arXiv subjects

Vijay Gupta

Publications and source records attributed to Vijay Gupta.

At least 55 records · Page 3Linked to original sources

arXiv2023

Maximization of Nonsubmodular Functions under Multiple Constraints with Applications

We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the problem with provable approximation guarantees. The first algorithm exploits the structure of a special class of the general problem instance to obtain a better time complexity. The second algorithm is suitable for the general problem. We characterize the approximation guarantees of the two algorithms, leveraging the notions of submodularity ratio and curvature introduced for set functions. We then discuss particular applications of the general problem formulation to problems that have been considered in the literature. We validate our theoretical results using numerical examples.

math.OC↗

arXiv2023

Faster Consensus via a Sparser Controller

In this paper, we investigate the architecture of an optimal controller that maximizes the convergence speed of a consensus protocol with single-integrator dynamics. Under the assumption that communication delays increase with the number of hops from which information is allowed to reach each agent, we address the optimal control design under delayed feedback and show that the optimal controller features, in general, a sparsely connected architecture.

math.OC↗

arXiv2023

Intrinsic and extrinsic deep learning on manifolds

We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an equivariant embedding from the manifold to its image in the Euclidean space. Moreover, intrinsic deep neural networks (iDNNs) incorporate the underlying intrinsic geometry of manifolds via exponential and log maps with respect to a Riemannian structure. Consequently, we prove that the empirical risk of the empirical risk minimizers (ERM) of eDNNs and iDNNs converge in optimal rates. Overall, The eDNNs framework is simple and easy to compute, while the iDNNs framework is accurate and fast converging. To demonstrate the utilities of our framework, various simulation studies, and real data analyses are presented with eDNNs and iDNNs.

stat.ML↗

arXiv2022

Cooperative Actor-Critic via TD Error Aggregation

In decentralized cooperative multi-agent reinforcement learning, agents can aggregate information from one another to learn policies that maximize a team-average objective function. Despite the willingness to cooperate with others, the individual agents may find direct sharing of information about their local state, reward, and value function undesirable due to privacy issues. In this work, we introduce a decentralized actor-critic algorithm with TD error aggregation that does not violate privacy issues and assumes that communication channels are subject to time delays and packet dropouts. The cost we pay for making such weak assumptions is an increased communication burden for every agent as measured by the dimension of the transmitted data. Interestingly, the communication burden is only quadratic in the graph size, which renders the algorithm applicable in large networks. We provide a convergence analysis under diminishing step size to verify that the agents maximize the team-average objective function.

eess.SY↗

arXiv2022

On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure

We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure.

math.OC↗

arXiv2022

Model-free Learning for Risk-constrained Linear Quadratic Regulator with Structured Feedback in Networked Systems

We develop a model-free learning algorithm for the infinite-horizon linear quadratic regulator (LQR) problem. Specifically, (risk) constraints and structured feedback are considered, in order to reduce the state deviation while allowing for a sparse communication graph in practice. By reformulating the dual problem as a nonconvex-concave minimax problem, we adopt the gradient descent max-oracle (GDmax), and for modelfree setting, the stochastic (S)GDmax using zero-order policy gradient. By bounding the Lipschitz and smoothness constants of the LQR cost using specifically defined sublevel sets, we can design the stepsize and related parameters to establish convergence to a stationary point (at a high probability). Numerical tests in a networked microgrid control problem have validated the convergence of our proposed SGDmax algorithm while demonstrating the effectiveness of risk constraints. The SGDmax algorithm has attained a satisfactory optimality gap compared to the classical LQR control, especially for the full feedback case.

math.OC↗

arXiv2022

Communication-Efficient Algorithms for Solving Pressure Poisson Equation for Multiphase Flows using Parallel Computers

Numerical solution of partial differential equations on parallel computers using domain decomposition usually requires synchronization and communication among the processors. These operations often have a significant overhead in terms of time and energy. In this paper, we propose communication-efficient parallel algorithms for solving partial differential equations that alleviate this overhead. First, we describe an asynchronous algorithm that removes the requirement of synchronization and checks for termination in a distributed fashion while maintaining the provision to restart iterations if necessary. Then, we build on the asynchronous algorithm to propose an event-triggered communication algorithm that communicates the boundary values to neighboring processors only at certain iterations, thereby reducing the number of messages while maintaining similar accuracy of solution. We demonstrate our algorithms on a successive over-relaxation solver for the Pressure Poisson equation arising from variable density incompressible multiphase flows in 3-D and show that our algorithms improve time and energy efficiency.

