# LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solvers

arXiv: https://arxiv.org/abs/2607.17708 · HTML: https://mlsanity.com/paper/2607.17708/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 52 references that are in the map.
- First posted on arXiv 20 Jul 2026.

## Builds on (most cited first, 30 of 41)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood](https://mlsanity.com/paper/2012.10384/) (2020)
- [Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/1911.09539/) (2019)
- [Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformer](https://mlsanity.com/paper/2110.02544/) (2021)
- [NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2110.07983/) (2021)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer](https://mlsanity.com/paper/2402.02317/) (2024)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)
- [Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attention](https://mlsanity.com/paper/2006.09100/) (2020)
- [ASP: Learn a Universal Neural Solver!](https://mlsanity.com/paper/2303.00466/) (2023)
- [Cross-Problem Learning for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2404.11677/) (2024)

## Abstract (arXiv)

Multi-task neural solvers aim to handle multiple Vehicle Routing Problem (VRP) variants within a unified model, avoiding separate training for each constraint combination. However, VRP variants differ in optimization difficulty, while existing methods lack stage-wise feedback on their training status, making the model biased to some specific variants. Although meta-learning can support adaptive training, it typically requires bi-level optimization and additional gradient updates, increasing computational cost. To address this limitation, we propose LLM-as-Trainer (LaT), a plug-and-play training paradigm that uses a pretrained large language model as an external trainer. LaT periodically analyzes cross-task validation metrics to generate a stage-wise guidance vector. This vector is combined with the current task's constraint vector and injected into each encoder layer, providing the neural solver with additional training information during subsequent policy optimization. Experiments on 16 VRP variants show that LaT improves the solution quality of several state-of-the-art multi-task neural solvers on both trained and unseen variants, supporting the effectiveness and generality of the proposed training paradigm.