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A Robust Accelerated Optimization Algorithm for Strongly convex functions

A Robust Accelerated Optimization Algorithm for Strongly Con...

引用

American Control Conference

作者： Cyrus, Saman Hu, Bin Van Scoy, Bryan Lessard, Laurent Univ Wisconsin Madison Dept Elect & Comp Engn Madison WI 53706 USA Univ Wisconsin Madison Wisconsin Inst Discovery Madison WI 53706 USA

ISBN: (纸本)9781538654286

This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient noise versus worst-case convergence rate. At one extreme, the algorithm is faster than Nesterov's Fast Gradient Method by a constant factor but more fragile to noise. At the other extreme, the algorithm reduces to the Gradient Method and is very robust to noise. The algorithm design technique is inspired by methods from classical control theory and the resulting algorithm has a simple analytical form. Algorithm performance is verified on a series of numerical simulations in both noise-free and relative gradient noise cases.

关键词： Robustness Convergence Gradient methods Radio frequency Acceleration convex functions"

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On the Time-Varying Constraints and Bandit Feedback of Online convex Optimization

On the Time-Varying Constraints and Bandit Feedback of Onlin...

引用

IEEE International Conference on Communications (ICC) / Workshop on Integrating UAVs into 5G

作者： Cao, Xuanyu Liu, K. J. Ray Interdisciplinary Centre for Security Reliability and Trust (SnT) University of Luxembourg Luxembourg

ISBN: (纸本)9781538631805

In this paper, online convex optimization (OCO) problem with time-varying constraints is studied from the perspective of an agent taking sequential actions. Both the objective function and the constraint functions are dynamic and unknown a priori to the agent. We first consider the scenario of function feedback, in which complete information about the objective function and constraint functions is revealed to the agent after an action is submitted. We propose a computationally efficient online algorithm, which only involves direct closed-form computations at each time instant. It is shown that the algorithm possesses sublinear regret with respect to the dynamic benchmark sequence and sublinear constraint violations, as long as the drift of the benchmark sequence is sublinear, or in other words, the underlying dynamic optimization problems do not vary too drastically. Furthermore, we investigate the scenario of bandit feedback, in which, after an action is chosen, only the values of the objective function and the constraint functions at several random points close to the action are announced to the agent. A bandit version of online algorithm is proposed and we also establish its sublinear expected regret and sublinear expected constraint violations. Finally, two numerical examples, namely online quadratic programming and online logistic regression, are presented to corroborate the effectiveness of the proposed algorithms and to confirm the theoretical guarantees.

关键词： Heuristic algorithms Benchmark testing Linear programming Optimization Signal processing algorithms Approximation algorithms convex functions"

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Distributed Smooth and Strongly convex Optimization with Inexact Dual Methods

Distributed Smooth and Strongly Convex Optimization with Ine...

引用

American Control Conference

作者： Fazlyab, Mahyar Paternain, Santiago Ribeiro, Alejandro Preciado, Victor M. Univ Penn Dept Elect & Syst Engn Philadelphia PA 19104 USA

ISBN: (纸本)9781538654286

In this paper, we consider a class of decentralized convex optimization problems in which a network of agents aims to minimize a global objective function that is a sum of private (local) smooth and strongly convex objectives. More specifically, we study decentralized inexact dual ascent method, in which the agents only approximately solve their private minimization and then update their dual variables using inexact dual ascent. We study the effect of inexact inner minimization on the convergence rate. In particular, we show that the overall convergence rate will not be affected by inexact minimization if the errors are decreased at an appropriate rate. We illustrate our findings in a distributed binary classification problem.

关键词： Minimization Linear programming Convergence Laplace equations Radio frequency Optimization convex functions"

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A Novel Online convex Optimization Algorithm Based on Virtual Queues

A Novel Online Convex Optimization Algorithm Based on Virtua...