cs.DC↗

arXiv2022

Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativity

Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often lack both analytical insights and formal guarantees. Recently, some robustness certificates have appeared in the literature based on system theoretic notions. This work proposes an incremental dissipativity-based robustness certificate for neural networks in the form of a linear matrix inequality for each layer. We also propose an equivalent spectral norm bound for this certificate which is scalable to neural networks with multiple layers. We demonstrate the improved performance against adversarial attacks on a feed-forward neural network trained on MNIST and an Alexnet trained using CIFAR-10.

cs.LG↗

arXiv2021

EventGraD: Event-Triggered Communication in Parallel Machine Learning

Communication in parallel systems imposes significant overhead which often turns out to be a bottleneck in parallel machine learning. To relieve some of this overhead, in this paper, we present EventGraD - an algorithm with event-triggered communication for stochastic gradient descent in parallel machine learning. The main idea of this algorithm is to modify the requirement of communication at every iteration in standard implementations of stochastic gradient descent in parallel machine learning to communicating only when necessary at certain iterations. We provide theoretical analysis of convergence of our proposed algorithm. We also implement the proposed algorithm for data-parallel training of a popular residual neural network used for training the CIFAR-10 dataset and show that EventGraD can reduce the communication load by up to 60% while retaining the same level of accuracy. In addition, EventGraD can be combined with other approaches such as Top-K sparsification to decrease communication further while maintaining accuracy.

cs.LG↗

arXiv2021

Resilient Consensus-based Multi-agent Reinforcement Learning with Function Approximation

Adversarial attacks during training can strongly influence the performance of multi-agent reinforcement learning algorithms. It is, thus, highly desirable to augment existing algorithms such that the impact of adversarial attacks on cooperative networks is eliminated, or at least bounded. In this work, we consider a fully decentralized network, where each agent receives a local reward and observes the global state and action. We propose a resilient consensus-based actor-critic algorithm, whereby each agent estimates the team-average reward and value function, and communicates the associated parameter vectors to its immediate neighbors. We show that in the presence of Byzantine agents, whose estimation and communication strategies are completely arbitrary, the estimates of the cooperative agents converge to a bounded consensus value with probability one, provided that there are at most $H$ Byzantine agents in the neighborhood of each cooperative agent and the network is $(2H+1)$-robust. Furthermore, we prove that the policy of the cooperative agents converges with probability one to a bounded neighborhood around a local maximizer of their team-average objective function under the assumption that the policies of the adversarial agents asymptotically become stationary.

cs.LG↗

arXiv2021

Intelligent Players in a Fictitious Play Framework

Fictitious play is a popular learning algorithm in which players that utilize the history of actions played by the players and the knowledge of their own payoff matrix can converge to the Nash equilibrium under certain conditions on the game. We consider the presence of an intelligent player that has access to the entire payoff matrix for the game. We show that by not conforming to fictitious play, such a player can achieve a better payoff than the one at the Nash Equilibrium. This result can be viewed both as a fragility of the fictitious play algorithm to a strategic intelligent player and an indication that players should not throw away additional information they may have, as suggested by classical fictitious play.

cs.GT↗

arXiv2021

Data-Driven Contract Design for Multi-Agent Systems with Collusion Detection

In applications such as participatory sensing and crowd sensing, self-interested agents exert costly effort towards achieving an objective for the system operator. We study such a setup where a principal incentivizes multiple agents of different types who can collude with each other to derive rent. The principal cannot observe the efforts exerted directly, but only the outcome of the task, which is a noisy function of the effort. The type of each agent influences the effort cost and task output. For a duopoly in which agents are coupled in their payments, we show that if the principal and the agents interact finitely many times, the agents can derive rent by colluding even if the principal knows the types of the agents. However, if the principal and the agents interact infinitely often, the principal can disincentivize agent collusion through a suitable data-driven contract.

eess.SP↗

arXiv2021

Adversarial attacks in consensus-based multi-agent reinforcement learning

Recently, many cooperative distributed multi-agent reinforcement learning (MARL) algorithms have been proposed in the literature. In this work, we study the effect of adversarial attacks on a network that employs a consensus-based MARL algorithm. We show that an adversarial agent can persuade all the other agents in the network to implement policies that optimize an objective that it desires. In this sense, the standard consensus-based MARL algorithms are fragile to attacks.

