Language models are increasingly being deployed for general problem solving across a wide range of tasks, but are still confined to token-level, left-to-right decision-making processes during inference.

Three sampling techniques are presented for comparative investigations.

We propose UTSP, an Unsupervised Learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge to be part of the optimal path. We then apply local search to generate our final prediction based on the heat map. Our loss function consists of two parts: one pushes the model to find the shortest path and the other serves as a surrogate for the constraint that the route should form a Hamiltonian Cycle. Experimental results show that UTSP outperforms the existing data-driven TSP heuristics. Our approach is parameter efficient as well as data efficient: the model takes 10% of the number of parameters and 0.2% of training samples compared with Reinforcement Learning or Supervised Learning methods.

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However, current systems focus on specific use-cases (e.g.

Our language also allowsustorepresent infinite search22 spaces, as substitutions are lazy and can create new hyperparameters and modules. Infinite search spaces are not23 possible with current hyperparameter optimization tools.