Certifiable Factor Graph Optimization

Zhexin Xu, Nikolas R. Sanderson, Hanna Jiamei Zhang, David M. Rosen

Keywords: Factor graphs, certifiable estimation, semidefinite optimization, Burer-Monteiro factorization, Riemannian Staircase, SLAM

TL;DR: This paper presents a unified factor graph framework for certifiable estimation that matches state-of-the-art performance while dramatically simplifying implementation

Abstract: We show that the factor graph and certifiable estimation paradigms can be naturally combined into a unified framework for certifiable factor graph optimization. The key insight is that the core constructions underlying certifiable estimation, namely Shor’s relaxation and Burer–Monteiro factorization, naturally inherit the factor graph structure of the original problem. As a result, the lifted problem has identical factor graph connectivity, with variables and factors obtained through one-to-one algebraic transformations, or lifts, of those in the original factor graph. This preservation of structure makes it possible to implement the Riemannian Staircase method within existing factor graph libraries simply by replacing the original variable and factor types with their lifted counterparts. Experiments on pose graph optimization and range-aided SLAM benchmarks confirm functional equivalence with state-of-the-art hand-designed certifiable estimators, while dramatically reducing implementation effort.

Submission Number: 38