In cooperative multi-agent robotic systems, coordination is necessary in order to complete a given task. Important examples include search and rescue, operations in hazardous environments, and environmental monitoring. Coordination, in turn, requires simultaneous satisfaction of safety critical constraints, in the form of state and input constraints, and a connectivity constraint, in order to ensure that at every time instant there exists a communication path between every pair of agents in the network. In this work, we present a model predictive controller that tackles the problem of performing multi-agent coordination while simultaneously satisfying safety critical and connectivity constraints. The former is formulated in the form of state and input constraints and the latter as a constraint on the second smallest eigenvalue of the associated communication graph Laplacian matrix, also known as Fiedler eigenvalue, which enforces the connectivity of the communication network. We propose a sequential quadratic programming formulation to solve the associated optimization problem that is amenable to distributed optimization, making the proposed solution suitable for control of multi-agent robotics systems relying on local computation. Finally, the effectiveness of the algorithm is highlighted with a numerical simulation.
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We consider \emph{Gibbs distributions}, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval $[\beta_{\min}, \beta_{\max}]$ and $H( \omega ) \in \{0 \} \cup [1, n]$. The \emph{partition function} is the normalization factor $Z(\beta)=\sum_{\omega \in\Omega}e^{\beta H(\omega)}$. Two important parameters of these distributions are the log partition ratio $q = \log \tfrac{Z(\beta_{\max})}{Z(\beta_{\min})}$ and the counts $c_x = |H^{-1}(x)|$. These are correlated with system parameters in a number of physical applications and sampling algorithms. Our first main result is to estimate the counts $c_x$ using roughly $\tilde O( \frac{q}{\varepsilon^2})$ samples for general Gibbs distributions and $\tilde O( \frac{n^2}{\varepsilon^2} )$ samples for integer-valued distributions (ignoring some second-order terms and parameters), and we show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs, independent sets, and perfect matchings. As a key subroutine, we also develop algorithms to compute the partition function $Z$ using $\tilde O(\frac{q}{\varepsilon^2})$ samples for general Gibbs distributions and using $\tilde O(\frac{n^2}{\varepsilon^2})$ samples for integer-valued distributions.
Blockchain enables peer-to-peer transactions in cyberspace without a trusted third party. The rapid growth of Ethereum and smart contract blockchains generally calls for well-designed Transaction Fee Mechanisms (TFMs) to allocate limited storage and computation resources. However, existing research on TFMs must consider the waiting time for transactions, which is essential for computer security and economic efficiency. Integrating data from the Ethereum blockchain and memory pool (mempool), we explore how two types of events affect transaction latency. First, we apply regression discontinuity design (RDD) to study the causal inference of the Merge, the most recent significant upgrade of Ethereum. Our results show that the Merge significantly reduces the long waiting time, network loads, and market congestion. In addition, we verify our results' robustness by inspecting other compounding factors, such as censorship and unobserved delays of transactions via private changes. Second, examining three major protocol changes during the merge, we identify block interval shortening as the most plausible cause for our empirical results. Furthermore, in a mathematical model, we show block interval as a unique mechanism design choice for EIP1559 TFM to achieve better security and efficiency, generally applicable to the market congestion caused by demand surges. Finally, we apply time series analysis to research the interaction of Non-Fungible token (NFT) drops and market congestion using Facebook Prophet, an open-source algorithm for generating time-series models. Our study identified NFT drops as a unique source of market congestion -- holiday effects -- beyond trend and season effects. Finally, we envision three future research directions of TFM.
The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph $G$. Our goal is to find a subgraph $S$ of $G$ with the minimum number of edges which is $2$-vertex-connected, namely $S$ remains connected after the deletion of an arbitrary node. 2VCSS is well-studied in terms of approximation algorithms, and the current best (polynomial-time) approximation factor is $10/7$ by Heeger and Vygen [SIDMA'17] (improving on earlier results by Khuller and Vishkin [STOC'92] and Garg, Vempala and Singla [SODA'93]).
