arXiv subjects

Angelia Nedić

Publications and source records attributed to Angelia Nedić.

At least 37 records · Page 2Linked to original sources

arXiv2024

Multi-Agent Resilient Consensus under Intermittent Faulty and Malicious Transmissions (Extended Version)

In this work, we consider the consensus problem in which legitimate agents share their values over an undirected communication network in the presence of malicious or faulty agents. Different from the previous works, we characterize the conditions that generalize to several scenarios such as intermittent faulty or malicious transmissions, based on trust observations. As the standard trust aggregation approach based on a constant threshold fails to distinguish intermittent malicious/faulty activity, we propose a new detection algorithm utilizing time-varying thresholds and the random trust values available to legitimate agents. Under these conditions, legitimate agents almost surely determine their trusted neighborhood correctly with geometrically decaying misclassification probabilities. We further prove that the consensus process converges almost surely even in the presence of malicious agents. We also derive the probabilistic bounds on the deviation from the nominal consensus value that would have been achieved with no malicious agents in the system. Numerical results verify the convergence among agents and exemplify the deviation under different scenarios.

eess.SY↗

arXiv2023

How Physicality Enables Trust: A New Era of Trust-Centered Cyberphysical Systems

Multi-agent cyberphysical systems enable new capabilities in efficiency, resilience, and security. The unique characteristics of these systems prompt a reevaluation of their security concepts, including their vulnerabilities, and mechanisms to mitigate these vulnerabilities. This survey paper examines how advancement in wireless networking, coupled with the sensing and computing in cyberphysical systems, can foster novel security capabilities. This study delves into three main themes related to securing multi-agent cyberphysical systems. First, we discuss the threats that are particularly relevant to multi-agent cyberphysical systems given the potential lack of trust between agents. Second, we present prospects for sensing, contextual awareness, and authentication, enabling the inference and measurement of ``inter-agent trust" for these systems. Third, we elaborate on the application of quantifiable trust notions to enable ``resilient coordination," where ``resilient" signifies sustained functionality amid attacks on multiagent cyberphysical systems. We refer to the capability of cyberphysical systems to self-organize, and coordinate to achieve a task as autonomy. This survey unveils the cyberphysical character of future interconnected systems as a pivotal catalyst for realizing robust, trust-centered autonomy in tomorrow's world.

cs.RO↗

arXiv2023

Projected Push-Pull For Distributed Constrained Optimization Over Time-Varying Directed Graphs (extended version)

We introduce the Projected Push-Pull algorithm that enables multiple agents to solve a distributed constrained optimization problem with private cost functions and global constraints, in a collaborative manner. Our algorithm employs projected gradient descent to deal with constraints and a lazy update rule to control the trade-off between the consensus and optimization steps in the protocol. We prove that our algorithm achieves geometric convergence over time-varying directed graphs while ensuring that the decision variable always stays within the constraint set. We derive explicit bounds for step sizes that guarantee geometric convergence based on the strong-convexity and smoothness of cost functions, and graph properties. Moreover, we provide additional theoretical results on the usefulness of lazy updates, revealing the challenges in the analysis of any gradient tracking method that uses projection operators in a distributed constrained optimization setting. We validate our theoretical results with numerical studies over different graph types, showing that our algorithm achieves geometric convergence empirically.

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arXiv2023

Nash equilibrium seeking over digraphs with row-stochastic matrices and network-independent step-sizes

In this paper, we address the challenge of Nash equilibrium (NE) seeking in non-cooperative convex games with partial-decision information. We propose a distributed algorithm, where each agent refines its strategy through projected-gradient steps and an averaging procedure. Each agent uses estimates of competitors' actions obtained solely from local neighbor interactions, in a directed communication network. Unlike previous approaches that rely on (strong) monotonicity assumptions, this work establishes the convergence towards a NE under a diagonal dominance property of the pseudo-gradient mapping, that can be checked locally by the agents. Further, this condition is physically interpretable and of relevance for many applications, as it suggests that an agent's objective function is primarily influenced by its individual strategic decisions, rather than by the actions of its competitors. In virtue of a novel block-infinity norm convergence argument, we provide explicit bounds for constant step-size that are independent of the communication structure, and can be computed in a totally decentralized way. Numerical simulations on an optical network's power control problem validate the algorithm's effectiveness.

