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12th International Conference on Learning Representations, ICLR 2024

作者： Lee, Joongkyu Oh, Min-Hwan Graduate School of Data Science Seoul National University Korea Republic of

In this work, we prove that, in linear MDPs, the feature dimension d is lower bounded by S/U in order to aptly represent transition probabilities, where S is the size of the state space and U is the maximum size of directly reachable states. Hence, d can still scale with S depending on the direct reachability of the environment. To address this limitation of linear MDPs, we propose a novel structural aggregation framework based on dynamics, named as the dynamics aggregation. For this newly proposed framework, we design a provably efficient hierarchical reinforcement learning algorithm in linear function approximation that leverages aggregated sub-structures. Our proposed algorithm exhibits statistical efficiency, achieving a regret of (Equation presented), where dψ represents the feature dimension of aggregated subMDPs and N signifies the number of aggregated subMDPs. We establish that the condition (Equation presented) is readily met in most real-world environments with hierarchical structures, enabling a substantial improvement in the regret bound compared to LSVI-UCB, which enjoys a regret of (Equation presented) (Jin et al., 2020). To the best of our knowledge, this work presents the first HRL algorithm with linear function approximation that offers provable guarantees. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： approximation algorithms

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Low Latency Allcast Over Broadcast Erasure Channels

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第3期69卷 1604-1617页

作者： Graham, Mark A. Ganesh, Ayalvadi J. Piechocki, Robert J. Univ Bristol Sch Math CDT Commun Bristol England RokeManor Meteor Court Gloucester GL4 3GG England Univ Bristol Sch Math Bristol BS8 1UG England Univ Bristol Dept Elect & Elect Engn Bristol BS8 1UB England

Consider n nodes communicating over an unreliable broadcast channel. Each node has a single packet that needs to be communicated to all other nodes. Time is slotted, and a time slot is long enough for each node to broadcast one packet. Each broadcast reaches a random subset of nodes. The objective is to minimise the time until all nodes have received all packets. We study two schemes, (i) random relaying, and (ii) random linear network coding, and analyse their performance in an asymptotic regime in which n tends to infinity. Simulation results for a wide range of n are also presented.

关键词： approximation algorithms Network coding Multicast algorithms Delays Topology Costs Upper bound broadcast channels random graphs

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Efficient and Accurate PageRank approximation on Large Graphs

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Proceedings of the ACM on Management of Data 2024年第4期2卷 1-26页

作者： Siyue Wu Dingming Wu Junyi Quan Tsz Nam Chan Kezhong Lu Shenzhen University Shenzhen China Shenzhen University Shenzhen HK

PageRank is a commonly used measurement in a wide range of applications, including search engines, recommendation systems, and social networks. However, this measurement suffers from huge computational overhead, which cannot be scaled to large graphs. Although many approximate algorithms have been proposed for computing PageRank values, these algorithms are either (i) not efficient or (ii) not accurate. Worse still, some of them cannot provide estimated PageRank values for all the vertices. In this paper, we first propose the CUR-Trans algorithm, which can reduce the time complexity for computing PageRank values and has lower error bound than existing matrix approximation-based PageRank algorithms. Then, we develop the T 2-Approx algorithm to further reduce the time complexity for computing this measurement. Experiment results on three large-scale graphs show that both the CUR-Trans algorithm and the T 2-Approx algorithm achieve the lowest response time for computing PageRank values with the best accuracy (for the CUR-Trans algorithm) or the competitive accuracy (for the T 2-Approx algorithm). Besides, the two proposed algorithms are able to provide estimated PageRank values for all the vertices.

