Alvin Pan

Krzysztof Choromanski, Arijit Sehanobish, Han Lin et al. · cambridge

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

Siddharth Singi, Zhanpeng He, Alvin Pan et al.

In a Human-in-the-Loop paradigm, a robotic agent is able to act mostly autonomously in solving a task, but can request help from an external expert when needed. However, knowing when to request such assistance is critical: too few requests can lead to the robot making mistakes, but too many requests can overload the expert. In this paper, we present a Reinforcement Learning based approach to this problem, where a semi-autonomous agent asks for external assistance when it has low confidence in the eventual success of the task. The confidence level is computed by estimating the variance of the return from the current state. We show that this estimate can be iteratively improved during training using a Bellman-like recursion. On discrete navigation problems with both fully- and partially-observable state information, we show that our method makes effective use of a limited budget of expert calls at run-time, despite having no access to the expert at training time.