Yue Wang

Neural implicit representations have emerged as a promising solution for providing dense geometry in Simultaneous Localization and Mapping (SLAM). However, existing methods in this direction fall short in terms of global consistency and low latency. This paper presents NGEL-SLAM to tackle the above challenges. To ensure global consistency, our system leverages a traditional feature-based tracking module that incorporates loop closure. Additionally, we maintain a global consistent map by representing the scene using multiple neural implicit fields, enabling quick adjustment to the loop closure. Moreover, our system allows for fast convergence through the use of octree-based implicit representations. The combination of rapid response to loop closure and fast convergence makes our system a truly low-latency system that achieves global consistency. Our system enables rendering high-fidelity RGB-D images, along with extracting dense and complete surfaces. Experiments on both synthetic and real-world datasets suggest that our system achieves state-of-the-art tracking and mapping accuracy while maintaining low latency.

In robust Markov decision processes (MDPs), the uncertainty in the transition kernel is addressed by finding a policy that optimizes the worst-case performance over an uncertainty set of MDPs. While much of the literature has focused on discounted MDPs, robust average-reward MDPs remain largely unexplored. In this paper, we focus on robust average-reward MDPs, where the goal is to find a policy that optimizes the worst-case average reward over an uncertainty set. We first take an approach that approximates average-reward MDPs using discounted MDPs. We prove that the robust discounted value function converges to the robust average-reward as the discount factor $\gamma$ goes to $1$, and moreover, when $\gamma$ is large, any optimal policy of the robust discounted MDP is also an optimal policy of the robust average-reward. We further design a robust dynamic programming approach, and theoretically characterize its convergence to the optimum. Then, we investigate robust average-reward MDPs directly without using discounted MDPs as an intermediate step. We derive the robust Bellman equation for robust average-reward MDPs, prove that the optimal policy can be derived from its solution, and further design a robust relative value iteration algorithm that provably finds its solution, or equivalently, the optimal robust policy.