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Federated learning (FL) aims to minimize the communication complexity of training a model over heterogeneous data distributed across many clients. A common approach is local methods, where clients take multiple optimization steps over local data before communicating with the server (e.g., FedAvg). Local methods can exploit similarity between clients' data. However, in existing analyses, this comes at the cost of slow convergence in terms of the dependence on the number of communication rounds R. On the other hand, global methods, where clients simply return a gradient vector in each round (e.g., SGD), converge faster in terms of R but fail to exploit the similarity between clients even when clients are homogeneous. We propose FedChain, an algorithmic framework that combines the strengths of local methods and global methods to achieve fast convergence in terms of R while leveraging the similarity between clients. Using FedChain, we instantiate algorithms that improve upon previously known rates in the general convex and PL settings, and are near-optimal (via an algorithm-independent lower bound that we show) for problems that satisfy strong convexity. Empirical results support this theoretical gain over existing methods.

The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current result about the well-studied switch Markov chain is that it is rapidly mixing on P-stable degree sequences (see DOI:10.1016/j.ejc.2021.103421). The switch Markov chain does not change any degree sequence. However, there are cases where degree intervals are specified rather than a single degree sequence. (A natural scenario where this problem arises is in hypothesis testing on social networks that are only partially observed.) Rechner, Strowick, and M\"uller-Hannemann introduced in 2018 the notion of degree interval Markov chain which uses three (separately well-studied) local operations (switch, hinge-flip and toggle), and employing on degree sequence realizations where any two sequences under scrutiny have very small coordinate-wise distance. Recently Amanatidis and Kleer published a beautiful paper (arXiv:2110.09068), showing that the degree interval Markov chain is rapidly mixing if the sequences are coming from a system of very thin intervals which are centered not far from a regular degree sequence. In this paper we extend substantially their result, showing that the degree interval Markov chain is rapidly mixing if the intervals are centred at P-stable degree sequences.

As scene segmentation systems reach visually accurate results, many recent papers focus on making these network architectures faster, smaller and more efficient. In particular, studies often aim at designingreal-time'systems. Achieving this goal is particularly relevant in the context of real-time video understanding for autonomous vehicles, and robots. In this paper, we argue that the commonly used performance metric of mean Intersection over Union (mIoU) does not fully capture the information required to estimate the true performance of these networks when they operate inreal-time'. We propose a change of objective in the segmentation task, and its associated metric that encapsulates this missing information in the following way: We propose to predict the future output segmentation map that will match the future input frame at the time when the network finishes the processing. We introduce the associated latency-aware metric, from which we can determine a ranking. We perform latency timing experiments of some recent networks on different hardware and assess the performances of these networks on our proposed task. We propose improvements to scene segmentation networks to better perform on our task by using multi-frames input and increasing capacity in the initial convolutional layers.

We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time. Additionally, we provide a sampling algorithm to construct the necessary random input in an efficient way. The theoretical error analysis is complemented by numerical experiments.

Developing controllers for obstacle avoidance between polytopes is a challenging and necessary problem for navigation in tight spaces. Traditional approaches can only formulate the obstacle avoidance problem as an offline optimization problem. To address these challenges, we propose a duality-based safety-critical optimal control using nonsmooth control barrier functions for obstacle avoidance between polytopes, which can be solved in real-time with a QP-based optimization problem. A dual optimization problem is introduced to represent the minimum distance between polytopes and the Lagrangian function for the dual form is applied to construct a control barrier function. We validate the obstacle avoidance with the proposed dual formulation for L-shaped (sofa-shaped) controlled robot in a corridor environment. We demonstrate real-time tight obstacle avoidance with non-conservative maneuvers on a moving sofa (piano) problem with nonlinear dynamics.

