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.

翻译：在机器人和计算机视觉领域的参数估计中，异常值污染和非凸优化景观构成了严峻挑战。虽然M估计通过鲁棒损失函数解决了异常值问题，但它会产生严重非凸的优化问题，难以全局求解。自适应重加权方案是实现M估计的一种特别有吸引力的策略：这些方法通过求解一系列更简单的加权最小二乘子问题，既能够使用标准最小二乘求解器，又能恢复出比简单局部搜索更高质量的估计结果。然而，自适应重加权仍然关键依赖于有效求解内部加权最小二乘问题，由于许多常见参数空间（如旋转和位姿）固有的非凸性，这一任务在许多机器人应用中仍然充满挑战。本文展示了如何仅通过光滑流形上的快速局部优化，轻松实现具有可认证正确求解器的自适应重加权M估计器来解决内部加权最小二乘子问题。我们的方法利用了近期可认证因子图优化的研究成果，在为内部加权最小二乘子问题提供全局最优性认证的同时，无缝集成到现有的基于因子图的软件库和工作流程中。在位姿图优化和路标SLAM任务上的实验评估表明，与基于局部搜索的替代方法相比，我们的自适应重加权可认证估计方法能够提供更高质量的估计结果，同时以可扩展的方式处理现实规模的优化问题。