Abstract

I will present an overview of the theory of quantitative homogenization for elliptic and parabolic equations, with an emphasis on the "coarse-graining" point of view. I will begin by trying to motivate the results with some applications to models in mathematical physics. Time permitting, I will also discuss some open problems. Geometric perception is the task of estimating geometric models (e.g., object pose and 3D structure) from sensor measurements and priors (e.g., point clouds and neural network detections). The ubiquitous existence of outliers —measurements that tell no or little information about the models to be estimated— makes it theoretically intractable to perform estimation with guaranteed optimality. Despite this theoretical intractability, safety-critical robotics applications still demand trustworthiness and performance guarantees on perception algorithms.

In this talk, I present certifiable outlier-robust geometric perception, a new paradigm to design tractable geometric estimation algorithms that enjoy rigorous performance guarantees, i.e., they return an optimal estimate with a certificate of optimality for a majority of problem instances, but declare failure and provide a measure of suboptimality for worst-case instances. Particularly, I present two general-purpose algorithms in this paradigm: (i) an estimator that uses graph theory to prune gross outliers and leverages graduated non-convexity to compute the optimal model estimate with high probability of success, and (ii) a certifier that employs sparse semidefinite programming (SDP) relaxation and a novel SDP solver to endow the estimator with an optimality certificate or escape local minima otherwise. The estimator is fast and robust against up to 99% random outliers in practical perception applications, and the certifier can compute high-accuracy optimality certificates for large-scale problems beyond the reach of existing SDP solvers. I showcase certifiable outlier-robust perception on robotics applications such as scan matching, satellite pose estimation, and vehicle pose and shape estimation.

Speaker

Heng Yang is an (incoming) Assistant Professor in the School of Engineering and Applied Sciences at Harvard University. He obtained his PhD from the Laboratory for Information and Decision Systems at MIT in 2022, M.S. at MIT in 2017, and B.Eng. at Tsinghua University in 2015. He is broadly interested in the algorithmic foundations of robot perception, decision-making, and learning, with particular focus on bringing large-scale convex optimization, semidefinite relaxation, statistics, and machine learning to safe and trustworthy autonomy. Heng Yang is a recipient of the Best Paper Award in Robot Vision at the 2020 IEEE International Conference on Robotics and Automation (ICRA), a Best Paper Award Honorable Mention from the 2020 IEEE Robotics and Automation Letters (RA-L), and a Best Paper Award Finalist at the 2021 Robotics: Science and Systems (RSS) conference.