关键词： approximation algorithms graph algorithms pagerank

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Practical Precoding via Asynchronous Stochastic Successive Convex approximation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 4177-4191页

作者： Idrees, Basil M. Akhtar, Javed Rajawat, Ketan Indian Inst Technol Kanpur Dept Elect Engn Kanpur 208016 Uttar Pradesh India

We consider stochastic optimization of a smooth non-convex loss function with a convex non-smooth regularizer. In the online setting, where a single sample of the stochastic gradient of the loss is available at every iteration, the problem can be solved using the proximal stochastic gradient descent (SGD) algorithm and its variants. However in many problems, especially those arising in communications and signal processing, information beyond the stochastic gradient may be available thanks to the structure of the loss function. By constructing a strongly convex surrogate of the loss function at every iteration, the stochastic SCA algorithms can exploit the structural properties of the loss function. In this work, we take a closer look at the stochastic SCA algorithm and develop its asynchronous variant which can be used for resource allocation in wireless networks. While the stochastic SCA algorithm is known to converge asymptotically, its iteration complexity has not been well-studied, and is the focus of the current work. The insights obtained from the non-asymptotic analysis allow us to develop a more practical asynchronous variant of the stochastic SCA algorithm which allows the use of surrogate calculated in earlier iterations. We characterize precise bound on the maximum delay the algorithm can tolerate, while still achieving the same convergence rate. We apply the algorithm to the problem of linear precoding in wireless sensor networks, where it can be implemented at low complexity but is shown to perform well in practice.

关键词： Signal processing algorithms Complexity theory Resource management Optimization approximation algorithms Wireless sensor networks Precoding Asynchronous stochastic optimization wireless sensor networks

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Query-Efficient Black-Box Adversarial Attacks Guided by a Transfer-Based Prior

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2022年第12期44卷 9536-9548页

作者： Dong, Yinpeng Cheng, Shuyu Pang, Tianyu Su, Hang Zhu, Jun Tsinghua Univ Beijing Natl Res Ctr Informat Sci & Technol Tsinghua Bosch Joint Ctr Machine Learning Inst Artificial IntelligenceDept Comp Sci & Tech Beijing 100084 Peoples R China Pazhou Lab Guangzhou 510330 Peoples R China

Adversarial attacks have been extensively studied in recent years since they can identify the vulnerability of deep learning models before deployed. In this paper, we consider the black-box adversarial setting, where the adversary needs to craft adversarial examples without access to the gradients of a target model. Previous methods attempted to approximate the true gradient either by using the transfer gradient of a surrogate white-box model or based on the feedback of model queries. However, the existing methods inevitably suffer from low attack success rates or poor query efficiency since it is difficult to estimate the gradient in a high-dimensional input space with limited information. To address these problems and improve black-box attacks, we propose two prior-guided random gradient-free (PRGF) algorithms based on biased sampling and gradient averaging, respectively. Our methods can take the advantage of a transfer-based prior given by the gradient of a surrogate model and the query information simultaneously. Through theoretical analyses, the transfer-based prior is appropriately integrated with model queries by an optimal coefficient in each method. Extensive experiments demonstrate that, in comparison with the alternative state-of-the-arts, both of our methods require much fewer queries to attack black-box models with higher success rates.

关键词： Estimation Optimization Analytical models Numerical models Deep learning approximation algorithms Weight measurement Adversarial examples black-box attacks zeroth-order optimization query efficiency transferability

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Fast Greedy Subset Selection From Large Candidate Solution Sets in Evolutionary Multiobjective Optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2022年第4期26卷 750-764页

作者： Chen, Weiyu Ishibuchi, Hisao Shang, Ke Southern Univ Sci & Technol Dept Comp Sci & Engn Guangdong Prov Key Lab Brain Inspired Intelligent Shenzhen 518055 Peoples R China

Subset selection plays an important role in the field of evolutionary multiobjective optimization (EMO). Especially, in an EMO algorithm with an unbounded external archive (UEA), subset selection is an essential post-processing procedure to select a prespecified number of solutions as the final result. In this article, we discuss the efficiency of greedy subset selection for the hypervolume, inverted generational distance (IGD), and IGD plus (IGD+) indicators. Greedy algorithms usually efficiently handle the subset selection. However, when a large number of solutions are given (e.g., subset selection from tens of thousands of solutions in a UEA), they often become time consuming. Our idea is to use the submodular property, which is known for the hypervolume indicator, to improve their efficiency. First, we prove that the IGD and IGD+ indicators are also submodular. Next, based on the submodular property, we propose an efficient greedy inclusion algorithm for each indicator. We demonstrate through computational experiments that the proposed algorithms are much faster than the standard greedy subset selection algorithms. The proposed algorithms also help the research on performance indicators.

