# Constraint-Informed Learning for Warm Starting Trajectory Optimization

arXiv: https://arxiv.org/abs/2312.14336 · HTML: https://mlsanity.com/paper/2312.14336/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2023.

## Built on by (most cited first, 7 of 7)

- [Data-Driven Performance Guarantees for Classical and Learned Optimizers](https://mlsanity.com/paper/2404.13831/) (2024)
- [Deep Learning Warm Starts for Trajectory Optimization on the International Space Station](https://mlsanity.com/paper/2505.05588/) (2025)
- [Agile Tradespace Exploration for Space Rendezvous Mission Design via Transformers](https://mlsanity.com/paper/2510.03544/) (2025)
- [Compositional Diffusion Models for Powered Descent Trajectory Generation with Flexible Constraints](https://mlsanity.com/paper/2410.04261/) (2024)
- [WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers](https://mlsanity.com/paper/2605.05728/) (2026)
- [Transformer-Informed Trajectory Optimization for Relative Motion in Cislunar Orbits](https://mlsanity.com/paper/2609.25460/) (2026)
- [RL-Guided PAC-NMPC for Probabilistically-Safe Perception-Based Navigation in Unknown Environments](https://mlsanity.com/paper/2609.39854/) (2026)

## Abstract (arXiv)

Future spacecraft and surface robotic missions require increasingly capable autonomy stacks for exploring challenging and unstructured domains, and trajectory optimization will be a cornerstone of such autonomy stacks. However, the nonlinear optimization solvers required remain too slow for use on relatively resource-constrained flight-grade computers. In this work, we turn towards amortized optimization, a learning-based technique for accelerating optimization run times, and present TOAST: Trajectory Optimization with Merit Function Warm Starts. Offline, using data collected from a simulation, we train a neural network to learn a mapping to the full primal and dual solutions given the problem parameters. Crucially, we build upon recent results from decision-focused learning and present a set of decision-focused loss functions using the notion of merit functions for optimization problems. We show that training networks with such constraint-informed losses can better encode the structure of the trajectory optimization problem and jointly learn to reconstruct the primal-dual solution while yielding improved constraint satisfaction. Through numerical experiments on a Lunar rover problem and a 3-degrees-of-freedom Mars powered descent guidance problem, we demonstrate that TOAST outperforms benchmark approaches in terms of both computation times and network prediction constraint satisfaction.