2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)最新文献_第8页

A Sequential Detection Theory for Statistically Periodic Random Processes 统计周期随机过程的顺序检测理论

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919699

T. Banerjee, Prudhvi K. Gurram, Gene T. Whipps

引用次数: 2

Acquisition Games with Partial-Asymmetric Information 部分信息不对称的获取博弈

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919935

V. Kavitha, M. Maheshwari, E. Altman

引用次数: 1

On Matrix Momentum Stochastic Approximation and Applications to Q-learning 矩阵动量随机逼近及其在q学习中的应用

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919828

Adithya M. Devraj, A. Bušić, Sean P. Meyn

{"title":"On Matrix Momentum Stochastic Approximation and Applications to Q-learning","authors":"Adithya M. Devraj, A. Bušić, Sean P. Meyn","doi":"10.1109/ALLERTON.2019.8919828","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919828","url":null,"abstract":"Stochastic approximation (SA) algorithms are recursive techniques used to obtain the roots of functions that can be expressed as expectations of a noisy parameterized family of functions. In this paper two new SA algorithms are introduced: 1) PolSA, an extension of Polyak’s momentum technique with a specially designed matrix momentum, and 2) NeSA, which can either be regarded as a variant of Nesterov’s acceleration method, or a simplification of PolSA. The rates of convergence of SA algorithms is well understood. Under special conditions, the mean square error of the parameter estimates is bounded by $sigma^{2}/n+o(1/n)$, where $sigma^{2} geq 0$ is an identifiable constant. If these conditions fail, the rate is typically sub-linear. There are two well known SA algorithms that ensure a linear rate, with minimal value of variance, $sigma^{2}$: the Ruppert-Polyak averaging technique, and the stochastic Newton-Raphson (SNR) algorithm. It is demonstrated here that under mild technical assumptions, the PolSA algorithm also achieves this optimality criteria. This result is established via novel coupling arguments: It is shown that the parameter estimates obtained from the PolSA algorithm couple with those of the optimal variance (but computationally more expensive) SNR algorithm, at a rate $O(1/n^{2})$. The newly proposed algorithms are extended to a reinforcement learning setting to obtain new Q-learning algorithms, and numerical results confirm the coupling of PolSA and SNR.","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":"130627511","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}

引用次数: 11

Iterative Collaborative Filtering for Sparse Noisy Tensor Estimation 稀疏噪声张量估计的迭代协同滤波

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919933

D. Shah, C. Yu

{"title":"Iterative Collaborative Filtering for Sparse Noisy Tensor Estimation","authors":"D. Shah, C. Yu","doi":"10.1109/ALLERTON.2019.8919933","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919933","url":null,"abstract":"We consider the task of tensor estimation, i.e. estimating a low-rank 3-order $n times n times n$ tensor from noisy observations of randomly chosen entries in the sparse regime. In the context of matrix (2-order tensor) estimation, a variety of algorithms have been proposed and analyzed in the literature including the popular collaborative filtering algorithm that is extremely well utilized in practice. However, in the context of tensor estimation, there is limited progress. No natural extensions of collaborative filtering are known beyond “flattening” the tensor into a matrix and applying standard collaborative filtering. As the main contribution of this work, we introduce a generalization of the collaborative filtering algorithm for the setting of tensor estimation and argue that it achieves sample complexity that (nearly) matches the conjectured lower bound on the sample complexity. Interestingly, our generalization uses the matrix obtained from the “flattened” tensor to compute similarity as in the classical collaborative filtering but by defining a novel “graph” using it. The algorithm recovers the tensor with mean-squared-error (MSE) decaying to 0 as long as each entry is observed independently with probability $p= Omega(n^{-3/2+epsilon})$ for any arbitrarily small $epsilon > 0$. It turns out that $p = Omega(n^{-3/2})$ is the conjectured lower bound as well as “connectivity threshold” of graph considered to compute similarity in our algorithm.","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":"130445710","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}

引用次数: 14

Slepian-Wolf Polar Coding with Unknown Correlation 未知相关性的睡眠-狼极性编码

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919653

Karthik Nagarjuna Tunuguntla, P. Siegel

引用次数: 0

Derandomized Asymmetrical Balanced Allocation 非随机非对称均衡分配

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919887

Dengwang Tang, V. Subramanian

{"title":"Derandomized Asymmetrical Balanced Allocation","authors":"Dengwang Tang, V. Subramanian","doi":"10.1109/ALLERTON.2019.8919887","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919887","url":null,"abstract":"Balls-in-bins model, in which n balls are sequentially placed into n bins according to some dispatching policy, is an important model with a wide range of applications despite its simplicity. The power-of-d choices (Pod) policy, in which each ball samples d independent uniform random bins and join the one with the least load (where ties are broken arbitrarily), can yield a maximum load of $frac{loglog n}{log d} + Theta(1)$ with high probability whenever $dgeq 2$. Vöking later proposed a variant of power-of-d scheme in which bins are divided into d groups, and d bins are sampled from each group respectively. One important feature of this scheme is that ties are broken asymmetrically based on groups. Comparing with Pod, this scheme reduces the maximum load to $frac{loglog n}{dlogphi_{d}}+Theta(1)$ where $1 lt phi_{d} lt 2$. Our recent work shows that one can replace independent uniform sampling with random walk based sampling while having the same performance of Pod in terms of the maximum load of all bins. In this work, we propose multiple derandomized variants of Vöking’s asymmetrical schemes and we show that they can yield the same performance as the original scheme, i.e. the maximum load is bounded by $frac{log log n}{d log phi_{d}}+Theta(1)$","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"66 3 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":"115781641","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}