cs.GT↗

arXiv2022

Dynamics based Privacy Preservation in Decentralized Optimization

With decentralized optimization having increased applications in various domains ranging from machine learning, control, sensor networks, to robotics, its privacy is also receiving increased attention. Existing privacy-preserving approaches for decentralized optimization achieve privacy preservation by patching decentralized optimization with information-technology privacy mechanisms such as differential privacy or homomorphic encryption, which either sacrifices optimization accuracy or incurs heavy computation/communication overhead. We propose an inherently privacy-preserving decentralized optimization algorithm by exploiting the robustness of decentralized optimization to uncertainties in optimization dynamics. More specifically, we present a general decentralized optimization framework, based on which we show that privacy can be enabled in decentralized optimization by adding randomness in optimization parameters. We further show that the added randomness has no influence on the accuracy of optimization, and prove that our inherently privacy-preserving algorithm has $R$-linear convergence when the global objective function is smooth and strongly convex. We also rigorously prove that the proposed algorithm can avoid the gradient of a node from being inferable by other nodes. Numerical simulation results confirm the theoretical predictions.

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arXiv2021

Distributed Augmented Lagrangian Method for Link-Based Resource Sharing Problems of Multi-Agent Systems

A multi-agent optimization problem motivated by the management of energy systems is discussed. The associated cost function is separable and convex although not necessarily strongly convex and there exist edge-based coupling equality constraints. In this regard, we propose a distributed algorithm based on solving the dual of the augmented problem. Furthermore, we consider that the communication network might be time-varying and the algorithm might be carried out asynchronously. The time-varying nature and the asynchronicity are modeled as random processes. Then, we show the convergence and the convergence rate of the proposed algorithm under the aforementioned conditions.

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arXiv2020

Accelerated Multi-Agent Optimization Method over Stochastic Networks

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically time-varying communication networks. We consider the standard assumptions of Nesterov's method and show that the sequence of the expected dual values converge toward the optimal value with the rate of $\mathcal{O}(1/k^2)$. Furthermore, we provide a simulation study of solving an optimal power flow problem with a well-known benchmark case.

math.OC↗

arXiv2020

On the Sample Complexity and Optimization Landscape for Quadratic Feasibility Problems

We consider the problem of recovering a complex vector $\mathbf{x}\in \mathbb{C}^n$ from $m$ quadratic measurements $\{\langle A_i\mathbf{x}, \mathbf{x}\rangle\}_{i=1}^m$. This problem, known as quadratic feasibility, encompasses the well known phase retrieval problem and has applications in a wide range of important areas including power system state estimation and x-ray crystallography. In general, not only is the the quadratic feasibility problem NP-hard to solve, but it may in fact be unidentifiable. In this paper, we establish conditions under which this problem becomes {identifiable}, and further prove isometry properties in the case when the matrices $\{A_i\}_{i=1}^m$ are Hermitian matrices sampled from a complex Gaussian distribution. Moreover, we explore a nonconvex {optimization} formulation of this problem, and establish salient features of the associated optimization landscape that enables gradient algorithms with an arbitrary initialization to converge to a \emph{globally optimal} point with a high probability. Our results also reveal sample complexity requirements for successfully identifying a feasible solution in these contexts.

