, MIS, CA, CFL OOD QP families SVM, Portfolio, LASSO

Benchmarks: synthetic LP test set synthetic QP test set OOD LP families (SC, MIS, CA, CFL) OOD QP families (SVM, Portfolio, LASSO) larger-size LP/QP instances

Metrics: mean relative objective error (%) per-epoch training time

Baselines: GraphCL GCC IGSD MVGRL InfoGraph DGI GAE

Builds on: GraphCL NT-Xent GraphNorm bipartite constraint-variable MPNN for LPs

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