引用

IEEE International Conference on Communications (ICC) / Workshop on Integrating UAVs into 5G

作者： Cao, Xuanyu Zhang, Junshan Poor, H. Vincent School of Electrical Engineering Korea University Seoul South Korea Department of Electronic Engineering Korea National University of Transportation Chungju South Korea

ISBN: (纸本)9781538631805

In this paper, online convex optimization (OCO) problems with time-varying objective and constraint functions are studied from the perspective of an agent who takes actions in real-time. Information about the current objective and constraint functions is revealed only after the corresponding action is already chosen. Inspired by a fast converging algorithm for time-invariant optimization in the very recent work [1], we develop a novel online algorithm based on virtual queues for constrained OCO. Optimal points of the dynamic optimization problems with full knowledge of the current objective and constraint functions are used as a dynamic benchmark sequence. Upper bounds on the regrets with respect to the dynamic benchmark and the constraint violations are derived for the presented algorithm in terms of the temporal variations of the underlying dynamic optimization problems. It is observed that the proposed algorithm possesses sublinear regret and sublinear constraint violations, as long as the temporal variations of the optimization problems are sublinear, i.e., the objective and constraint functions do not vary too drastically across time. The performance bounds of the proposed algorithm are superior to those of the state-of-the-art OCO method in most scenarios.

关键词： Heuristic algorithms Optimization Benchmark testing Signal processing algorithms Renewable energy sources Upper bound convex functions"

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Scalable Optimal Flexibility Control of Distributed Loads in the Power Grid

Scalable Optimal Flexibility Control of Distributed Loads in...

引用

American Control Conference

作者： Ghaemi, Reza Abbaszadeh, Masoud Bonanni, Pierino GE Global Res Niskayuna NY 12309 USA

ISBN: (纸本)9781538654286

The rapid penetration of uncertain and unpredictable renewable energy resources into the power grid has made generation planning and real-time power balancing a challenge, thus rendering demand side advanced control a necessity. In this work, we introduce a distributed optimization framework for load flexibility control in the grid. The proposed scheme is based on Newton iteration to provide fast convergence, and is scalable to large numbers of loads at the aggregation level. The developed optimization framework is based on interior point methods and concepts of model predictive control. It uses load-aggregator communications to solve a large-scale optimization problem in a computationally distributed manner without geometric structural assumptions.

关键词： Optimization Convergence Optimal control Linear programming Power grids Frequency control convex functions"

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Cellular-Enabled UAV Communication: Trajectory Optimization Under Connectivity Constraint

Cellular-Enabled UAV Communication: Trajectory Optimization ...

引用

IEEE International Conference on Communications (ICC) / Workshop on Integrating UAVs into 5G

作者： Zhang, Shuowen Zeng, Yong Zhang, Rui Natl Univ Singapore ECE Dept Singapore Singapore

ISBN: (纸本)9781538631805

In this paper, we study a cellular-enabled unmanned aerial vehicle (UAV) communication system consisting of one UAV and multiple ground base stations (GBSs). The UAV has a mission of flying from an initial location to a final location, during which it needs to maintain reliable wireless connection with the cellular network by associating with one of the GBSs at each time instant. We aim to minimize the UAV mission completion time by optimizing its trajectory, subject to a quality of connectivity constraint of the GBS-UAV link specified by a minimum received signal-to-noise ratio (SNR) target, which needs to be satisfied throughout the mission. This problem is non-convex and difficult to be optimally solved. We first propose an effective approach to check its feasibility based on graph connectivity verification. Then, by examining the GBS-UAV association sequence during the UAV mission, we obtain useful insights on the optimal UAV trajectory, based on which an efficient algorithm is proposed to find an approximate solution to the trajectory optimization problem by leveraging techniques in convex optimization and graph theory. Numerical results show that our proposed trajectory design achieves near-optimal performance.

关键词： Trajectory Unmanned aerial vehicles Signal to noise ratio Cellular networks Wireless communication convex functions"

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Data-Driven Feedforward Learning using Non-Causal Rational Basis functions: Application to an Industrial Flatbed Printer

Data-Driven Feedforward Learning using Non-Causal Rational B...

引用

American Control Conference

作者： Blanken, Lennart Isil, Goksan Koekebakker, Sjirk Oomen, Tom Eindhoven Univ Technol Dept Mech Engn Control Syst Technol Grp NL-5600 MB Eindhoven Netherlands Oce Technol BV Venlo Netherlands

ISBN: (纸本)9781538654286

Data-driven feedforward learning enables high performance for industrial motion systems based on measured data from previous motion tasks. The key aspect herein is the chosen feedforward parametrization, which should parsimoniously model the inverse system. At present, high performance comes at the cost of parametrizations that are nonlinear in the parameters and consequences thereof. A linear parametrization is proposed that enables parsimonious modeling of inverse systems for feedforward through the use of non-causal rational orthonormal basis functions. The benefits of the proposed parametrization are experimentally demonstrated on an industrial printer, including pre-actuation and cyclic pole repetition.