eess.SP↗

arXiv2020

A general framework for decentralized optimization with first-order methods

Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation problems. More recently, the emergence of sophisticated computing and large-scale data science needs have led to a resurgence of activity in this area. In this article, we discuss decentralized first-order gradient methods, which have found tremendous success in control, signal processing, and machine learning problems, where such methods, due to their simplicity, serve as the first method of choice for many complex inference and training tasks. In particular, we provide a general framework of decentralized first-order methods that is applicable to undirected and directed communication networks alike, and show that much of the existing work on optimization and consensus can be related explicitly to this framework. We further extend the discussion to decentralized stochastic first-order methods that rely on stochastic gradients at each node and describe how local variance reduction schemes, previously shown to have promise in the centralized settings, are able to improve the performance of decentralized methods when combined with what is known as gradient tracking. We motivate and demonstrate the effectiveness of the corresponding methods in the context of machine learning and signal processing problems that arise in decentralized environments.

cs.LG↗

arXiv2020

A Dual Approach for Optimal Algorithms in Distributed Optimization over Networks

We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different cases, namely: each function $f_i$ is strongly convex and smooth, each function is either strongly convex or smooth, and when it is convex but neither strongly convex nor smooth. Our approach is based on the dual of an appropriately formulated primal problem, which includes a graph that models the communication restrictions. We propose distributed algorithms that achieve the same optimal rates as their centralized counterparts (up to constant and logarithmic factors), with an additional optimal cost related to the spectral properties of the network. Initially, we focus on functions for which we can explicitly minimize its Legendre-Fenchel conjugate, i.e., admissible or dual friendly functions. Then, we study distributed optimization algorithms for non-dual friendly functions, as well as a method to improve the dependency on the parameters of the functions involved. Numerical analysis of the proposed algorithms is also provided.

math.OC↗

arXiv2020

Distributed Stochastic Gradient Tracking Methods

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method (DSGT) and a gossip-like stochastic gradient tracking method (GSGT). We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant stepsize choice). Under DSGT, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size $n$, which is a comparable performance to a centralized stochastic gradient algorithm. Moreover, we show that when the network is well-connected, GSGT incurs lower communication cost than DSGT while maintaining a similar computational cost. Numerical example further demonstrates the effectiveness of the proposed methods.

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arXiv2020

Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters

We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of agents/machines/computers, and each agent holds a private continuous probability measure and seeks to compute the barycenter of all the measures in the network by getting samples from its local measure and exchanging information with its neighbors. Motivated by this problem, we develop, and analyze, a novel accelerated primal-dual stochastic gradient method for general stochastic convex optimization problems with linear equality constraints. Then, we apply this method to the decentralized distributed optimization setting to obtain a new algorithm for the distributed semi-discrete regularized Wasserstein barycenter problem. Moreover, we show explicit non-asymptotic complexity for the proposed algorithm.

math.OC↗

arXiv2020

Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks

We design the first fully-distributed algorithm for generalized Nash equilibrium seeking in aggregative games on a time-varying communication network, under partial-decision information, i.e., the agents have no direct access to the aggregate decision. The algorithm is derived by integrating dynamic tracking into a projected pseudo-gradient algorithm. The convergence analysis relies on the framework of monotone operator splitting and the Krasnosel'skii-Mann fixed-point iteration with errors.

math.OC↗

arXiv2020

Push-Pull Gradient Methods for Distributed Optimization in Networks

In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents' cost functions while obeying the network connectivity structure. In order to minimize the sum of the cost functions, we consider new distributed gradient-based methods where each node maintains two estimates, namely, an estimate of the optimal decision variable and an estimate of the gradient for the average of the agents' objective functions. From the viewpoint of an agent, the information about the gradients is pushed to the neighbors, while the information about the decision variable is pulled from the neighbors hence giving the name "push-pull gradient methods". The methods utilize two different graphs for the information exchange among agents, and as such, unify the algorithms with different types of distributed architecture, including decentralized (peer-to-peer), centralized (master-slave), and semi-centralized (leader-follower) architecture. We show that the proposed algorithms and their many variants converge linearly for strongly convex and smooth objective functions over a network (possibly with unidirectional data links) in both synchronous and asynchronous random-gossip settings. In particular, under the random-gossip setting, "push-pull" is the first class of algorithms for distributed optimization over directed graphs. Moreover, we numerically evaluate our proposed algorithms in both scenarios, and show that they outperform other existing linearly convergent schemes, especially for ill-conditioned problems and networks that are not well balanced.