1. Species distribution models and maps from large-scale biodiversity data are necessary for conservation management. One current issue is that biodiversity data are prone to taxonomic misclassifications. Methods to account for these misclassifications in multispecies distribution models have assumed that the classification probabilities are constant throughout the study. In reality, classification probabilities are likely to vary with several covariates. Failure to account for such heterogeneity can lead to bias in parameter estimates. 2. Here we present a general multispecies distribution model that accounts for heterogeneity in the classification process. The proposed model assumes a multinomial generalised linear model for the classification confusion matrix. We compare the performance of the heterogeneous classification model to that of the homogeneous classification model by assessing how well they estimate the parameters in the model and their predictive performance on hold-out samples. We applied the model to gull data from Norway, Denmark and Finland, obtained from GBIF. 3. Our simulation study showed that accounting for heterogeneity in the classification process increased precision by 30% and reduced accuracy and recall by 6%. Applying the model framework to the gull dataset did not improve the predictive performance between the homogeneous and heterogeneous models due to the smaller misclassified sample sizes. However, when machine learning predictive scores are used as weights to inform the species distribution models about the classification process, the precision increases by 70%. 4. We recommend multiple multinomial regression to be used to model the variation in the classification process when the data contains relatively larger misclassified samples. Machine prediction scores should be used when the data contains relatively smaller misclassified samples.
This paper reviews background and examples of Bayesian predictive synthesis (BPS), and develops details in a subset of BPS mixture models. BPS expands on standard Bayesian model uncertainty analysis for model mixing to provide a broader foundation for calibrating and combining predictive densities from multiple models or other sources. One main focus here is BPS as a framework for justifying and understanding generalized "linear opinion pools," where multiple predictive densities are combined with flexible mixing weights that depend on the forecast outcome itself, i.e., the setting of outcome-dependent model mixing. BPS also defines approaches to incorporating and exploiting dependencies across models defining forecasts, and to formally addressing the problem of model set incompleteness within the subjective Bayesian framework. In addition to an overview of general mixture-based BPS, new methodological developments for dynamic BPS -- involving calibration and pooling of sets of predictive distributions in a univariate time series setting -- are presented. These developments are exemplified in summaries of an analysis in a univariate financial time series study.
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.
Recent years have witnessed significant advances in technologies and services in modern network applications, including smart grid management, wireless communication, cybersecurity as well as multi-agent autonomous systems. Considering the heterogeneous nature of networked entities, emerging network applications call for game-theoretic models and learning-based approaches in order to create distributed network intelligence that responds to uncertainties and disruptions in a dynamic or an adversarial environment. This paper articulates the confluence of networks, games and learning, which establishes a theoretical underpinning for understanding multi-agent decision-making over networks. We provide an selective overview of game-theoretic learning algorithms within the framework of stochastic approximation theory, and associated applications in some representative contexts of modern network systems, such as the next generation wireless communication networks, the smart grid and distributed machine learning. In addition to existing research works on game-theoretic learning over networks, we highlight several new angles and research endeavors on learning in games that are related to recent developments in artificial intelligence. Some of the new angles extrapolate from our own research interests. The overall objective of the paper is to provide the reader a clear picture of the strengths and challenges of adopting game-theoretic learning methods within the context of network systems, and further to identify fruitful future research directions on both theoretical and applied studies.
This paper aims to mitigate straggler effects in synchronous distributed learning for multi-agent reinforcement learning (MARL) problems. Stragglers arise frequently in a distributed learning system, due to the existence of various system disturbances such as slow-downs or failures of compute nodes and communication bottlenecks. To resolve this issue, we propose a coded distributed learning framework, which speeds up the training of MARL algorithms in the presence of stragglers, while maintaining the same accuracy as the centralized approach. As an illustration, a coded distributed version of the multi-agent deep deterministic policy gradient(MADDPG) algorithm is developed and evaluated. Different coding schemes, including maximum distance separable (MDS)code, random sparse code, replication-based code, and regular low density parity check (LDPC) code are also investigated. Simulations in several multi-robot problems demonstrate the promising performance of the proposed framework.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.
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