# A First Guess is Rarely the Final Answer: Learning to Search in the Traveling Salesperson Problem

arXiv: https://arxiv.org/abs/2604.06940 · HTML: https://mlsanity.com/paper/2604.06940/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Combinatorial Optimization: A Survey](https://mlsanity.com/paper/2003.03600/) (2020)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [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)
- [Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning](https://mlsanity.com/paper/2004.01608/) (2020)
- [Efficient Active Search for Combinatorial Optimization Problems](https://mlsanity.com/paper/2106.05126/) (2021)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [EFormer: An Effective Edge-based Transformer for Vehicle Routing Problems](https://mlsanity.com/paper/2506.16428/) (2025)

## Abstract (arXiv)

Most neural solvers for the Traveling Salesperson Problem (TSP) are trained to output a single solution, even though practitioners rarely stop there: at test time, they routinely spend extra compute on sampling or post-hoc search. This raises a natural question: can the search procedure itself be learned? Neural improvement methods take this perspective by learning a policy that applies local modifications to a candidate solution, accumulating gains over an improvement trajectory. Yet learned improvement for TSP remains comparatively immature, with existing methods still falling short of robust, scalable performance. We argue that a key reason is design mismatch: many approaches reuse state representations, architectural choices, and training recipes inherited from single-solution methods, rather than being built around the mechanics of local search. This mismatch motivates NICO-TSP (Neural Improvement for Combinatorial Optimization): a 2-opt improvement framework for TSP. NICO-TSP represents the current tour with exactly n edge tokens aligned with the neighborhood operator, scores 2-opt moves directly without tour positional encodings, and trains via a two-stage procedure: imitation learning to short-horizon optimal trajectories, followed by critic-free group-based reinforcement learning over longer rollouts. Under compute-matched evaluations that measure improvement as a function of both search steps and wall-clock time, NICO-TSP delivers consistently stronger and markedly more step-efficient improvement than prior learned and heuristic search baselines, generalizes far more reliably to larger out-of-distribution instances, and serves both as a competitive replacement for classical local search and as a powerful test-time refinement module for constructive solvers.