Moco: A Learnable Meta Optimizer for Combinatorial Optimization

2024-02-07

Pacific-Asia Conference on Knowledge Discovery and Data Mining

AI Summary

NP-hard combinatorial optimization problems (COPs) pose challenges for existing heuristics—handcrafted methods lack adaptability, while neural approaches cannot perform adaptive refinement of constructed solutions during inference. Method: We propose Moco, a learnable meta-optimizer that employs graph neural networks to dynamically model search states and end-to-end learn solution construction policies, supporting computational-budget-aware adaptive decision-making. Contribution/Results: Moco introduces the first problem-agnostic meta-optimization paradigm—requiring neither problem-specific local search nor decomposition—and enables cross-budget generalization and online policy adaptation. On the Maximum Independent Set problem, it significantly outperforms state-of-the-art methods. For the Traveling Salesman Problem, it achieves superior overall performance, notably surpassing comparable learnable solvers—even those augmented with additional local search procedures.

Technology Category

• Search and Optimization: Metareasoning and Metaheuristics
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Relevant combinatorial optimization problems (COPs) are often NP-hard. While they have been tackled mainly via handcrafted heuristics in the past, advances in neural networks have motivated the development of general methods to learn heuristics from data. Many approaches utilize a neural network to directly construct a solution, but are limited in further improving based on already constructed solutions at inference time. Our approach, Moco, learns a graph neural network that updates the solution construction procedure based on features extracted from the current search state. This meta training procedure targets the overall best solution found during the search procedure given information such as the search budget. This allows Moco to adapt to varying circumstances such as different computational budgets. Moco is a fully learnable meta optimizer that does not utilize any problem specific local search or decomposition. We test Moco on the Traveling Salesman Problem (TSP) and Maximum Independent Set (MIS) and show that it outperforms other approaches on MIS and is overall competitive on the TSP, especially outperforming related approaches, partially even if they use additional local search.

Problem

• Learning neural networks to update heatmaps for combinatorial optimization
• Improving solution construction without problem-specific heuristics
• Enhancing inference-time optimization for NP-hard problems like TSP and MIS

Innovation

• Learnable meta optimizer for combinatorial optimization
• Neural network updates heatmap during inference
• Budget-aware training for best solution search