Pramod K. Varshney

Ziyang Lu, M. Cenk Gursoy, Chilukuri K. Mohan et al.

In this paper, multi-target tracking and scanning are considered in a radar system operating in the track-while-scan mode. Specifically, time allocation for radar scanning and tracking of multiple maneuvering targets under a time budget constraint is addressed, aiming to jointly optimize the performance of both tracking and scanning in a cognitive radar. We first present the details of the model for tracking and scanning and formulate the time management task as a constrained optimization problem. Subsequently, we design a \gls{cdrl} framework to find the time allocation strategy for the problem. In the proposed \gls{cdrl} framework, the parameters of the neural networks and the dual variable are learned simultaneously. The deep deterministic policy gradient (DDPG) algorithm is introduced to tackle continuous action space and its performance is compared with deep Q-learning, heuristic approaches, and an optimization-based approach. Numerical results show that the radar with the proposed \gls{cdrl} framework can autonomously allocate more time to the tracking task that requires greater attention while providing time for scanning and also constraining the total time budget below the predefined threshold.

Pranay Sharma, Rohan Panda, Gauri Joshi et al.

In this paper, we consider nonconvex minimax optimization, which is gaining prominence in many modern machine learning applications such as GANs. Large-scale edge-based collection of training data in these applications calls for communication-efficient distributed optimization algorithms, such as those used in federated learning, to process the data. In this paper, we analyze Local stochastic gradient descent ascent (SGDA), the local-update version of the SGDA algorithm. SGDA is the core algorithm used in minimax optimization, but it is not well-understood in a distributed setting. We prove that Local SGDA has \textit{order-optimal} sample complexity for several classes of nonconvex-concave and nonconvex-nonconcave minimax problems, and also enjoys \textit{linear speedup} with respect to the number of clients. We provide a novel and tighter analysis, which improves the convergence and communication guarantees in the existing literature. For nonconvex-PL and nonconvex-one-point-concave functions, we improve the existing complexity results for centralized minimax problems. Furthermore, we propose a momentum-based local-update algorithm, which has the same convergence guarantees, but outperforms Local SGDA as demonstrated in our experiments.

Thakshila Wimalajeewa, Pramod K. Varshney

In this paper, we consider the problem of collaboratively estimating the sparsity pattern of a sparse signal with multiple measurement data in distributed networks. We assume that each node makes Compressive Sensing (CS) based measurements via random projections regarding the same sparse signal. We propose a distributed greedy algorithm based on Orthogonal Matching Pursuit (OMP), in which the sparse support is estimated iteratively while fusing indices estimated at distributed nodes. In the proposed distributed framework, each node has to perform less number of iterations of OMP compared to the sparsity index of the sparse signal. Thus, with each node having a very small number of compressive measurements, a significant performance gain in support recovery is achieved via the proposed collaborative scheme compared to the case where each node estimates the sparsity pattern independently and then fusion is performed to get a global estimate. We further extend the algorithm to estimate the sparsity pattern in a binary hypothesis testing framework, where the algorithm first detects the presence of a sparse signal collaborating among nodes with a fewer number of iterations of OMP and then increases the number of iterations to estimate the sparsity pattern only if the signal is detected.

Swarnendu Kar, Pramod K. Varshney

Information about the strength of gas sources in buildings has a number of applications in the area of building automation and control, including temperature and ventilation control, fire detection and security systems. Here, we consider the problem of estimating the strength of a gas source in an enclosure when some of the parameters of the gas transport process are unknown. Traditionally, these problems are either solved by the Maximum-Likelihood (ML) method which is accurate but computationally intense, or by Recursive Least Squares (RLS, also Kalman) filtering which is simpler but less accurate. In this paper, we suggest a different statistical estimation procedure based on the concept of Method of Moments. We outline techniques that make this procedure computationally efficient and amenable for recursive implementation. We provide a comparative analysis of our proposed method based on experimental results as well as Monte-Carlo simulations. When used with the building control systems, these algorithms can estimate the gaseous strength in a room both quickly and accurately, and can potentially provide improved indoor air quality in an efficient manner.

Weiming Li, Xueqian Wang, Gang Li et al.

Change detection (CD) in heterogeneous remote sensing images has been widely used for disaster monitoring and land-use management. In the past decade, the heterogeneous CD problem has significantly benefited from the development of deep neural networks (DNNs). However, the purely data-driven DNNs perform like a black box where the lack of interpretability limits the trustworthiness and controllability of DNNs in most practical CD applications. As a powerful knowledge-driven tool, copula theory performs well in modeling relationships among random variables. To enhance the interpretability of existing neural networks for CD, we propose a knowledge-data-driven heterogeneous CD method based on a copula-guided neural network, named NN-Copula-CD. In our NN-Copula-CD, the mathematical characteristics of copula are employed as the loss functions to supervise a neural network to learn the dependence between bi-temporal heterogeneous superpixel pairs, and then the changed regions are identified via binary classification based on the degrees of dependence of all the superpixel pairs in the bi-temporal images. We conduct in-depth experiments on three datasets with heterogeneous images, where both quantitative and visual results demonstrate the effectiveness of our proposed NN-Copula-CD method.

