Some New Results in Distributed Tracking and Optimization

The current age of Big Data is built on the foundation of distributed systems, and efficient distributed algorithms to run on these systems.With the rapid increase in the volume of the data being fed into these systems, storing and processing all this data at a central location becomes infeasible. Such a central \textit{server} requires a gigantic amount of computational and storage resources. Even when it is possible to have central servers, it is not always desirable, due to privacy concerns. Also, sending huge amounts of data to such servers incur often infeasible bandwidth requirements. In this dissertation, we consider two kinds of distributed architectures: 1) star-shaped topology, where multiple worker nodes are connected to, and communicate with a server, but the workers do not communicate with each other; and 2) mesh topology or network of interconnected workers, where each worker can communicate with a small number of neighboring workers. In the first half of this dissertation (Chapters 2 and 3), we consider distributed systems with mesh topology.We study two different problems in this context. First, we study the problem of simultaneous localization and multi-target tracking. Multiple mobile agents localize themselves cooperatively, while also tracking multiple, unknown number of mobile targets, in the presence of measurement-origin uncertainty. In situations with limited GPS signal availability, agents (like self-driving cars in urban canyons, or autonomous vehicles in hazardous environments) need to rely on inter-agent measurements for localization. The agents perform the additional task of tracking multiple targets (pedestrians and road-signs for self-driving cars). We propose a decentralized algorithm for this problem. To be effective in real-time applications, we propose efficient Gaussian and Gaussian-mixture based filters, rather than the computationally expensive particle-based methods in the existing literature. Our novel factor-graph based approach gives better performance, in terms of both agent localization errors, and target-location and cardinality errors. Next, we study an online convex optimization problem, where a network of agents cooperate to minimize a global time-varying objective function. Only the local functions are revealed to individual agents. The agents also need to satisfy their individual constraints. We propose a primal-dual update based decentralized algorithm for this problem. Under standard assumptions, we prove that the proposed algorithm achieves sublinear regret and constraint violation across the network. In other words, over a long enough time horizon, the decisions taken by the agents are, on average, as good as if all the information was revealed ahead of time. In addition, the individual constraint violations of the agents, averaged over time, are zero. In the next part of the dissertation (Chapters 4), we study distributed systems with a star-shaped topology. The problem we study is distributed nonconvex optimization. With the recent success of deep learning, coupled with the use of distributed systems to solve large-scale problems, this problem has gained prominence over the past decade. The recently proposed paradigm of Federated Learning (which has already been deployed by Google/Apple in Android/iOS phones) has further catalyzed research in this direction. The problem we consider is minimizing the average of local smooth, nonconvex functions. Each node has access only to its own loss function, but can communicate with the server, which aggregates updates from all the nodes, before distributing them to all the nodes. With the advent of more and more complex neural network architectures, these updates can be high dimensional. To save resources, the problem needs to be solved via communication-efficient approaches. We propose a novel algorithm, which combines the idea of variance-reduction, with the paradigm of carrying out multiple local updates at each node before averaging. We prove the convergence of the approach to a first-order stationary point. Our algorithm is optimal in terms of computation, and state-of-the-art in terms of the communication requirements. Lastly in Chapter 5, we consider the situation when the nodes do not have access to function gradients, and need to minimize the loss function using only function values. This problem lies in the domain of zeroth-order optimization. For simplicity of analysis, we study this problem only in the single-node case. This problem finds application in simulation-based optimization, and adversarial example generation for attacking deep neural networks. We propose a novel function value based gradient estimator, which has better variance, and better query-efficiency compared to existing estimators. The proposed estimator covers the most commonly used existing estimators as special cases. We conduct a comprehensive convergence analysis under different conditions. We also demonstrate its effectiveness through a real-world application to generating adversarial examples from a black-box deep neural network

Do Socially Responsible Indices Outperform the Market During Black Swan Events: Evidence from Indian Markets During Global Financial and COVID-19 Crises

This paper aims to examine and compare the effect of black swan events on the performance of companies with strong Environmental, Social, and (Corporate) Governance (ESG) backgrounds with that of other companies. Compared to established firms, companies with ESG backgrounds are perceived to be stable that will help them outperform established companies that are volatile during times of crisis. This research focuses on SENSEX for conventional market index and BSE GREEENEX and S&P BSE CARBONEX for ESG indices. We evaluated performances of the three indices during U.S. Debt Ceiling Crisis (2011-12), Black Monday China, BREXIT and Demonetization (2015-16), and COVID-19 (2020) crisis. We checked whether ESG indices outperformed conventional index significantly using Student\u27s T-test. We have also compared the volatility of the three indices during the different black swan periods using the GARCH model