引用次数: 0

Cubic Regularized ADMM with Convergence to a Local Minimum in Non-convex Optimization 非凸优化中收敛到局部极小的三次正则ADMM

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919772

Zai Shi, A. Eryilmaz

{"title":"Cubic Regularized ADMM with Convergence to a Local Minimum in Non-convex Optimization","authors":"Zai Shi, A. Eryilmaz","doi":"10.1109/ALLERTON.2019.8919772","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919772","url":null,"abstract":"How to escape saddle points is a critical issue in non-convex optimization. Previous methods on this issue mainly assume that the objective function is Hessian-Lipschitz, which leave a gap for applications using non-Hessian-Lipschitz functions. In this paper, we propose Cubic Regularized Alternating Direction Method of Multipliers (CR-ADMM) to escape saddle points of separable non-convex functions containing a non-Hessian-Lipschitz component. By carefully choosing a parameter, we prove that CR-ADMM converges to a local minimum of the original function with a rate of $O(1 /T^{1/3})$ in time horizon T, which is faster than gradient-based methods. We also show that when one or more steps of CR-ADMM are not solved exactly, CRADMM can converge to a neighborhood of the local minimum. Through the experiments of matrix factorization problems, CRADMM is shown to have a faster rate and a lower optimality gap compared with other gradient-based methods. Our approach can also find applications in other scenarios where regularized non-convex cost minimization is performed, such as parameter optimization of deep neural networks.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"58 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":"123903203","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}

引用次数: 0

Stability of Wireless Random Access Systems 无线随机接入系统的稳定性

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919898

Ahmad Alammouri, J. Andrews, F. Baccelli

{"title":"Stability of Wireless Random Access Systems","authors":"Ahmad Alammouri, J. Andrews, F. Baccelli","doi":"10.1109/ALLERTON.2019.8919898","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919898","url":null,"abstract":"We characterize the stability, metastability, and the stationary regime of traffic dynamics in a single-cell uplink wireless system. The traffic is represented in terms of spatial birth-death processes, in which users arrive as a Poisson point process in time and space, each with a file to transmit to the base station. The service rate of each user is based on its signal to interference plus noise ratio, where the interference is from other active users in the cell. Once the file is fully transmitted, the user leaves the cell. We derive the necessary and sufficient condition for network stability, which is independent of the specific path loss function as long as it satisfies mild bound- edness conditions. A novel observation, shown through mean- field analysis and simulations, is that for a certain range of arrival rates, the network appears stable for possibly a long time, but can suddenly become unstable. This property is called metastability which is widely known in statistical physics but rarely observed in wireless communication. Finally, using mean- field analysis, we propose a heuristic characterization of the network steady-state regime when it exists, and demonstrate that it is tight for the whole range of arrival rates.","PeriodicalId":120479,"journal":{"name":"2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","volume":"114 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":"123396858","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}

引用次数: 4

On the Asymptotic Sample Complexity of HGR Maximal Correlation Functions in Semi-supervised Learning 半监督学习中HGR极大相关函数的渐近样本复杂度

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919892

Xiangxiang Xu, Shao-Lun Huang

{"title":"On the Asymptotic Sample Complexity of HGR Maximal Correlation Functions in Semi-supervised Learning","authors":"Xiangxiang Xu, Shao-Lun Huang","doi":"10.1109/ALLERTON.2019.8919892","DOIUrl":"https://doi.org/10.1109/ALLERTON.2019.8919892","url":null,"abstract":"The Hirschfeld-Gebelein-Rényi (HGR) maximal correlation has been shown useful in many machine learning applications, where the alternating conditional expectation (ACE) algorithm is widely adopted to estimate the HGR maximal correlation functions from data samples. In this paper, we consider the asymptotic sample complexity of estimating the HGR maximal correlation functions in semi-supervised learning, where both labeled and unlabeled data samples are used for the estimation. First, we propose a generalized ACE algorithm to deal with the unlabeled data samples. Then, we develop a mathematical framework to characterize the learning errors between the maximal correlation functions computed from the true distribution and the functions estimated from the generalized ACE algorithm. We establish the analytical expressions for the error exponents of the learning errors, which indicate the number of training samples required for estimating the HGR maximal correlation functions by the generalized ACE algorithm. Moreover, with our theoretical results, we investigate the sampling strategy for different types of samples in semisupervised learning with a total sampling budget constraint, and an optimal sampling strategy is developed to maximize the error exponent of the learning error. Finally, the numerical simulations are presented to support our theoretical results.","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":"124957656","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}

引用次数: 2

Spectral Analysis of the Adjacency Matrix of Random Geometric Graphs 随机几何图邻接矩阵的谱分析

2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton) Pub Date : 2019-09-01 DOI: 10.1109/ALLERTON.2019.8919798

Mounia Hamidouche, L. Cottatellucci, Konstantin Avrachenkov

引用次数: 3