V. Sriram Siddhardh Nadendla, Swastik Brahma, Pramod K. Varshney

In this paper, we propose a novel sealed-bid auction framework to address the problem of dynamic spectrum allocation in cognitive radio (CR) networks. We design an optimal auction mechanism that maximizes the moderator's expected utility, when the spectrum is not available with certainty. We assume that the moderator employs collaborative spectrum sensing in order to make a reliable inference about spectrum availability. Due to the presence of a collision cost whenever the moderator makes an erroneous inference, and a sensing cost at each CR, we investigate feasibility conditions that guarantee a non-negative utility at the moderator. We present tight theoretical-bounds on instantaneous network throughput and also show that our algorithm provides maximum throughput if the CRs have i.i.d. valuations. Since the moderator fuses CRs' sensing decisions to obtain a global inference regarding spectrum availability, we propose a novel strategy-proof fusion rule that encourages the CRs to simultaneously reveal truthful sensing decisions, along with truthful valuations to the moderator. Numerical examples are also presented to provide insights into the performance of the proposed auction under different scenarios.

Nandan Sriranga, Baocheng Geng, Pramod K. Varshney

In this work, we consider a binary hypothesis testing problem involving a group of human decision-makers. Due to the nature of human behavior, each human decision-maker observes the phenomenon of interest sequentially up to a random length of time. The humans use a belief model to accumulate the log-likelihood ratios until they cease observing the phenomenon. The belief model is used to characterize the perception of the human decision-maker towards observations at different instants of time, i.e., some decision-makers may assign greater importance to observations that were observed earlier, rather than later and vice-versa. The global decision-maker is a machine that fuses human decisions using the Chair-Varshney rule with different weights for the human decisions, where the weights are determined by the number of observations that were used by the humans to arrive at their respective decisions.

Geethu Joseph, Chen Zhong, M. Cenk Gursoy et al.

In this paper, we address the problem of detecting anomalies among a given set of binary processes via learning-based controlled sensing. Each process is parameterized by a binary random variable indicating whether the process is anomalous. To identify the anomalies, the decision-making agent is allowed to observe a subset of the processes at each time instant. Also, probing each process has an associated cost. Our objective is to design a sequential selection policy that dynamically determines which processes to observe at each time with the goal to minimize the delay in making the decision and the total sensing cost. We cast this problem as a sequential hypothesis testing problem within the framework of Markov decision processes. This formulation utilizes both a Bayesian log-likelihood ratio-based reward and an entropy-based reward. The problem is then solved using two approaches: 1) a deep reinforcement learning-based approach where we design both deep Q-learning and policy gradient actor-critic algorithms; and 2) a deep active inference-based approach. Using numerical experiments, we demonstrate the efficacy of our algorithms and show that our algorithms adapt to any unknown statistical dependence pattern of the processes.

Swatantra Kafle, Geethu Joseph, Pramod K. Varshney

This paper addresses the classical problem of one-bit compressed sensing using a deep learning-based reconstruction algorithm that leverages a trained generative model to enhance the signal reconstruction performance. The generator, a pre-trained neural network, learns to map from a low-dimensional latent space to a higher-dimensional set of sparse vectors. This generator is then used to reconstruct sparse vectors from their one-bit measurements by searching over its range. The presented algorithm provides an excellent reconstruction performance because the generative model can learn additional structural information about the signal beyond sparsity. Furthermore, we provide theoretical guarantees on the reconstruction accuracy and sample complexity of the algorithm. Through numerical experiments using three publicly available image datasets, MNIST, Fashion-MNIST, and Omniglot, we demonstrate the superior performance of the algorithm compared to other existing algorithms and show that our algorithm can recover both the amplitude and the direction of the signal from one-bit measurements.

Ziyang Lu, M. Cenk Gursoy, Chilukuri K. Mohan et al.

In this paper, we tackle the task of adaptive time allocation in integrated sensing and communication systems equipped with radar and communication units. The dual-functional radar-communication system's task involves allocating dwell times for tracking multiple targets and utilizing the remaining time for data transmission towards estimated target locations. We introduce a novel constrained deep reinforcement learning (CDRL) approach, designed to optimize resource allocation between tracking and communication under time budget constraints, thereby enhancing target communication quality. Our numerical results demonstrate the efficiency of our proposed CDRL framework, confirming its ability to maximize communication quality in highly dynamic environments while adhering to time constraints.

Ziyang Lu, M. Cenk Gursoy, Chilukuri K. Mohan et al.

Deep reinforcement learning has been extensively studied in decision-making processes and has demonstrated superior performance over conventional approaches in various fields, including radar resource management (RRM). However, a notable limitation of neural networks is their ``black box" nature and recent research work has increasingly focused on explainable AI (XAI) techniques to describe the rationale behind neural network decisions. One promising XAI method is local interpretable model-agnostic explanations (LIME). However, the sampling process in LIME ignores the correlations between features. In this paper, we propose a modified LIME approach that integrates deep learning (DL) into the sampling process, which we refer to as DL-LIME. We employ DL-LIME within deep reinforcement learning for radar resource management. Numerical results show that DL-LIME outperforms conventional LIME in terms of both fidelity and task performance, demonstrating superior performance with both metrics. DL-LIME also provides insights on which factors are more important in decision making for radar resource management.

Daofu Zhang, Mehrdad Pournaderi, Hanne M. Clifford et al.

This paper studies the adversarial robustness of conformal novelty detection. In particular, we focus on AdaDetect, a powerful learning-based framework for novelty detection with finite-sample false discovery rate (FDR) control. While AdaDetect provides rigorous statistical guarantees under benign conditions, its behavior under adversarial perturbations remains unexplored. We first formulate an oracle attack setting that quantifies the worst-case degradation of FDR, deriving an upper bound that characterizes the statistical cost of attacks. This idealized formulation directly motivates a practical and effective attack scheme that only requires query access to AdaDetect's output labels. Coupling these formulations with two popular and complementary black-box adversarial algorithms, we systematically evaluate the vulnerability of AdaDetect on synthetic and real-world datasets. Our results show that adversarial perturbations can significantly increase the FDR while maintaining high detection power, exposing fundamental limitations of current error-controlled novelty detection methods and motivating the development of more robust alternatives.

