# Learning Multiple Initial Solutions to Optimization Problems

arXiv: https://arxiv.org/abs/2411.02158 · HTML: https://mlsanity.com/paper/2411.02158/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 52 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 30 of 40)

- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [DeepMind Control Suite](https://mlsanity.com/paper/1801.00690/) (2018)
- [Learning Dexterous In-Hand Manipulation](https://mlsanity.com/paper/1808.00177/) (2018)
- [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021)
- [Neural Network Dynamics for Model-Based Deep Reinforcement Learning with Model-Free Fine-Tuning](https://mlsanity.com/paper/1708.02596/) (2017)
- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://mlsanity.com/paper/1604.07446/) (2016)
- [Parting with Misconceptions about Learning-based Vehicle Motion Planning](https://mlsanity.com/paper/2306.07962/) (2023)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Learning to Navigate in Complex Environments](https://mlsanity.com/paper/1611.03673/) (2016)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Model Predictive Path Integral Control using Covariance Variable Importance Sampling](https://mlsanity.com/paper/1509.01149/) (2015)
- [A Survey of Optimization Methods from a Machine Learning Perspective](https://mlsanity.com/paper/1906.06821/) (2019)
- [Exploring Model-based Planning with Policy Networks](https://mlsanity.com/paper/1906.08649/) (2019)
- [Winner Takes It All: Training Performant RL Populations for Combinatorial Optimization](https://mlsanity.com/paper/2210.03475/) (2022)
- [Reinforcement-Learning based Portfolio Management with Augmented Asset Movement Prediction States](https://mlsanity.com/paper/2002.05780/) (2020)
- [cuRobo: Parallelized Collision-Free Minimum-Jerk Robot Motion Generation](https://mlsanity.com/paper/2310.17274/) (2023)
- [From Pixels to Torques: Policy Learning with Deep Dynamical Models](https://mlsanity.com/paper/1502.02251/) (2015)
- [Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs](https://mlsanity.com/paper/2107.10201/) (2021)
- [DiffStack: A Differentiable and Modular Control Stack for Autonomous Vehicles](https://mlsanity.com/paper/2212.06437/) (2022)
- [PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimization](https://mlsanity.com/paper/2402.14048/) (2024)
- [Learning Warm-Start Points for AC Optimal Power Flow](https://mlsanity.com/paper/1905.08860/) (2019)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [Learning Model Predictive Controllers with Real-Time Attention for Real-World Navigation](https://mlsanity.com/paper/2209.10780/) (2022)
- [The Voice of Optimization](https://mlsanity.com/paper/1812.09991/) (2018)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/2007.00017/) (2020)
- [DiffusionSeeder: Seeding Motion Optimization with Diffusion for Rapid Motion Planning](https://mlsanity.com/paper/2410.16727/) (2024)
- [Warm Start of Mixed-Integer Programs for Model Predictive Control of Hybrid Systems](https://mlsanity.com/paper/1910.08251/) (2019)

## Built on by (most cited first, 4 of 4)

- [Inference-Time Enhancement of Generative Robot Policies via Predictive World Modeling](https://mlsanity.com/paper/2502.00622/) (2025)
- [Generating Symbolic World Models via Test-time Scaling of Large Language Models](https://mlsanity.com/paper/2502.04728/) (2025)
- [Unified Generation-Refinement Planning: Bridging Guided Flow Matching and Sampling-Based MPC for Social Navigation](https://mlsanity.com/paper/2508.01192/) (2025)
- [GLENS: Global Search via Learning from Solver Iterates with Diffusion Models](https://mlsanity.com/paper/2606.00366/) (2026)

## Abstract (arXiv)

Sequentially solving similar optimization problems under strict runtime constraints is essential for many applications, such as robot control, autonomous driving, and portfolio management. The performance of local optimization methods in these settings is sensitive to the initial solution: poor initialization can lead to slow convergence or suboptimal solutions. To address this challenge, we propose learning to predict multiple diverse initial solutions given parameters that define the problem instance. We introduce two strategies for utilizing multiple initial solutions: (i) a single-optimizer approach, where the most promising initial solution is chosen using a selection function, and (ii) a multiple-optimizers approach, where several optimizers, potentially run in parallel, are each initialized with a different solution, with the best solution chosen afterward. Notably, by including a default initialization among predicted ones, the cost of the final output is guaranteed to be equal or lower than with the default initialization. We validate our method on three optimal control benchmark tasks: cart-pole, reacher, and autonomous driving, using different optimizers: DDP, MPPI, and iLQR. We find significant and consistent improvement with our method across all evaluation settings and demonstrate that it efficiently scales with the number of initial solutions required. The code is available at MISO (https://github.com/EladSharony/miso).