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We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where no structural assumption is made on the system matrix $A^* \in \mathbb{R}^{n \times n}$, and have consequently analyzed the ordinary least squares (OLS) estimator in detail. We assume prior structural information on $A^*$ is available, which can be captured in the form of a convex set $\mathcal{K}$ containing $A^*$. For the solution of the ensuing constrained least squares estimator, we derive non-asymptotic error bounds in the Frobenius norm that depend on the local size of $\mathcal{K}$ at $A^*$. To illustrate the usefulness of these results, we instantiate them for three examples, namely when (i) $A^*$ is sparse and $\mathcal{K}$ is a suitably scaled $\ell_1$ ball; (ii) $\mathcal{K}$ is a subspace; (iii) $\mathcal{K}$ consists of matrices each of which is formed by sampling a bivariate convex function on a uniform $n \times n$ grid (convex regression). In all these situations, we show that $A^*$ can be reliably estimated for values of $T$ much smaller than what is needed for the unconstrained setting.

In this work, we propose a learning based neural model that provides both the longitudinal and lateral control commands to simultaneously navigate multiple vehicles. The goal is to ensure that each vehicle reaches a desired target state without colliding with any other vehicle or obstacle in an unconstrained environment. The model utilizes an attention based Graphical Neural Network paradigm that takes into consideration the state of all the surrounding vehicles to make an informed decision. This allows each vehicle to smoothly reach its destination while also evading collision with the other agents. The data and corresponding labels for training such a network is obtained using an optimization based procedure. Experimental results demonstrates that our model is powerful enough to generalize even to situations with more vehicles than in the training data. Our method also outperforms comparable graphical neural network architectures. Project page which includes the code and supplementary information can be found at //yininghase.github.io/multi-agent-control/

The main goal of this paper is to investigate distributed dynamic programming (DP) to solve networked multi-agent Markov decision problems (MDPs). We consider a distributed multi-agent case, where each agent does not have an access to the rewards of other agents except for its own reward. Moreover, each agent can share their parameters with its neighbors over a communication network represented by a graph. We propose a distributed DP in the continuous-time domain, and prove its convergence through control theoretic viewpoints. The proposed analysis can be viewed as a preliminary ordinary differential equation (ODE) analysis of a distributed temporal difference learning algorithm, whose convergence can be proved using Borkar-Meyn theorem and the single time-scale approach.

This paper proposes the Doubly Compressed Momentum-assisted stochastic gradient tracking algorithm $\texttt{DoCoM}$ for communication-efficient decentralized optimization. The algorithm features two main ingredients to achieve a near-optimal sample complexity while allowing for communication compression. First, the algorithm tracks both the averaged iterate and stochastic gradient using compressed gossiping consensus. Second, a momentum step is incorporated for adaptive variance reduction with the local gradient estimates. We show that $\texttt{DoCoM}$ finds a near-stationary solution at all participating agents satisfying $\mathbb{E}[ \| \nabla f( \theta ) \|^2 ] = \mathcal{O}( 1 / T^{2/3} )$ in $T$ iterations, where $f(\theta)$ is a smooth (possibly non-convex) objective function. Notice that the proof is achieved via analytically designing a new potential function that tightly tracks the one-iteration progress of $\texttt{DoCoM}$. As a corollary, our analysis also established the linear convergence of $\texttt{DoCoM}$ to a global optimal solution for objective functions with the Polyak-{\L}ojasiewicz condition. Numerical experiments demonstrate that our algorithm outperforms several state-of-the-art algorithms in practice.

In a decentralized machine learning system, data is typically partitioned among multiple devices or nodes, each of which trains a local model using its own data. These local models are then shared and combined to create a global model that can make accurate predictions on new data. In this paper, we start exploring the role of the network topology connecting nodes on the performance of a Machine Learning model trained through direct collaboration between nodes. We investigate how different types of topologies impact the "spreading of knowledge", i.e., the ability of nodes to incorporate in their local model the knowledge derived by learning patterns in data available in other nodes across the networks. Specifically, we highlight the different roles in this process of more or less connected nodes (hubs and leaves), as well as that of macroscopic network properties (primarily, degree distribution and modularity). Among others, we show that, while it is known that even weak connectivity among network components is sufficient for information spread, it may not be sufficient for knowledge spread. More intuitively, we also find that hubs have a more significant role than leaves in spreading knowledge, although this manifests itself not only for heavy-tailed distributions but also when "hubs" have only moderately more connections than leaves. Finally, we show that tightly knit communities severely hinder knowledge spread.

