Implementing Robust M-Estimators with Certifiable Factor Graph Optimization

2026-03-21

AI Summary

This work addresses the challenges of outlier sensitivity and non-convexity in parameter estimation for robotics and computer vision by proposing an adaptive reweighted M-estimation framework that reformulates robust estimation as a sequence of weighted least-squares subproblems. The key innovation lies in the first-ever seamless integration of certifiably globally optimal factor graph optimization into this framework, guaranteeing global optimality for each subproblem while maintaining compatibility with existing factor graph software ecosystems. By combining fast manifold-based local optimization with robust loss functions, the method significantly outperforms conventional local search strategies in pose graph optimization and landmark-based SLAM tasks, achieving notable improvements in both accuracy and scalability.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Parameter estimation in robotics and computer vision faces formidable challenges from both outlier contamination 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 demonstrates that our adaptively reweighted certifiable estimation approach provides higher-quality estimates than alternative local search-based methods, while scaling tractably to realistic problem sizes.

Problem

• outlier robustness
• nonconvex optimization
• M-estimation
• weighted least squares
• parameter estimation

Innovation

• certifiable optimization
• M-estimation
• adaptive reweighting
• factor graph
• nonconvex optimization