{"title":"Relationships between certain f -divergences","authors":"J. Melbourne, M. Madiman, M. Salapaka","doi":"10.1109/ALLERTON.2019.8919677","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919677","url":null,"abstract":"We investigate the concavity deficit of the entropy functional. Some properties of the skew-divergence are developed and a “skew” $chi^{2}$ divergence is introduced. Various relationships between these f - divergences and others are established, including a reverse Pinsker type inequality for the skew divergence, which in turn yields a sharpening on the upper bound for the entropic concavity deficit.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128517614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nested Distributed Gradient Methods with Stochastic Computation Errors","authors":"Charikleia Iakovidou, Ermin Wei","doi":"10.1109/ALLERTON.2019.8919853","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919853","url":null,"abstract":"In this work, we consider the problem of a network of agents collectively minimizing a sum of convex functions. The agents in our setting can only access their local objective functions and exchange information with their immediate neighbors. Motivated by applications where computation is imperfect, including, but not limited to, empirical risk minimization (ERM) and online learning, we assume that only noisy estimates of the local gradients are available. To tackle this problem, we adapt a class of Nested Distributed Gradient methods (NEAR-DGD) to the stochastic gradient setting. These methods have minimal storage requirements, are communication aware and perform well in settings where gradient computation is costly, while communication is relatively inexpensive. We investigate the convergence properties of our method under standard assumptions for stochastic gradients, i.e. unbiasedness and bounded variance. Our analysis indicates that our method converges to a neighborhood of the optimal solution with a linear rate for local strongly convex functions and appropriate constant steplengths. We also show that distributed optimization with stochastic gradients achieves a noise reduction effect similar to mini-batching, which scales favorably with network size. Finally, we present numerical results to demonstrate the effectiveness of our method.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124178252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Elementary Approach to Convergence Guarantees of Optimization Algorithms for Deep Networks","authors":"Vincent Roulet, Zaïd Harchaoui","doi":"10.1109/ALLERTON.2019.8919835","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919835","url":null,"abstract":"We present an approach to obtain convergence guarantees of optimization algorithms for deep networks based on elementary arguments and computations. The convergence analysis revolves around the analytical and computational structures of optimization oracles central to the implementation of deep networks in machine learning software. We provide a systematic way to compute the smoothness constants that govern the convergence behavior of first-order optimization algorithms used to train deep networks. A diverse set of example components and architectures arising in modern deep networks intersperse the exposition to illustrate the approach.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129034388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muhammad Royyan, M. Vehkapera, Themistoklis Charalambous, R. Wichman
{"title":"Adaptive Coded Modulation for Stabilization of Wireless Networked Control Systems over Binary Erasure Channels","authors":"Muhammad Royyan, M. Vehkapera, Themistoklis Charalambous, R. Wichman","doi":"10.1109/ALLERTON.2019.8919747","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919747","url":null,"abstract":"This paper proposes adaptive coded modulation for stabilization of wireless networked control systems (WNCSs). We combine a well-known data rate theorem with adaptive coded modulation to guarantee stability and optimize the spectral efficiency in WNCSs. We believe that this is the first work in adaptive coded modulation for stabilization. In addition, we propose three schemes to optimize various objectives with given constraints. Our proposed schemes are as follows: maximizing throughput with energy constraint (MaxTEC), minimizing energy with throughput constraint (MinETC), and minimizing delay with energy constraint (MinDEC). The numerical results show that each scheme is able to select the optimal modulation to optimize objectives at given channel conditions and constraints.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"17 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132360845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Feasibility and Detection of Replay Attack in Networked Constrained Cyber-Physical Systems","authors":"M. Hosseinzadeh, B. Sinopoli, E. Garone","doi":"10.1109/ALLERTON.2019.8919762","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919762","url":null,"abstract":"This paper analyzes the effect of replay attacks on constrained cyber-physical systems which are subject to linear probabilistic constraints. In order to inject an exogenous control input without being detected the attacker will hijack the sensors, observe and record their readings for a certain amount of time and repeat them afterwards while carrying out his attack. The conditions under which the attacker can induce perturbation in the control loop without being detected is studied. Then, in order to make the system resilient to the replay attack, a random signal (serving as the authentication signal) is added to the control input. Since this signal can hamper the performance of the system, finally, the optimization of the authentication signals is proposed to maximize the detection rate while keeping the process deterioration bounded. The effectiveness of the proposed scheme is demonstrated on a simulated case study.