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We study algorithms for detecting and including glass objects in an optimization-based Simultaneous Localization and Mapping (SLAM) algorithm in this work. When LiDAR data is the primary exteroceptive sensory input, glass objects are not correctly registered. This occurs as the incident light primarily passes through the glass objects or reflects away from the source, resulting in inaccurate range measurements for glass surfaces. Consequently, the localization and mapping performance is impacted, thereby rendering navigation in such environments unreliable. Optimization-based SLAM solutions, which are also referred to as Graph SLAM, are widely regarded as state of the art. In this paper, we utilize a simple and computationally inexpensive glass detection scheme for detecting glass objects and present the methodology to incorporate the identified objects into the occupancy grid maintained by such an algorithm (Google Cartographer). We develop both local (submap level) and global algorithms for achieving the objective mentioned above and compare the maps produced by our method with those produced by an existing algorithm that utilizes particle filter based SLAM.

This paper studies a distributed multi-agent convex optimization problem. The system comprises multiple agents in this problem, each with a set of local data points and an associated local cost function. The agents are connected to a server, and there is no inter-agent communication. The agents' goal is to learn a parameter vector that optimizes the aggregate of their local costs without revealing their local data points. In principle, the agents can solve this problem by collaborating with the server using the traditional distributed gradient-descent method. However, when the aggregate cost is ill-conditioned, the gradient-descent method (i) requires a large number of iterations to converge, and (ii) is highly unstable against process noise. We propose an iterative pre-conditioning technique to mitigate the deleterious effects of the cost function's conditioning on the convergence rate of distributed gradient-descent. Unlike the conventional pre-conditioning techniques, the pre-conditioner matrix in our proposed technique updates iteratively to facilitate implementation on the distributed network. In the distributed setting, we provably show that the proposed algorithm converges linearly with an improved rate of convergence than the traditional and adaptive gradient-descent methods. Additionally, for the special case when the minimizer of the aggregate cost is unique, our algorithm converges superlinearly. We demonstrate our algorithm's superior performance compared to prominent distributed algorithms for solving real logistic regression problems and emulating neural network training via a noisy quadratic model, thereby signifying the proposed algorithm's efficiency for distributively solving non-convex optimization. Moreover, we empirically show that the proposed algorithm results in faster training without compromising the generalization performance.

This paper considers the multi-agent linear least-squares problem in a server-agent network architecture. The system comprises multiple agents, each with a set of local data points. The agents are connected to a server, and there is no inter-agent communication. The agents' goal is to compute a linear model that optimally fits the collective data. The agents, however, cannot share their data points. In principle, the agents can solve this problem by collaborating with the server using the server-agent network variant of the classical gradient-descent method. However, when the data points are ill-conditioned, the gradient-descent method requires a large number of iterations to converge. We propose an iterative pre-conditioning technique to mitigate the deleterious impact of the data points' conditioning on the convergence rate of the gradient-descent method. Unlike the conventional preconditioning techniques, the pre-conditioner matrix used in our proposed technique evolves iteratively. We show that our proposed algorithm converges linearly with an improved rate of convergence in comparison to both the classical and the accelerated gradient-descent methods. For the special case, when the solution of the least-squares problem is unique, our algorithm converges to the solution superlinearly. Through numerical experiments on benchmark least-squares problems, we validate our theoretical findings, and also demonstrate our algorithm's improved robustness against process noise. (C) 2021 Elsevier Ltd. All rights reserved.

This paper considers the multi-agent linear least-squares problem in a server-agent network. In this problem, the system comprises multiple agents, each having a set of local data points, that are connected to a server. The goal for the agents is to compute a linear mathematical model that optimally fits the collective data points held by all the agents, without sharing their individual local data points. This goal can be achieved, in principle, using the server-agent variant of the traditional iterative gradient-descent method. The gradient-descent method converges linearly to a solution, and its rate of convergence is lower bounded by the conditioning of the agents' collective data points. If the data points are ill-conditioned, the gradient-descent method may require a large number of iterations to converge. We propose an iterative pre-conditioning technique that mitigates the deleterious effect of the conditioning of data points on the rate of convergence of the gradient-descent method. We rigorously show that the resulting pre-conditioned gradient-descent method, with the proposed iterative pre-conditioning, achieves superlinear convergence when the least-squares problem has a unique solution. In general, the convergence is linear with improved rate of convergence in comparison to the traditional gradient-descent method and the state-of-the-art accelerated gradient-descent methods. We further illustrate the improved rate of convergence of our proposed algorithm through experiments on different real-world least-squares problems in both noise-free and noisy computation environment., Comment: Update: figures for the rest of the datasets have been added