# Improving Max-Sum through Decimation to Solve Loopy Distributed Constraint Optimization Problems

## TL;DR

This paper introduces DeciMaxSum, a novel method that enhances Max-Sum algorithm performance on loopy distributed constraint optimization problems by using belief-propagation-guided decimation, showing improved results on benchmark tests.

## Contribution

The paper proposes DeciMaxSum, a new decimation-based approach inspired by belief propagation, to improve Max-Sum performance on loopy DCOPs, with empirical validation.

## Key findings

- DeciMaxSum outperforms state-of-the-art methods on benchmark problems.
- Certain policy combinations significantly improve convergence.
- Empirical results demonstrate better solution quality and efficiency.

## Abstract

In the context of solving large distributed constraint optimization problems (DCOP), belief-propagation and approximate inference algorithms are candidates of choice. However, in general, when the factor graph is very loopy (i.e. cyclic), these solution methods suffer from bad performance, due to non-convergence and many exchanged messages. As to improve performances of the Max-Sum inference algorithm when solving loopy constraint optimization problems, we propose here to take inspiration from the belief-propagation-guided dec-imation used to solve sparse random graphs (k-satisfiability). We propose the novel DeciMaxSum method, which is parameterized in terms of policies to decide when to trigger decimation, which variables to decimate, and which values to assign to decimated variables. Based on an empirical evaluation on a classical BP benchmark (the Ising model), some of these combinations of policies exhibit better performance than state-of-the-art competitors.