Qiaojia Zhu, Xiaojing Shen, Haiqi Liu et al.

Cooperative and non-cooperative localization frequently arise together in wireless sensor networks, particularly when sensor positions are uncertain and targets are unable to communicate with the network. While joint processing can eliminate the delay in target estimation found in sequential approaches, it introduces complex variable coupling, posing challenges in both modeling and optimization. This paper presents a joint modeling approach that formulates cooperative and non-cooperative localization as a single optimization problem. To address the resulting coupling, we introduce auxiliary variables that enable structural decoupling and distributed computation. Building on this formulation, we develop the Scaled Proximal Alternating Direction Method of Multipliers for Joint Cooperative and Non-Cooperative Localization (SP-ADMM-JCNL). Leveraging the problem's structured design, we provide theoretical guarantees that the algorithm generates a sequence converging globally to the Karush-Kuhn-Tucker (KKT) point of the reformulated problem and further to a critical point of the original non-convex objective function, with a sublinear rate of O(1/T). Experiments on both synthetic and benchmark datasets demonstrate that SP-ADMM-JCNL achieves accurate and reliable localization performance.

Ziyang Lu, Subodh Kalia, M. Cenk Gursoy et al.

The time allocation problem in multi-function cognitive radar systems focuses on the trade-off between scanning for newly emerging targets and tracking the previously detected targets. We formulate this as a multi-objective optimization problem and employ deep reinforcement learning to find Pareto-optimal solutions and compare deep deterministic policy gradient (DDPG) and soft actor-critic (SAC) algorithms. Our results demonstrate the effectiveness of both algorithms in adapting to various scenarios, with SAC showing improved stability and sample efficiency compared to DDPG. We further employ the NSGA-II algorithm to estimate an upper bound on the Pareto front of the considered problem. This work contributes to the development of more efficient and adaptive cognitive radar systems capable of balancing multiple competing objectives in dynamic environments.

Mengchen Fan, Baocheng Geng, Keren Li et al.

This paper introduces a representative-based approach for distributed learning that transforms multiple raw data points into a virtual representation. Unlike traditional distributed learning methods such as Federated Learning, which do not offer human interpretability, our method makes complex machine learning processes accessible and comprehensible. It achieves this by condensing extensive datasets into digestible formats, thus fostering intuitive human-machine interactions. Additionally, this approach maintains privacy and communication efficiency, and it matches the training performance of models using raw data. Simulation results show that our approach is competitive with or outperforms traditional Federated Learning in accuracy and convergence, especially in scenarios with complex models and a higher number of clients. This framework marks a step forward in integrating human intuition with machine intelligence, which potentially enhances human-machine learning interfaces and collaborative efforts.

Geethu Joseph, M. Cenk Gursoy, Pramod K. Varshney

We address the problem of monitoring a set of binary stochastic processes and generating an alert when the number of anomalies among them exceeds a threshold. For this, the decision-maker selects and probes a subset of the processes to obtain noisy estimates of their states (normal or anomalous). Based on the received observations, the decisionmaker first determines whether to declare that the number of anomalies has exceeded the threshold or to continue taking observations. When the decision is to continue, it then decides whether to collect observations at the next time instant or defer it to a later time. If it chooses to collect observations, it further determines the subset of processes to be probed. To devise this three-step sequential decision-making process, we use a Bayesian formulation wherein we learn the posterior probability on the states of the processes. Using the posterior probability, we construct a Markov decision process and solve it using deep actor-critic reinforcement learning. Via numerical experiments, we demonstrate the superior performance of our algorithm compared to the traditional model-based algorithms.

Geethu Joseph, Chen Zhong, M. Cenk Gursoy et al.

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes a subset of the processes at any given time instant and obtains a noisy binary indicator of whether or not the corresponding process is anomalous. In this setting, we develop an anomaly detection algorithm that chooses the processes to be observed at a given time instant, decides when to stop taking observations, and declares the decision on anomalous processes. The objective of the detection algorithm is to identify the anomalies with an accuracy exceeding the desired value while minimizing the delay in decision making. We devise a centralized algorithm where the processes are jointly selected by a common agent as well as a decentralized algorithm where the decision of whether to select a process is made independently for each process. Our algorithms rely on a Markov decision process defined using the marginal probability of each process being normal or anomalous, conditioned on the observations. We implement the detection algorithms using the deep actor-critic reinforcement learning framework. Unlike prior work on this topic that has exponential complexity in the number of processes, our algorithms have computational and memory requirements that are both polynomial in the number of processes. We demonstrate the efficacy of these algorithms using numerical experiments by comparing them with state-of-the-art methods.

Chen Quan, Baocheng Geng, Yunghsiang S. Han et al.

This paper employs an audit bit based mechanism to mitigate the effect of Byzantine attacks. In this framework, the optimal attacking strategy for intelligent attackers is investigated for the traditional audit bit based scheme (TAS) to evaluate the robustness of the system. We show that it is possible for an intelligent attacker to degrade the performance of TAS to the system without audit bits. To enhance the robustness of the system in the presence of intelligent attackers, we propose an enhanced audit bit based scheme (EAS). The optimal fusion rule for the proposed scheme is derived and the detection performance of the system is evaluated via the probability of error for the system. Simulation results show that the proposed EAS improves the robustness and the detection performance of the system. Moreover, based on EAS, another new scheme called the reduced audit bit based scheme (RAS) is proposed which further improves system performance. We derive the new optimal fusion rule and the simulation results show that RAS outperforms EAS and TAS in terms of both robustness and detection performance of the system. Then, we extend the proposed RAS for a wide-area cluster based distributed wireless sensor networks (CWSNs). Simulation results show that the proposed RAS significantly reduces the communication overhead between the sensors and the FC, which prolongs the lifetime of the network.