eess.SY↗

arXiv2021

Optimal Stationary State Estimation Over Multiple Markovian Packet Drop Channels

In this paper, we investigate the state estimation problem over multiple Markovian packet drop channels. In this problem setup, a remote estimator receives measurement data transmitted from multiple sensors over individual channels. By the method of Markovian jump linear systems, an optimal stationary estimator that minimizes the error variance in the steady state is obtained, based on the mean-square (MS) stabilizing solution to the coupled algebraic Riccati equations. An explicit necessary and sufficient condition is derived for the existence of the MS stabilizing solution, which coincides with that of the standard Kalman filter. More importantly, we provide a sufficient condition under which the MS detectability with multiple Markovian packet drop channels can be decoupled, and propose a locally optimal stationary estimator but computationally more tractable. Analytic sufficient and necessary MS detectability conditions are presented for the decoupled subsystems subsequently. Finally, numerical simulations are conducted to illustrate the results on the MS stabilizing solution, the MS detectability, and the performance of the optimal and locally optimal stationary estimators.

eess.SY↗

arXiv2021

Data-Driven Incident Detection in Power Distribution Systems

In a power distribution network with energy storage systems (ESS) and advanced controls, traditional monitoring and protection schemes are not well suited for detecting anomalies such as malfunction of controllable devices. In this work, we propose a data-driven technique for the detection of incidents relevant to the operation of ESS in distribution grids. This approach leverages the causal relationship observed among sensor data streams, and does not require prior knowledge of the system model or parameters. Our methodology includes a data augmentation step which allows for the detection of incidents even when sensing is scarce. The effectiveness of our technique is illustrated through case studies which consider active power dispatch and reactive power control of ESS.

eess.SP↗

arXiv2021

On Stability and Convergence of Distributed Filters

Recent years have bore witness to the proliferation of distributed filtering techniques, where a collection of agents communicating over an ad-hoc network aim to collaboratively estimate and track the state of a system. These techniques form the enabling technology of modern multi-agent systems and have gained great importance in the engineering community. Although most distributed filtering techniques come with a set of stability and convergence criteria, the conditions imposed are found to be unnecessarily restrictive. The paradigm of stability and convergence in distributed filtering is revised in this manuscript. Accordingly, a general distributed filter is constructed and its estimation error dynamics is formulated. The conducted analysis demonstrates that conditions for achieving stable filtering operations are the same as those required in the centralized filtering setting. Finally, the concepts are demonstrated in a Kalman filtering framework and validated using simulation examples.

eess.SP↗

arXiv2021

Distributed Resource Allocation over Time-varying Balanced Digraphs with Discrete-time Communication

This work is concerned with the problem of distributed resource allocation in continuous-time setting but with discrete-time communication over infinitely jointly connected and balanced digraphs. We provide a passivity-based perspective for the continuous-time algorithm, based on which an intermittent communication scheme is developed. Particularly, a periodic communication scheme is first derived through analyzing the passivity degradation over output sampling of the distributed dynamics at each node. Then, an asynchronous distributed event-triggered scheme is further developed. The sampled-based event-triggered communication scheme is exempt from Zeno behavior as the minimum inter-event time is lower bounded by the sampling period. The parameters in the proposed algorithm rely only on local information of each individual nodes, which can be designed in a truly distributed fashion

cs.MA↗

arXiv2021

Renewable Power Trades and Network Congestion Externalities

Integrating renewable energy production into the electricity grid is an important policy goal to address climate change. However, such an integration faces economic and technological challenges. As power generation by renewable sources increases, power transmission patterns over the electric grid change. Due to physical laws, these new transmission patterns lead to non-intuitive grid congestion externalities. We derive the conditions under which negative network externalities due to power trades occur. Calibration using a stylized framework and data from Europe shows that each additional unit of power traded between northern and western Europe reduces transmission capacity for the southern and eastern regions by 27% per unit traded. Such externalities suggest that new investments in the electric grid infrastructure cannot be made piecemeal. In our example, power infrastructure investment in northern and western Europe needs an accompanying investment in southern and eastern Europe as well. An economic challenge is regions facing externalities do not always have the financial ability to invest in infrastructure. Power transit fares can help finance power infrastructure investment in regions facing network congestion externalities. The resulting investment in the overall electricity grid facilitates integration of renewable energy production.

eess.SY↗