Correlation Aware Sparsified Mean Estimation Using Random Projection

We study the problem of communication-efficient distributed vector mean estimation, a commonly used subroutine in distributed optimization and Federated Learning (FL). Rand-$k$ sparsification is a commonly used technique to reduce communication cost, where each client sends $k < d$ of its coordinates to the server. However, Rand-$k$ is agnostic to any correlations, that might exist between clients in practical scenarios. The recently proposed Rand-$k$-Spatial estimator leverages the cross-client correlation information at the server to improve Rand-$k$'s performance. Yet, the performance of Rand-$k$-Spatial is suboptimal. We propose the Rand-Proj-Spatial estimator with a more flexible encoding-decoding procedure, which generalizes the encoding of Rand-$k$ by projecting the client vectors to a random $k$-dimensional subspace. We utilize Subsampled Randomized Hadamard Transform (SRHT) as the projection matrix and show that Rand-Proj-Spatial with SRHT outperforms Rand-$k$-Spatial, using the correlation information more efficiently. Furthermore, we propose an approach to incorporate varying degrees of correlation and suggest a practical variant of Rand-Proj-Spatial when the correlation information is not available to the server. Experiments on real-world distributed optimization tasks showcase the superior performance of Rand-Proj-Spatial compared to Rand-$k$-Spatial and other more sophisticated sparsification techniques.Comment: 32 pages, 13 figures. Proceedings of the 37th Conference on Neural Information Processing Systems (NeurIPS 2023), New Orleans, US

Antimicrobial Activity of Ethanolic Extracts of Syzygium aromaticum and Allium sativum Against Food Associated Bacteria and Fungi

The successful control of food spoilage microorganisms require the use of indigenous antimicrobials in foods including certain botanical compounds that have been historically used for flavour enhancement as well as preservation. The present study was designed to evaluate the in vitro antimicrobial activity of ethanolic extracts of Syzygium aromaticum (clove) and Allium sativum (garlic) against Gram-positive and Gram-negative food associated bacteria (Bacillus subtilis, B. megaterium, B. polymyxa, B. sphaericus, Staphylococcus aureus and Escherichia coli) and molds (Penicillium oxalicum, Aspergillus flavus, A. luchuensis, Rhizopus stolonifer, Scopulariopsis sp. and Mucor sp.) assayed by agar well diffusion method and poisoned food technique, respectively. Clove extract showed better antimicrobial activity than the garlic extract. The zone of inhibition in clove ethanolic extract against all the food associated bacteria was in the range of 25mm to 32mm and in molds the percent mycelial growth inhibition ranged from 70% to 100%. The growth inhibition zone in garlic ethanolic extract against bacteria was in the range of 20mm to 31mm and in molds the percent mycelial growth inhibition ranged between 20% and 50%. The clove ethanolic extract exhibited the maximum zone of inhibition against E. coli whereas garlic ethanolic extract showed maximum activity against B. subtilis. Both the extracts exhibited maximum percent mycelial growth inhibition against R. stolonifer. However garlic extract was not effective against P. oxalicum. The MIC values of clove ethanolic extract for different bacterial isolates ranged from 5.0mg/ml to 20mg/ml and 10 mg/ml to 20mg/ml against molds. The MIC values of garlic ethanolic extract for different bacterial and fungal isolates ranged from 10 mg/ml to 20mg/ml. The value of MBC and MFC equaled the MIC. Based on this finding, it may be suggested that these extracts may be used as natural antimicrobial additives to reclaim the shelf-life of foods

ANN based short-term traffic flow forecasting in undivided two lane highway

Abstract Short term traffic forecasting is one of the important fields of study in the transportation domain. Short term traffic forecasting is very useful to develop a more advanced transportation system to control traffic signals and avoid congestions. Several studies have made efforts for short term traffic flow forecasting for divided and undivided highways across the world. However, all these studies relied on the dataset which are greatly varied between countries due to the technology used for transportation data collection. India is a developing country in which efforts are being done to improve the transportation system to avoid congestion and travel time. Two-lane undivided highways with mixed traffic constitute a large portion of Indian road network. This study is an attempt to develop a short term traffic forecasting model using back propagation artificial neural network for two lane undivided highway with mixed traffic conditions in India. The results were compared with random forest, support vector machine, k-nearest neighbor classifier, regression tree and multiple regression models. It was found that back-propagation neural network performs better than other approaches and achieved an R2 value 0.9962, which is a good score

On Noise-Enhanced Distributed Inference in the Presence of Byzantines

This paper considers the noise-enhanced distributed detection problem in the presence of Byzantine (malicious) nodes by suitably adding stochastic resonance (SR) noise. We consider two metrics - the minimum number of Byzantines (alpha_blind) needed to blind the fusion center as a security metric and the Kullback- Leibler divergence (DKL) as a detection performance metric. We show that alpha_blind increases when SR noise is added at the honest nodes. When Byzantines also start adding SR noise to their observations, we see no gain in terms of alpha_blind . However, the detection performance of the network does improve with SR. We also consider a game theoretic formulation where this problem of distributed detection in the presence of Byzantines is modeled as a minimax game between the Byzantines and the inference network, and numerically find Nash equilibria. The case when SR noise is added to the signals received at the fusion center (FC) from the sensors is also considered. Our numerical results indicate that while there is no gain in terms of , the network-wide performance measured in terms of alpha_blind the deflection coefficient does improve in this cas