Prashant Khanduri, Pranay Sharma, Haibo Yang et al.

Federated Learning (FL) refers to the paradigm where multiple worker nodes (WNs) build a joint model by using local data. Despite extensive research, for a generic non-convex FL problem, it is not clear, how to choose the WNs' and the server's update directions, the minibatch sizes, and the local update frequency, so that the WNs use the minimum number of samples and communication rounds to achieve the desired solution. This work addresses the above question and considers a class of stochastic algorithms where the WNs perform a few local updates before communication. We show that when both the WN's and the server's directions are chosen based on a stochastic momentum estimator, the algorithm requires $\tilde{\mathcal{O}}(ε^{-3/2})$ samples and $\tilde{\mathcal{O}}(ε^{-1})$ communication rounds to compute an $ε$-stationary solution. To the best of our knowledge, this is the first FL algorithm that achieves such {\it near-optimal} sample and communication complexities simultaneously. Further, we show that there is a trade-off curve between local update frequencies and local minibatch sizes, on which the above sample and communication complexities can be maintained. Finally, we show that for the classical FedAvg (a.k.a. Local SGD, which is a momentum-less special case of the STEM), a similar trade-off curve exists, albeit with worse sample and communication complexities. Our insights on this trade-off provides guidelines for choosing the four important design elements for FL algorithms, the update frequency, directions, and minibatch sizes to achieve the best performance.

Geethu Joseph, Chen Zhong, M. Cenk Gursoy et al.

In this paper, we address the anomaly detection problem where the objective is to find the anomalous processes among a given set of processes. To this end, the decision-making agent probes a subset of processes at every time instant and obtains a potentially erroneous estimate of the binary variable which indicates whether or not the corresponding process is anomalous. The agent continues to probe the processes until it obtains a sufficient number of measurements to reliably identify the anomalous processes. In this context, we develop a sequential selection algorithm that decides which processes to be probed at every instant to detect the anomalies with an accuracy exceeding a desired value while minimizing the delay in making the decision and the total number of measurements taken. Our algorithm is based on active inference which is a general framework to make sequential decisions in order to maximize the notion of free energy. We define the free energy using the objectives of the selection policy and implement the active inference framework using a deep neural network approximation. Using numerical experiments, we compare our algorithm with the state-of-the-art method based on deep actor-critic reinforcement learning and demonstrate the superior performance of our algorithm.

Geethu Joseph, M. Cenk Gursoy, Pramod K. Varshney

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes one process at a time and obtains a noisy binary indicator of whether or not the corresponding process is anomalous. In this setting, we develop an anomaly detection algorithm that chooses the process to be observed at a given time instant, decides when to stop taking observations, and makes a decision regarding the anomalous processes. The objective of the detection algorithm is to arrive at a decision with an accuracy exceeding a desired value while minimizing the delay in decision making. Our algorithm relies on a Markov decision process defined using the marginal probability of each process being normal or anomalous, conditioned on the observations. We implement the detection algorithm using the deep actor-critic reinforcement learning framework. Unlike prior work on this topic that has exponential complexity in the number of processes, our algorithm has computational and memory requirements that are both polynomial in the number of processes. We demonstrate the efficacy of our algorithm using numerical experiments by comparing it with the state-of-the-art methods.

Chengxi Li, Gang Li, Pramod K. Varshney

In this paper, we investigate the problem of decentralized federated learning (DFL) in Internet of things (IoT) systems, where a number of IoT clients train models collectively for a common task without sharing their private training data in the absence of a central server. Most of the existing DFL schemes are composed of two alternating steps, i.e., model updating and model averaging. However, averaging model parameters directly to fuse different models at the local clients suffers from client-drift especially when the training data are heterogeneous across different clients. This leads to slow convergence and degraded learning performance. As a possible solution, we propose the decentralized federated earning via mutual knowledge transfer (Def-KT) algorithm where local clients fuse models by transferring their learnt knowledge to each other. Our experiments on the MNIST, Fashion-MNIST, CIFAR-10, and CIFAR-100 datasets reveal that the proposed Def-KT algorithm significantly outperforms the baseline DFL methods with model averaging, i.e., Combo and FullAvg, especially when the training data are not independent and identically distributed (non-IID) across different clients.

Pranay Sharma, Kaidi Xu, Sijia Liu et al.

In this work, we focus on the study of stochastic zeroth-order (ZO) optimization which does not require first-order gradient information and uses only function evaluations. The problem of ZO optimization has emerged in many recent machine learning applications, where the gradient of the objective function is either unavailable or difficult to compute. In such cases, we can approximate the full gradients or stochastic gradients through function value based gradient estimates. Here, we propose a novel hybrid gradient estimator (HGE), which takes advantage of the query-efficiency of random gradient estimates as well as the variance-reduction of coordinate-wise gradient estimates. We show that with a graceful design in coordinate importance sampling, the proposed HGE-based ZO optimization method is efficient both in terms of iteration complexity as well as function query cost. We provide a thorough theoretical analysis of the convergence of our proposed method for non-convex, convex, and strongly-convex optimization. We show that the convergence rate that we derive generalizes the results for some prominent existing methods in the nonconvex case, and matches the optimal result in the convex case. We also corroborate the theory with a real-world black-box attack generation application to demonstrate the empirical advantage of our method over state-of-the-art ZO optimization approaches.