Stability certification and identification of the stabilizable operating region of a dynamical system are two important concerns to ensure its operational safety/security and robustness. With the advent of machine-learning tools, these issues are especially important for systems with machine-learned components in the feedback loop. Here, in presence of unknown discrete variation (DV) of its parameters within a bounded range, a system controlled by a static feedback controller in which the closed-loop (CL) equilibria are subject to variation-induced drift is equivalently represented using a class of time-invariant systems, each with the same control policy. To develop a general theory for stability and stabilizability of such a class of neural-network (NN) controlled nonlinear systems, a Lyapunov-based convex stability certificate is proposed and is further used to devise an estimate of a local Lipschitz upper bound for the NN and a corresponding operating domain in the state space containing an initialization set, starting from where the CL local asymptotic stability of each system in the class is guaranteed, while the trajectory of the original system remains confined to the domain if the DV of the parameters satisfies a certain quasi-stationarity condition. To compute such a robustly stabilizing NN controller, a stability-guaranteed training (SGT) algorithm is also proposed. The effectiveness of the proposed framework is demonstrated using illustrative examples.

Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time series are limited: Gaussian DLMs require continuous data, while Poisson-based alternatives often lack sufficient modeling flexibility. We introduce a novel semiparametric methodology for count time series by warping a Gaussian DLM. The warping function has two components: a (nonparametric) transformation operator that provides distributional flexibility and a rounding operator that ensures the correct support for the discrete data-generating process. We develop conjugate inference for the warped DLM, which enables analytic and recursive updates for the state space filtering and smoothing distributions. We leverage these results to produce customized and efficient algorithms for inference and forecasting, including Monte Carlo simulation for offline analysis and an optimal particle filter for online inference. This framework unifies and extends a variety of discrete time series models and is valid for natural counts, rounded values, and multivariate observations. Simulation studies illustrate the excellent forecasting capabilities of the warped DLM. The proposed approach is applied to a multivariate time series of daily overdose counts and demonstrates both modeling and computational successes.

Multi-camera vehicle tracking is one of the most complicated tasks in Computer Vision as it involves distinct tasks including Vehicle Detection, Tracking, and Re-identification. Despite the challenges, multi-camera vehicle tracking has immense potential in transportation applications including speed, volume, origin-destination (O-D), and routing data generation. Several recent works have addressed the multi-camera tracking problem. However, most of the effort has gone towards improving accuracy on high-quality benchmark datasets while disregarding lower camera resolutions, compression artifacts and the overwhelming amount of computational power and time needed to carry out this task on its edge and thus making it prohibitive for large-scale and real-time deployment. Therefore, in this work we shed light on practical issues that should be addressed for the design of a multi-camera tracking system to provide actionable and timely insights. Moreover, we propose a real-time city-scale multi-camera vehicle tracking system that compares favorably to computationally intensive alternatives and handles real-world, low-resolution CCTV instead of idealized and curated video streams. To show its effectiveness, in addition to integration into the Regional Integrated Transportation Information System (RITIS), we participated in the 2021 NVIDIA AI City multi-camera tracking challenge and our method is ranked among the top five performers on the public leaderboard.

Given a heterogeneous group of robots executing a complex task represented in Linear Temporal Logic, and a new set of tasks for the group, we define the task update problem and propose a framework for automatically updating individual robot tasks given their respective existing tasks and capabilities. Our heuristic, token-based, conflict resolution task allocation algorithm generates a near-optimal assignment for the new task. We demonstrate the scalability of our approach through simulations of multi-robot tasks.

Obtaining a dynamic population distribution is key to many decision-making processes such as urban planning, disaster management and most importantly helping the government to better allocate socio-technical supply. For the aspiration of these objectives, good population data is essential. The traditional method of collecting population data through the census is expensive and tedious. In recent years, machine learning methods have been developed to estimate the population distribution. Most of the methods use data sets that are either developed on a small scale or not publicly available yet. Thus, the development and evaluation of the new methods become challenging. We fill this gap by providing a comprehensive data set for population estimation in 98 European cities. The data set comprises digital elevation model, local climate zone, land use classifications, nighttime lights in combination with multi-spectral Sentinel-2 imagery, and data from the Open Street Map initiative. We anticipate that it would be a valuable addition to the research community for the development of sophisticated machine learning-based approaches in the field of population estimation.