This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and closed model set containing the object. It complements the article "Statistical Estimation and Optimal Recovery" published in the Annals of Statistics in 1994. There, Donoho showed (among other things) that, for Gaussian noise, linear maps provide near-optimal estimation schemes relatively to a performance measure relevant in Statistical Estimation. Here, we advocate for a different performance measure arguably more relevant in Optimal Recovery. We show that, relatively to this new measure, linear maps still provide near-optimal estimation schemes even if the noise is merely log-concave. Our arguments, which make a connection to the deterministic noise situation and bypass properties specific to the Gaussian case, offer an alternative to parts of Donoho's proof.

Federated Learning (FL) has emerged to allow multiple clients to collaboratively train machine learning models on their private data. However, training and deploying large models for broader applications is challenging in resource-constrained environments. Fortunately, Split Federated Learning (SFL) offers an excellent solution by alleviating the computation and communication burden on the clients SFL often assumes labeled data for local training on clients, however, it is not the case in practice.Prior works have adopted semi-supervised techniques for leveraging unlabeled data in FL, but data non-IIDness poses another challenge to ensure training efficiency. Herein, we propose Pseudo-Clustering Semi-SFL, a novel system for training models in scenarios where labeled data reside on the server. By introducing Clustering Regularization, model performance under data non-IIDness can be improved. Besides, our theoretical and experimental investigations into model convergence reveal that the inconsistent training processes on labeled and unlabeled data impact the effectiveness of clustering regularization. Upon this, we develop a control algorithm for global updating frequency adaptation, which dynamically adjusts the number of supervised training iterations to mitigate the training inconsistency. Extensive experiments on benchmark models and datasets show that our system provides a 3.3x speed-up in training time and reduces the communication cost by about 80.1% while reaching the target accuracy, and achieves up to 6.9% improvement in accuracy under non-IID scenarios compared to the state-of-the-art.

Autonomous shape and structure formation is an important problem in the domain of large-scale multi-agent systems. In this paper, we propose a 3D structure representation method and a distributed structure formation strategy where settled agents guide free moving agents to a prescribed location to settle in the structure. Agents at the structure formation frontier looking for neighbors to settle act as beacons, generating a surface gradient throughout the formed structure propagated by settled agents. Free-moving agents follow the surface gradient along the formed structure surface to the formation frontier, where they eventually reach the closest beacon and settle to continue the structure formation following a local bidding process. Agent behavior is governed by a finite state machine implementation, along with potential field-based motion control laws. We also discuss appropriate rules for recovering from stagnation points. Simulation experiments are presented to show planar and 3D structure formations with continuous and discontinuous boundary/surfaces, which validate the proposed strategy, followed by a scalability analysis.

In this paper, we consider decentralized optimization problems where agents have individual cost functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained formulation includes consensus or single-task optimization as special cases, and allows for more general task relatedness models such as multitask smoothness and coupled optimization. In order to cope with communication constraints, we propose and study an adaptive decentralized strategy where the agents employ differential randomized quantizers to compress their estimates before communicating with their neighbors. The analysis shows that, under some general conditions on the quantization noise, and for sufficiently small step-sizes $\mu$, the strategy is stable both in terms of mean-square error and average bit rate: by reducing $\mu$, it is possible to keep the estimation errors small (on the order of $\mu$) without increasing indefinitely the bit rate as $\mu\rightarrow 0$. Simulations illustrate the theoretical findings and the effectiveness of the proposed approach, revealing that decentralized learning is achievable at the expense of only a few bits.

Effective multi-robot teams require the ability to move to goals in complex environments in order to address real-world applications such as search and rescue. Multi-robot teams should be able to operate in a completely decentralized manner, with individual robot team members being capable of acting without explicit communication between neighbors. In this paper, we propose a novel game theoretic model that enables decentralized and communication-free navigation to a goal position. Robots each play their own distributed game by estimating the behavior of their local teammates in order to identify behaviors that move them in the direction of the goal, while also avoiding obstacles and maintaining team cohesion without collisions. We prove theoretically that generated actions approach a Nash equilibrium, which also corresponds to an optimal strategy identified for each robot. We show through extensive simulations that our approach enables decentralized and communication-free navigation by a multi-robot system to a goal position, and is able to avoid obstacles and collisions, maintain connectivity, and respond robustly to sensor noise.