Sijia Liu, Pin-Yu Chen, Bhavya Kailkhura et al.

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning applications. It is used for solving optimization problems similarly to gradient-based methods. However, it does not require the gradient, using only function evaluations. Specifically, ZO optimization iteratively performs three major steps: gradient estimation, descent direction computation, and solution update. In this paper, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles and recent advances in convergence analysis. Moreover, we demonstrate promising applications of ZO optimization, such as evaluating robustness and generating explanations from black-box deep learning models, and efficient online sensor management.

Geethu Joseph, M. Cenk Gursoy, Pramod K. Varshney

We consider the problem of detecting anomalies among a given set of processes using their noisy binary sensor measurements. The noiseless sensor measurement corresponding to a normal process is 0, and the measurement is 1 if the process is anomalous. The decision-making algorithm is assumed to have no knowledge of the number of anomalous processes. The algorithm is allowed to choose a subset of the sensors at each time instant until the confidence level on the decision exceeds the desired value. Our objective is to design a sequential sensor selection policy that dynamically determines which processes to observe at each time and when to terminate the detection algorithm. The selection policy is designed such that the anomalous processes are detected with the desired confidence level while incurring minimum cost which comprises the delay in detection and the cost of sensing. We cast this problem as a sequential hypothesis testing problem within the framework of Markov decision processes, and solve it using the actor-critic deep reinforcement learning algorithm. This deep neural network-based algorithm offers a low complexity solution with good detection accuracy. We also study the effect of statistical dependence between the processes on the algorithm performance. Through numerical experiments, we show that our algorithm is able to adapt to any unknown statistical dependence pattern of the processes.

Saikiran Bulusu, Bhavya Kailkhura, Bo Li et al.

Deep Learning (DL) is vulnerable to out-of-distribution and adversarial examples resulting in incorrect outputs. To make DL more robust, several posthoc (or runtime) anomaly detection techniques to detect (and discard) these anomalous samples have been proposed in the recent past. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection for DL based applications. We provide a taxonomy for existing techniques based on their underlying assumptions and adopted approaches. We discuss various techniques in each of the categories and provide the relative strengths and weaknesses of the approaches. Our goal in this survey is to provide an easier yet better understanding of the techniques belonging to different categories in which research has been done on this topic. Finally, we highlight the unsolved research challenges while applying anomaly detection techniques in DL systems and present some high-impact future research directions.

Pranay Sharma, Swatantra Kafle, Prashant Khanduri et al.

In this paper, we propose a distributed algorithm for stochastic smooth, non-convex optimization. We assume a worker-server architecture where $N$ nodes, each having $n$ (potentially infinite) number of samples, collaborate with the help of a central server to perform the optimization task. The global objective is to minimize the average of local cost functions available at individual nodes. The proposed approach is a non-trivial extension of the popular parallel-restarted SGD algorithm, incorporating the optimal variance-reduction based SPIDER gradient estimator into it. We prove convergence of our algorithm to a first-order stationary solution. The proposed approach achieves the best known communication complexity $O(ε^{-1})$ along with the optimal computation complexity. For finite-sum problems (finite $n$), we achieve the optimal computation (IFO) complexity $O(\sqrt{Nn}ε^{-1})$. For online problems ($n$ unknown or infinite), we achieve the optimal IFO complexity $O(ε^{-3/2})$. In both the cases, we maintain the linear speedup achieved by existing methods. This is a massive improvement over the $O(ε^{-2})$ IFO complexity of the existing approaches. Additionally, our algorithm is general enough to allow non-identical distributions of data across workers, as in the recently proposed federated learning paradigm.

Baocheng Geng, Qunwei Li, Pramod K. Varshney

We consider the $M$-ary classification problem via crowdsourcing, where crowd workers respond to simple binary questions and the answers are aggregated via decision fusion. The workers have a reject option to skip answering a question when they do not have the expertise, or when the confidence of answering that question correctly is low. We further consider that there are spammers in the crowd who respond to the questions with random guesses. Under the payment mechanism that encourages the reject option, we study the behavior of honest workers and spammers, whose objectives are to maximize their monetary rewards. To accurately characterize human behavioral aspects, we employ prospect theory to model the rationality of the crowd workers, whose perception of costs and probabilities are distorted based on some value and weight functions, respectively. Moreover, we estimate the number of spammers and employ a weighted majority voting decision rule, where we assign an optimal weight for every worker to maximize the system performance. The probability of correct classification and asymptotic system performance are derived. We also provide simulation results to demonstrate the effectiveness of our approach.

Tiexing Wang, Qunwei Li, Donald J. Bucci et al.

This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set of closely located distributions (based on a certain distance metric between distributions). The maximum intra-cluster distance is assumed to be smaller than the minimum inter-cluster distance, and both values are assumed to be known. The goal is to group the data sequences together if their underlying generative distributions (which are unknown) belong to one cluster. Distribution distance metrics based k-medoids algorithms are proposed for known and unknown number of distribution clusters. Upper bounds on the error probability and convergence results in the large sample regime are also provided. It is shown that the error probability decays exponentially fast as the number of samples in each data sequence goes to infinity. The error exponent has a simple form regardless of the distance metric applied when certain conditions are satisfied. In particular, the error exponent is characterized when either the Kolmogrov-Smirnov distance or the maximum mean discrepancy are used as the distance metric. Simulation results are provided to validate the analysis.