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arXiv2019

Optimal Distributed Optimization on Slowly Time-Varying Graphs

We study optimal distributed first-order optimization algorithms when the network (i.e., communication constraints between the agents) changes with time. This problem is motivated by scenarios where agents experience network malfunctions. We provide a sufficient condition that guarantees a convergence rate with optimal (up lo logarithmic terms) dependencies on the network and function parameters if the network changes are constrained to a small percentage $α$ of the total number of iterations. We call such networks slowly time-varying networks. Moreover, we show that Nesterov's method has an iteration complexity of $Ω\big( \big(\sqrt{κ_Φ\cdot \barχ} + α\log(κ_Φ\cdot \barχ)\big) \log(1 / \varepsilon)\big)$ for decentralized algorithms, where $κ_Φ$ is condition number of the objective function, and $\barχ$ is a worst case bound on the condition number of the sequence of communication graphs. Additionally, we provide an explicit upper bound on $α$ in terms of the condition number of the objective function and network topologies.

math.OC↗

arXiv2019

On stochastic and deterministic quasi-Newton methods for non-Strongly convex optimization: Asymptotic convergence and rate analysis

Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods, both full and limited-memory variants, require the objective function to be strongly convex. However, this assumption is fairly restrictive and does not hold for applications such as minimizing the logistic regression loss function. To the best of our knowledge, no rate statements currently exist for SQN methods in the absence of such an assumption. Also, among the existing first-order methods for addressing stochastic optimization problems with merely convex objectives, those equipped with provable convergence rates employ averaging. However, this averaging technique has a detrimental impact on inducing sparsity. Motivated by these gaps, the main contributions of the paper are as follows: (i) Addressing large scale stochastic optimization problems, we develop an iteratively regularized stochastic limited-memory BFGS (IRS-LBFGS) algorithm, where the stepsize, regularization parameter, and the Hessian inverse approximation matrix are updated iteratively. We establish the convergence to an optimal solution of the original problem both in an almost-sure and mean senses. We derive the convergence rate in terms of the objective function's values and show that it is of the order $\mathcal{O}\left(k^{-\left(\frac{1}{3}-ε\right)}\right)$, where $ε$ is an arbitrary small positive scalar; (ii) In deterministic regime, we show that the regularized limited-memory BFGS algorithm displays a rate of the order $\mathcal{O}\left(\frac{1}{k^{1 -ε'}}\right)$, where $ε'$ is an arbitrary small positive scalar. We present our numerical experiments performed on a large scale text classification problem.

math.OC↗

arXiv2019

A Push-Pull Gradient Method for Distributed Optimization in Networks

In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents' cost functions while obeying the network connectivity structure. In order to minimize the sum of the cost functions, we consider a new distributed gradient-based method where each node maintains two estimates, namely, an estimate of the optimal decision variable and an estimate of the gradient for the average of the agents' objective functions. From the viewpoint of an agent, the information about the decision variable is pushed to the neighbors, while the information about the gradients is pulled from the neighbors (hence giving the name "push-pull gradient method"). The method unifies the algorithms with different types of distributed architecture, including decentralized (peer-to-peer), centralized (master-slave), and semi-centralized (leader-follower) architecture. We show that the algorithm converges linearly for strongly convex and smooth objective functions over a directed static network. In our numerical test, the algorithm performs well even for time-varying directed networks.

math.OC↗

arXiv2019

A Distributed Stochastic Gradient Tracking Method

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method. We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant step size choice). More importantly, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size, which is a comparable performance to a centralized stochastic gradient algorithm. Numerical examples further demonstrate the effectiveness of the method.

math.OC↗