Certifiable Factor Graph Optimization

Abstract

We show that the factor graph and certifiable estimation paradigms, which have thus far been treated as essentially independent in the literature, can be naturally synthesized into a unified framework for certifiable factor graph optimization that combines the ease of use of the former with the strong performance guarantees of the latter. The key insight enabling our synthesis is that the core mathematical constructions used to develop certifiable estimators (Shor's relaxation and Burer-Monteiro factorization) inherit a factor graph structure from the original problem: applying these transformations to a QCQP-representable estimation task with an associated factor graph model yields a lifted problem with identical factor graph connectivity whose constituent variables and factors are simple one-to-one algebraic transformations (lifts) of those appearing in the original QCQP's factor graph. This correspondence enables the Riemannian Staircase methodology for certifiable estimation to be easily instantiated and deployed using the same mature, highly-performant factor graph libraries and workflows already ubiquitously employed throughout robotics and computer vision. Experimental evaluation on a variety of pose graph optimization, landmark SLAM, and range-aided SLAM benchmarks demonstrates that our certifiable factor graph optimization methodology enables the implementation of certifiable estimators that are functionally equivalent to current state-of-the-art hand-designed, problem-specific methods, while dramatically reducing the required implementation effort from the order of months to hours.