Kush R. Varshney, Prashant Khanduri, Pranay Sharma et al.

As artificial intelligence is increasingly affecting all parts of society and life, there is growing recognition that human interpretability of machine learning models is important. It is often argued that accuracy or other similar generalization performance metrics must be sacrificed in order to gain interpretability. Such arguments, however, fail to acknowledge that the overall decision-making system is composed of two entities: the learned model and a human who fuses together model outputs with his or her own information. As such, the relevant performance criteria should be for the entire system, not just for the machine learning component. In this work, we characterize the performance of such two-node tandem data fusion systems using the theory of distributed detection. In doing so, we work in the population setting and model interpretable learned models as multi-level quantizers. We prove that under our abstraction, the overall system of a human with an interpretable classifier outperforms one with a black box classifier.

Baocheng Geng, Qunwei Li, Pramod K. Varshney

In this paper, we present a novel sequential paradigm for classification in crowdsourcing systems. Considering that workers are unreliable and they perform the tests with errors, we study the construction of decision trees so as to minimize the probability of mis-classification. By exploiting the connection between probability of mis-classification and entropy at each level of the decision tree, we propose two algorithms for decision tree design. Furthermore, the worker assignment problem is studied when workers can be assigned to different tests of the decision tree to provide a trade-off between classification cost and resulting error performance. Numerical results are presented for illustration.

Aditya Vempaty, Bhavya Kailkhura, Pramod K. Varshney

The emerging paradigm of Human-Machine Inference Networks (HuMaINs) combines complementary cognitive strengths of humans and machines in an intelligent manner to tackle various inference tasks and achieves higher performance than either humans or machines by themselves. While inference performance optimization techniques for human-only or sensor-only networks are quite mature, HuMaINs require novel signal processing and machine learning solutions. In this paper, we present an overview of the HuMaINs architecture with a focus on three main issues that include architecture design, inference algorithms including security/privacy challenges, and application areas/use cases.

Bhavya Kailkhura, Jayaraman J. Thiagarajan, Charvi Rastogi et al.

This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in arbitrary dimensions. Second, we connect the proposed metric (defined in the spatial domain) to the objective measure of the design performance (defined in the spectral domain). This connection serves as an analytic framework for evaluating the qualitative properties of space-filling designs in general. Using the theoretical insights provided by this spatial-spectral analysis, we derive the notion of optimal space-filling designs, which we refer to as space-filling spectral designs. Third, we propose an efficient estimator to evaluate the space-filling properties of sample designs in arbitrary dimensions and use it to develop an optimization framework to generate high quality space-filling designs. Finally, we carry out a detailed performance comparison on two different applications in 2 to 6 dimensions: a) image reconstruction and b) surrogate modeling on several benchmark optimization functions and an inertial confinement fusion (ICF) simulation code. We demonstrate that the propose spectral designs significantly outperform existing approaches especially in high dimensions.

Qunwei Li, Pramod K. Varshney

We explore the design of an effective crowdsourcing system for an $M$-ary classification task. Crowd workers complete simple binary microtasks whose results are aggregated to give the final decision. We consider the scenario where the workers have a reject option so that they are allowed to skip microtasks when they are unable to or choose not to respond to binary microtasks. We present an aggregation approach using a weighted majority voting rule, where each worker's response is assigned an optimized weight to maximize crowd's classification performance.

Sijia Liu, Yanzhi Wang, Makan Fardad et al.

Memristors have recently received significant attention as ubiquitous device-level components for building a novel generation of computing systems. These devices have many promising features, such as non-volatility, low power consumption, high density, and excellent scalability. The ability to control and modify biasing voltages at the two terminals of memristors make them promising candidates to perform matrix-vector multiplications and solve systems of linear equations. In this article, we discuss how networks of memristors arranged in crossbar arrays can be used for efficiently solving optimization and machine learning problems. We introduce a new memristor-based optimization framework that combines the computational merit of memristor crossbars with the advantages of an operator splitting method, alternating direction method of multipliers (ADMM). Here, ADMM helps in splitting a complex optimization problem into subproblems that involve the solution of systems of linear equations. The capability of this framework is shown by applying it to linear programming, quadratic programming, and sparse optimization. In addition to ADMM, implementation of a customized power iteration (PI) method for eigenvalue/eigenvector computation using memristor crossbars is discussed. The memristor-based PI method can further be applied to principal component analysis (PCA). The use of memristor crossbars yields a significant speed-up in computation, and thus, we believe, has the potential to advance optimization and machine learning research in artificial intelligence (AI).

Qunwei Li, Bhavya Kailkhura, Ryan Goldhahn et al.

Many machine learning problems can be formulated as consensus optimization problems which can be solved efficiently via a cooperative multi-agent system. However, the agents in the system can be unreliable due to a variety of reasons: noise, faults and attacks. Providing erroneous updates leads the optimization process in a wrong direction, and degrades the performance of distributed machine learning algorithms. This paper considers the problem of decentralized learning using ADMM in the presence of unreliable agents. First, we rigorously analyze the effect of erroneous updates (in ADMM learning iterations) on the convergence behavior of multi-agent system. We show that the algorithm linearly converges to a neighborhood of the optimal solution under certain conditions and characterize the neighborhood size analytically. Next, we provide guidelines for network design to achieve a faster convergence. We also provide conditions on the erroneous updates for exact convergence to the optimal solution. Finally, to mitigate the influence of unreliable agents, we propose \textsf{ROAD}, a robust variant of ADMM, and show its resilience to unreliable agents with an exact convergence to the optimum.

