# Complexity Bounds and Approaches to Learning Projected Gradient Descent Solver Iterates

arXiv: https://arxiv.org/abs/2607.22467 · HTML: https://mlsanity.com/paper/2607.22467/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 13 references that are in the map.
- First posted on arXiv 24 Jul 2026.

## Builds on (most cited first, 10 of 10)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization](https://mlsanity.com/paper/2403.05571/) (2024)
- [Amortized Global Search for Efficient Preliminary Trajectory Design with Deep Generative Models](https://mlsanity.com/paper/2308.03960/) (2023)
- [Constraint-Aware Diffusion Models for Trajectory Optimization](https://mlsanity.com/paper/2406.00990/) (2024)
- [Global Search for Optimal Low Thrust Spacecraft Trajectories using Diffusion Models and the Indirect Method](https://mlsanity.com/paper/2501.07005/) (2025)
- [Aligning Diffusion Model with Problem Constraints for Trajectory Optimization](https://mlsanity.com/paper/2504.00342/) (2025)
- [Global Search of Optimal Spacecraft Trajectories using Amortization and Deep Generative Models](https://mlsanity.com/paper/2412.20023/) (2024)
- [Transfer Learning of Multiobjective Indirect Low-Thrust Trajectories Using Diffusion Models and Markov Chain Monte Carlo](https://mlsanity.com/paper/2605.09125/) (2026)
- [GLENS: Global Search via Learning from Solver Iterates with Diffusion Models](https://mlsanity.com/paper/2606.00366/) (2026)

## Abstract (arXiv)

Data scarcity poses a fundamental challenge in training generative models to produce initial guesses for parametric optimization problems that are otherwise numerically expensive to solve. We therefore study a k-neighborhood data collection strategy that augments datasets of converged solutions with intermediate solver iterates, increasing the amount of training data without additional solver runs. To understand the benefits of this approach, we derive a generalization bound based on Rademacher complexity that reveals the role of the k-neighborhoods and related parameters. To achieve this result, we focus on one-sided box-constrained quadratic programs solved by projected gradient descent. We illustrate the behavior of this solver on two examples. The approach proposed in this paper enables a more capable DDDAS paradigm by improving the efficiency of the data-model-optimization loop. We finish by discussing two views of learning solver-iterate data and connect our analysis with GLENS, a new data-efficient global search method.