Pretrained Cost Model for Distributed Constraint Optimization Problems

Abstract

Distributed Constraint Optimization Problems (DCOPs) are an important subclass of combinatorial optimization problems, where information and controls are distributed among multiple autonomous agents. Previously, Machine Learning (ML) has been largely applied to solve combinatorial optimization problems by learning effective heuristics. However, existing ML-based heuristic methods are often not generalizable to different search algorithms. Most importantly, these methods usually require full knowledge about the problems to be solved, which are not suitable for distributed settings where centralization is not realistic due to geographical limitations or privacy concerns. To address the generality issue, we propose a novel directed acyclic graph representation schema for DCOPs and leverage the Graph Attention Networks (GATs) to embed graph representations. Our model, GAT-PCM, is then pretrained with optimally labelled data in an offline manner, so as to construct effective heuristics to boost a broad range of DCOP algorithms where evaluating the quality of a partial assignment is critical, such as local search or backtracking search. Furthermore, to enable decentralized model inference, we propose a distributed embedding schema of GAT-PCM where each agent exchanges only embedded vectors, and show its soundness and complexity. Finally, we demonstrate the effectiveness of our model by combining it with a local search or a backtracking search algorithm. Extensive empirical evaluations indicate that the GAT-PCM-boosted algorithms significantly outperform the state-of-the-art methods in various benchmarks.

Empowering distributed constraint optimization with deep learning

“…(1) DBP with a damping factor of 0.9 and its splitting constraint factor graph version (DBP-SCFG) with a splitting ratio of 0.95 [36]; (2) GAT-PCM-LNS with a destroy probability of 0.2 [170], which is a local search method combining the LNS framework [82,122] with neural-learned repair heuristics; (3) Mini-bucket Elimination (MBE) with an i-bound of 9 [194], which is a memory-bounded inference algorithm; (4) Toulbar2 with timeout of 1200s [195], which is a highly optimized exact solver written in C++. The hyperparameters for DBP and GAT-PCM-LNS are set according to the original papers, while the memory budget for MBE and timeout for Toulbar2 are set based on our computational resources.…”

“…The method is referred as "Damped Max-sum" in[36]. We use Damped BP for a coherent presentation.3 This chapter has been published in[186].…”