关键词： Feedforward systems Task analysis Printers Printing Control systems Numerical models convex functions"

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Multiple Pursuer-Based Intercept via Forward Stochastic Reachability

Multiple Pursuer-Based Intercept via Forward Stochastic Reac...

引用

American Control Conference

作者： Vinod, Abraham P. HomChaudhuri, Baisravan Hintz, Christoph Parikh, Anup Buerger, Stephen P. Oishi, Meeko M. K. Brunson, Greg Ahmad, Shakeeb Fierro, Rafael Univ New Mexico Elect & Comp Engn Albuquerque NM 87131 USA Sandia Natl Labs Natl Technol & Engn Solut Sandia LLC Livermore CA 94550 USA

ISBN: (纸本)9781538654286

We discuss the multiple pursuer-based intercept of a threat unmanned aerial system (UAS) with stochastic dynamics via multiple pursuing UASs, using forward stochastic reachability and receding horizon control techniques. We formulate a stochastic model for the threat that can emulate the potentially adversarial behavior and is amenable to the existing scalable results in forward stochastic reachability literature. The optimal state for the intercept for each individual pursuer is obtained via a log-concave optimization problem, and the open-loop control paths are obtained via a convex optimization problem. With stochasticity modeled as a Gaussian process, we can approximate the optimization problem as a quadratic program, to enable real-time path planning We also incorporate real-time sensing into the path planning by using a receding horizon controller, to improve the intercept probabilities. We validate the proposed framework via hardware experiments.

关键词： Stochastic processes Real-time systems Sensors Computational modeling Fourier transforms Optimization convex functions"

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System-Aware Compression

System-Aware Compression

引用

IEEE International Symposium on Information Theory (ISIT)

作者： Dar, Yehuda Elad, Michael Bruckstein, Alfred M. Technion Israel Inst Technol Comp Sci Dept Haifa Israel

ISBN: (纸本)9781538647813

Many information systems employ lossy compression as a crucial intermediate stage among other processing components. While the important distortion is defined by the system's input and output signals, the compression usually ignores the system structure, therefore, leading to an overall suboptimal rate-distortion performance. In this paper we propose a compression methodology for an operational rate-distortion optimization considering a known system layout, modeled using linear operators and noise. Using the alternating direction method of multipliers (ADMM) technique, we show that the design of the new globally-optimized compression reduces to a standard compression of a "system adjusted" signal. Essentially, the proposed framework leverages standard compression techniques to address practical settings of the remote source coding problem. We further explain the main ideas of our method by theoretically studying the case of a cyclo-stationary Gaussian signal. We present experimental results for coding of one-dimensional signals and for video compression using the HEVC standard, showing significant gains by the adjustment to an acquisition-rendering system.

关键词： Optimization Rate-distortion Standards Distortion Measurement convex functions"

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Generalizing Bottleneck Problems

Generalizing Bottleneck Problems

引用

IEEE International Symposium on Information Theory (ISIT)

作者： Hsu, Hsiang Asoodeh, Shahab Salamatian, Salman Calmon, Flavio P. Harvard Univ Cambridge MA 02138 USA Univ Chicago Chicago IL 60637 USA MIT Cambridge MA 02139 USA

ISBN: (纸本)9781538647813

Given a pair of random variables (X, Y) similar to P-XY and two convex functions f(1) and f(2), we introduce two bottleneck functionals as the lower and upper boundaries of the two-dimensional convex set that consists of the pairs (I-f1 (W;X);I-f2 (W;Y)), where I-f denotes f-information and W varies over the set of all discrete random variables satisfying the Markov condition W -> X -> Y. Applying Witsenhausen and Wyner's approach, we provide an algorithm for computing boundaries of this set for f(1), f(2), and discrete P-XY. In the binary symmetric case, we fully characterize the set when (i) f(1)(t) = f(2)(t) = t log t, (ii) f(1)(t) = f(2)(t) = t(2) - 1, and (iii) f(1) and f2 are both l(beta) norm function for beta >= 2. We then argue that upper and lower boundaries in (i) correspond to Mrs. Gerber's Lemma and its inverse (which we call Mr. Gerber's Lemma), in (ii) correspond to estimation-theoretic variants of Information Bottleneck and Privacy Funnel, and in (iii) correspond to Arimoto Information Bottleneck and Privacy Funnel. An extended version of this paper is available in [1].

关键词： Privacy Random variables Mutual information Measurement Geometry convex functions"

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