Implementing Robust M-Estimators with Certifiable Factor Graph Optimization
Zhexin Xu, Hanna Zhang, Helena Calatrava, Pau Closas, David Rosen
AI summary
Problem
Robust M-estimation in robotics and computer vision typically relies on adaptive reweighting schemes that require solving nonconvex inner weighted least squares subproblems, which are usually handled by initialization-sensitive local methods that lack global optimality guarantees.
Approach
The method integrates an adaptive reweighting framework with the Certi-FGO certifiable factor graph optimization technique, leveraging Shor’s relaxation and Burer-Monteiro factorization to solve inner subproblems globally via fast Riemannian optimization on smooth manifolds.
Key results
- Proposes a general robust implementation combining adaptive reweighting with certifiable factor graphs
- Eliminates the need for hand-designed, problem-specific certifiable solvers
- Demonstrates consistently higher-quality estimates than local search methods on pose-graph optimization and landmark SLAM
- Maintains computational tractability on realistic, large-scale problem sizes
Why it matters
Enables robotics and computer vision practitioners to deploy robust, globally optimal estimators in standard factor graph software libraries without sacrificing scalability.
Abstract
Parameter estimation in robotics and computer vision faces formidable challenges from both outlier contam- ination and nonconvex optimization landscapes. While M- estimation addresses the problem of outliers through robust loss functions, it creates severely nonconvex problems that are difficult to solve globally. Adaptive reweighting schemes provide one particularly appealing strategy for implementing M-estimation in practice: these methods solve a sequence of simpler weighted least squares (WLS) subproblems, enabling both the use of standard least squares solvers and the recovery of higher-quality estimates than simple local search. However, adaptive reweighting still crucially relies upon solving the inner WLS problems effectively, a task that remains challenging in many robotics applications due to the intrinsic nonconvexity of many common parameter spaces (e.g. rotations and poses). In this paper, we show how one can easily implement adaptively-reweighted M-estimators with certifiably correct solvers for the inner WLS subproblems using only fast local optimization over smooth manifolds. Our approach exploits recent work on certifiable factor graph optimization to provide global optimality certificates for the inner WLS subproblems while seamlessly integrating into existing factor graph-based software libraries and workflows. Experimental evaluation on pose-graph optimization and landmark SLAM tasks demon- strates that our adaptively reweighted certifiable estimation approach provides higher-quality estimates than alternative local search-based methods, while scaling tractably to realistic problem sizes.