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"16 45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134498320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non-Equilibrium Learning and Cyber-Physical Security","authors":"K. Vamvoudakis, Aris Kanellopoulos","doi":"10.1109/ALLERTON.2019.8919756","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919756","url":null,"abstract":"This paper introduces a framework for non-equilibrium behavior analysis in cyber-physical systems for security purposes. To categorize the player, we employ the principles of reinforcement learning in order to derive an iterative method of optimal responses that determine the policy of an agent with level-$k$ intelligence in a general non-zerosum, nonlinear environment. For the special case of zero-sum, linear quadratic games we derive appropriate non-equilibrium game Riccati equations. To obviate the need for complete knowledge of the system dynamics, we employ a Q-learning algorithm as a best response solver. We then design an estimator that determines the distribution of intelligence levels in the adversarial environment of the system. Finally, simulation results showcase the efficacy of our approach.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131534393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Explicit Low-complexity Codes for Multiple Access Channel Resolvability","authors":"Rumia Sultana, Rémi A. Chou","doi":"10.1109/ALLERTON.2019.8919797","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919797","url":null,"abstract":"We design an explicit low-complexity coding scheme that achieves the multiple access channel resolvability region for an arbitrary discrete memoryless multiple access channel whose input alphabets have prime cardinalities. Unlike previous works, we do not assume channel symmetry and rely on rate-splitting to avoid time sharing when it is known to be unnecessary. The idea of our construction is to reduce the problem of multiple access channel resolvability to a combination of several source resolvability problems. Our coding scheme relies on polar codes for source coding to implement source resolvability, and a block Markov coding scheme that performs randomness recycling in the different encoding blocks.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114303616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Byzantine Fault-Tolerant Parallelized Stochastic Gradient Descent for Linear Regression","authors":"Nirupam Gupta, N. Vaidya","doi":"10.1109/ALLERTON.2019.8919735","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919735","url":null,"abstract":"This paper addresses the problem of Byzantine fault-tolerance in parallelized stochastic gradient descent (SGD) method solving for a linear regression problem. We consider a synchronous system comprising of a master and multiple workers, where up to a (known) constant number of workers are Byzantine faulty. Byzantine faulty workers may send incorrect information to the master during an execution of the parallelized SGD method. To mitigate the detrimental impact of Byzantine faulty workers, we replace the averaging of gradients in the traditional parallelized SGD method by a provably more robust gradient aggregation rule. The crux of the proposed gradient aggregation rule is a gradient-filter, named comparative gradient clipping(CGC) filter. We show that the resultant parallelized SGD method obtains a good estimate of the regression parameter even in presence of bounded fraction of Byzantine faulty workers. The upper bound derived for the asymptotic estimation error only grows linearly with the fraction of Byzantine faulty workers.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114306929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Sequential and Scalable Approach to Community Detection in Dynamic Graphs","authors":"Andre Beckus, George K. Atia","doi":"10.1109/ALLERTON.2019.8919954","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919954","url":null,"abstract":"We study a sequential sketch-based approach for the clustering of time-evolving graphs. We present a dynamic extension to the static Stochastic Block Model, which accommo- dates growing and shrinking graphs, as well as the movement of nodes between clusters. We then propose an online algorithm which constructs and maintains a small sketch consisting of nodes sampled from the full graph. The sketch is clustered and a retrieval algorithm is used to infer cluster membership of nodes in each successive graph snapshot. We demonstrate that the use of a small sketch not only improves computational complexity, but also improves the success rate when sketches are properly proportioned. We present a sampling method which chooses nodes according to node degree, whereby very small clusters can be successfully tracked.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121932304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Han Wang, Mahyar Fazlyab, Shaoru Chen, V. Preciado
{"title":"Robust Convergence Analysis of Three-Operator Splitting","authors":"Han Wang, Mahyar Fazlyab, Shaoru Chen, V. Preciado","doi":"10.1109/ALLERTON.2019.8919695","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919695","url":null,"abstract":"Operator splitting methods solve composite optimization problems by breaking them into smaller sub-problems that can be solved sequentially or in parallel. In this paper, we propose a unified framework for certifying both linear and sublinear convergence rates for three-operator splitting (TOS) method under a variety of assumptions about the objective function. By viewing the algorithm as a dynamical system with feedback uncertainty (the oracle model), we leverage robust control theory to analyze the worst-case performance of the algorithm using matrix inequalities. We then show how these matrix inequalities can be used to verify sublinear/linear convergence of the TOS algorithm and guide the search for selecting the parameters of the algorithm (both symbolically and numerically) for optimal worst-case performance. We illustrate our results numerically by solving an input-constrained optimal control problem.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122257190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}