Offline Decision Transformers for Neural Combinatorial Optimization: Surpassing Heuristics on the Traveling Salesman Problem

TL;DR

This paper introduces an offline RL approach using Decision Transformer for neural combinatorial optimization, specifically the TSP, outperforming classical heuristics by synthesizing and surpassing existing solutions.

Contribution

It applies offline RL with a Pointer Network and expectile regression to improve TSP solutions, overcoming limitations of online RL methods.

Findings

Consistently outperforms classical heuristics on TSP instances

Demonstrates the effectiveness of offline RL in combinatorial optimization

Shows potential to leverage existing heuristic data for better solutions

Abstract

Combinatorial optimization problems like the Traveling Salesman Problem are critical in industry yet NP-hard. Neural Combinatorial Optimization has shown promise, but its reliance on online reinforcement learning (RL) hampers deployment and underutilizes decades of algorithmic knowledge. We address these limitations by applying the offline RL framework, Decision Transformer, to learn superior strategies directly from datasets of heuristic solutions; it aims to not only to imitate but to synthesize and outperform them. Concretely, we (i) integrate a Pointer Network to handle the instance-dependent, variable action space of node selection, and (ii) employ expectile regression for optimistic conditioning of Return-to-Go, which is crucial for instances with widely varying optimal values. Experiments show that our method consistently produces higher-quality tours than the four classical heuristics it is trained on, demonstrating the potential of offline RL to unlock and exceed the performance embedded in existing domain knowledge.