Qunwei Li, Yi Zhou, Yingbin Liang et al.

In many modern machine learning applications, structures of underlying mathematical models often yield nonconvex optimization problems. Due to the intractability of nonconvexity, there is a rising need to develop efficient methods for solving general nonconvex problems with certain performance guarantee. In this work, we investigate the accelerated proximal gradient method for nonconvex programming (APGnc). The method compares between a usual proximal gradient step and a linear extrapolation step, and accepts the one that has a lower function value to achieve a monotonic decrease. In specific, under a general nonsmooth and nonconvex setting, we provide a rigorous argument to show that the limit points of the sequence generated by APGnc are critical points of the objective function. Then, by exploiting the Kurdyka-Łojasiewicz (\KL) property for a broad class of functions, we establish the linear and sub-linear convergence rates of the function value sequence generated by APGnc. We further propose a stochastic variance reduced APGnc (SVRG-APGnc), and establish its linear convergence under a special case of the \KL property. We also extend the analysis to the inexact version of these methods and develop an adaptive momentum strategy that improves the numerical performance.

Qunwei Li, Pramod K. Varshney

We explore the design of an effective crowdsourcing system for an $M$-ary classification task. Crowd workers complete simple binary microtasks whose results are aggregated to give the final classification decision. We consider the scenario where the workers have a reject option so that they are allowed to skip microtasks when they are unable to or choose not to respond to binary microtasks. Additionally, the workers report quantized confidence levels when they are able to submit definitive answers. We present an aggregation approach using a weighted majority voting rule, where each worker's response is assigned an optimized weight to maximize crowd's classification performance. We obtain a couterintuitive result that the classification performance does not benefit from workers reporting quantized confidence. Therefore, the crowdsourcing system designer should employ the reject option without requiring confidence reporting.

Qunwei Li, Bhavya Kailkhura, Jayaraman J. Thiagarajan et al.

Influential node detection is a central research topic in social network analysis. Many existing methods rely on the assumption that the network structure is completely known \textit{a priori}. However, in many applications, network structure is unavailable to explain the underlying information diffusion phenomenon. To address the challenge of information diffusion analysis with incomplete knowledge of network structure, we develop a multi-task low rank linear influence model. By exploiting the relationships between contagions, our approach can simultaneously predict the volume (i.e. time series prediction) for each contagion (or topic) and automatically identify the most influential nodes for each contagion. The proposed model is validated using synthetic data and an ISIS twitter dataset. In addition to improving the volume prediction performance significantly, we show that the proposed approach can reliably infer the most influential users for specific contagions.

V. Sriram Siddhardh Nadendla, Swastik Brahma, Pramod K. Varshney

Detection rules have traditionally been designed for rational agents that minimize the Bayes risk (average decision cost). With the advent of crowd-sensing systems, there is a need to redesign binary hypothesis testing rules for behavioral agents, whose cognitive behavior is not captured by traditional utility functions such as Bayes risk. In this paper, we adopt prospect theory based models for decision makers. We consider special agent models namely optimists and pessimists in this paper, and derive optimal detection rules under different scenarios. Using an illustrative example, we also show how the decision rule of a human agent deviates from the Bayesian decision rule under various behavioral models, considered in this paper.

V. Sriram Siddhardh Nadendla, Vinod Sharma, Pramod K. Varshney

In this paper, we model a complete-information zero-sum game between a centralized detection network with a multiple access channel (MAC) between the sensors and the fusion center (FC), and a jammer with multiple transmitting antennas. We choose error probability at the FC as the performance metric, and investigate pure strategy equilibria for this game, and show that the jammer has no impact on the FC's error probability by employing pure strategies at the Nash equilibrium. Furthermore, we also show that the jammer has an impact on the expected utility if it employs mixed strategies.

Qunwei Li, Aditya Vempaty, Lav R. Varshney et al.

Consider designing an effective crowdsourcing system for an $M$-ary classification task. Crowd workers complete simple binary microtasks whose results are aggregated to give the final result. We consider the novel scenario where workers have a reject option so they may skip microtasks when they are unable or choose not to respond. For example, in mismatched speech transcription, workers who do not know the language may not be able to respond to microtasks focused on phonological dimensions outside their categorical perception. We present an aggregation approach using a weighted majority voting rule, where each worker's response is assigned an optimized weight to maximize the crowd's classification performance. We evaluate system performance in both exact and asymptotic forms. Further, we consider the setting where there may be a set of greedy workers that complete microtasks even when they are unable to perform it reliably. We consider an oblivious and an expurgation strategy to deal with greedy workers, developing an algorithm to adaptively switch between the two based on the estimated fraction of greedy workers in the anonymous crowd. Simulation results show improved performance compared with conventional majority voting.

Prashant Khanduri, Bhavya Kailkhura, Jayaraman J. Thiagarajan et al.

This paper considers the problem of high dimensional signal detection in a large distributed network whose nodes can collaborate with their one-hop neighboring nodes (spatial collaboration). We assume that only a small subset of nodes communicate with the Fusion Center (FC). We design optimal collaboration strategies which are universal for a class of deterministic signals. By establishing the equivalence between the collaboration strategy design problem and sparse PCA, we solve the problem efficiently and evaluate the impact of collaboration on detection performance.

Nianxia Cao, Sora Choi, Engin Masazade et al.

In this paper, we propose a multiobjective optimization framework for the sensor selection problem in uncertain Wireless Sensor Networks (WSNs). The uncertainties of the WSNs result in a set of sensor observations with insufficient information about the target. We propose a novel mutual information upper bound (MIUB) based sensor selection scheme, which has low computational complexity, same as the Fisher information (FI) based sensor selection scheme, and gives estimation performance similar to the mutual information (MI) based sensor selection scheme. Without knowing the number of sensors to be selected a priori, the multiobjective optimization problem (MOP) gives a set of sensor selection strategies that reveal different trade-offs between two conflicting objectives: minimization of the number of selected sensors and minimization of the gap between the performance metric (MIUB and FI) when all the sensors transmit measurements and when only the selected sensors transmit their measurements based on the sensor selection strategy. Illustrative numerical results that provide valuable insights are presented.

Bhavya Kailkhura, Swastik Brahma, Pramod K. Varshney

This paper considers the problem of detection in distributed networks in the presence of data falsification (Byzantine) attacks. Detection approaches considered in the paper are based on fully distributed consensus algorithms, where all of the nodes exchange information only with their neighbors in the absence of a fusion center. In such networks, we characterize the negative effect of Byzantines on the steady-state and transient detection performance of the conventional consensus based detection algorithms. To address this issue, we study the problem from the network designer's perspective. More specifically, we first propose a distributed weighted average consensus algorithm that is robust to Byzantine attacks. We show that, under reasonable assumptions, the global test statistic for detection can be computed locally at each node using our proposed consensus algorithm. We exploit the statistical distribution of the nodes' data to devise techniques for mitigating the influence of data falsifying Byzantines on the distributed detection system. Since some parameters of the statistical distribution of the nodes' data might not be known a priori, we propose learning based techniques to enable an adaptive design of the local fusion or update rules.

Bhavya Kailkhura, V. Sriram Siddhardh Nadendla, Pramod K. Varshney

The distributed inference framework comprises of a group of spatially distributed nodes which acquire observations about a phenomenon of interest. Due to bandwidth and energy constraints, the nodes often quantize their observations into a finite-bit local message before sending it to the fusion center (FC). Based on the local summary statistics transmitted by nodes, the FC makes a global decision about the presence of the phenomenon of interest. The distributed and broadcast nature of such systems makes them quite vulnerable to different types of attacks. This paper addresses the problem of secure communication in the presence of eavesdroppers. In particular, we focus on efficient mitigation schemes to mitigate the impact of eavesdropping. We present an overview of the distributed inference schemes under secrecy constraints and describe the currently available approaches in the context of distributed detection and estimation followed by a discussion on avenues for future research.

V. Sriram Siddhardh Nadendla, Pramod K. Varshney

In this paper, we investigate the design of distributed detection networks in the presence of an eavesdropper (Eve). We consider the problem of designing binary quantizers at the sensors that maximize the Kullback-Leibler (KL) Divergence at the fusion center (FC), subject to a tolerable constraint on the KL Divergence at Eve. In the case of i.i.d. received symbols at both the FC and Eve, we prove that the structure of the optimal binary quantizers is a likelihood ratio test (LRT). We also present an algorithm to find the threshold of the optimal LRT, and illustrate it for the case of Additive White Gaussian Noise (AWGN) observation models at the sensors. In the case of non-i.i.d. received symbols at both FC and Eve, we propose a dynamic-programming based algorithm to find efficient quantizers at the sensors. Numerical results are presented to illustrate the performance of the proposed network design.

Bhavya Kailkhura, Swastik Brahma, Berkan Dulek et al.

In this paper, the problem of distributed detection in tree networks in the presence of Byzantines is considered. Closed form expressions for optimal attacking strategies that minimize the miss detection error exponent at the fusion center (FC) are obtained. We also look at the problem from the network designer's (FC's) perspective. We study the problem of designing optimal distributed detection parameters in a tree network in the presence of Byzantines. Next, we model the strategic interaction between the FC and the attacker as a Leader-Follower (Stackelberg) game. This formulation provides a methodology for predicting attacker and defender (FC) equilibrium strategies, which can be used to implement the optimal detector. Finally, a reputation based scheme to identify Byzantines is proposed and its performance is analytically evaluated. We also provide some numerical examples to gain insights into the solution.

Bhavya Kailkhura, Yunghsiang S. Han, Swastik Brahma et al.

In this letter, we consider the problem of distributed Bayesian detection in the presence of data falsifying Byzantines in the network. The problem of distributed detection is formulated as a binary hypothesis test at the fusion center (FC) based on 1-bit data sent by the sensors. Adopting Chernoff information as our performance metric, we study the detection performance of the system under Byzantine attack in the asymptotic regime. The expression for minimum attacking power required by the Byzantines to blind the FC is obtained. More specifically, we show that above a certain fraction of Byzantine attackers in the network, the detection scheme becomes completely incapable of utilizing the sensor data for detection. When the fraction of Byzantines is not sufficient to blind the FC, we also provide closed form expressions for the optimal attacking strategies for the Byzantines that most degrade the detection performance.

Bhavya Kailkhura, Swastik Brahma, Yunghsiang S. Han et al.

In this paper, we consider the problem of distributed detection in tree topologies in the presence of Byzantines. The expression for minimum attacking power required by the Byzantines to blind the fusion center (FC) is obtained. More specifically, we show that when more than a certain fraction of individual node decisions are falsified, the decision fusion scheme becomes completely incapable. We obtain closed form expressions for the optimal attacking strategies that minimize the detection error exponent at the FC. We also look at the possible counter-measures from the FC's perspective to protect the network from these Byzantines. We formulate the robust topology design problem as a bi-level program and provide an efficient algorithm to solve it. We also provide some numerical results to gain insights into the solution.