关键词： Optimization Greedy algorithms Statistics Sociology approximation algorithms Evolutionary computation Clustering algorithms Evolutionary many-objective optimization evolutionary multiobjective optimization (EMO) performance indicators submodularity subset selection

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Robust and Adaptive Sequential Submodular Optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第1期67卷 89-104页

作者： Tzoumas, Vasileios Jadbabaie, Ali Pappas, George J. Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA MIT Lab Informat & Decis Syst Cambridge MA 02139 USA MIT Inst Data Syst & Soc Cambridge MA 02139 USA Univ Penn Dept Elect & Syst Engn Philadelphia PA 19104 USA

Emerging applications of control, estimation, and machine learning, from target tracking to decentralized model fitting, pose resource constraints that limit which of the available sensors, actuators, or data can be simultaneously used across time. Therefore, many researchers have proposed solutions within discrete optimization frameworks where the optimization is performed over finite sets. By exploiting notions of discrete convexity, such as submodularity, the researchers have been able to provide scalable algorithms with provable suboptimality bounds. In this article, we consider such problems but in adversarial environments, where in every step a number of the chosen elements in the optimization is removed due to failures/attacks. Specifically, we consider for the first time a sequential version of the problem that allows us to observe the failures and adapt, while the attacker also adapts to our response. We call the novel problem robust sequential submodular maximization (RSM). Generally, the problem is computationally hard and no scalable algorithm is known for its solution. However, in this article, we propose robust and adaptive maximization (RAM), the first scalable algorithm. RAM runs in an online fashion, adapting in every step to the history of failures. Also, it guarantees a near-optimal performance, even against any number of failures among the used elements. Particularly, RAM has both provable per-instance a priori bounds and tight and/or optimal a posteriori bounds. Finally, we demonstrate RAM's near-optimality in simulations across various application scenarios, along with its robustness against several failure types, from worst-case to random.

关键词： Sensors Random access memory Optimization History Target tracking Greedy algorithms Actuators Algorithm design and analysis approximation algorithms autonomous systems combinatorial mathematics control estimation fault-tolerant systems mobile robots multirobot systems

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Toward Optimal Deployment for Full-View Point Coverage in Camera Sensor Networks

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IEEE INTERNET OF THINGS JOURNAL 2022年第21期9卷 22008-22021页

作者： Shi, Kun Liu, Shuxian Li, Chao Liu, Haoyu He, Shibo Zhang, Qi Chen, Jiming Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Peoples R China China State Shipbldg Corp Syst Engn Res Inst Beijing 100036 Peoples R China NetEase Games Fuxi AI Lab Hangzhou 310052 Peoples R China

Recent years have witnessed the fast proliferation of camera sensors networks (CSNs) in numerous Internet of Things (IoT) applications. In order to a capture distinct image of targets from interesting directions, we leverage a special type of coverage called full-view coverage. Full-view coverage guarantees to obtain the images of a point from every direction, whereas it demands much more sensors than a conventional coverage. To this end, we investigate the problem of deploying the minimum number of rotatable camera sensors to achieve the full-view coverage of a set of target points, namely, optimal deployment for the full-view point coverage (OFP) problem. In this work, camera sensors are capable of rotating freely with infinite orientations, thus not only the deployment locations but also the orientations for each camera sensor are required to be optimized. To tackle this challenging problem, we first prove that the OFP problem is NP-hard. Then, we propose two approximation algorithms-iterative screening algorithm (ISA) and improved ISA (IISA) to solve the OFP. We further perform extensive simulations and conduct physical testings to demonstrate the superiority and effectiveness of our proposed solutions. Experimental results show that IISA can generally reduce the total number of required camera sensors by more than 20% compared with the state-of-the-art work.

关键词： Cameras Sensors Internet of Things approximation algorithms Testing Redundancy Image recognition Camera sensor network full-view coverage optimal deployment

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From Spectrum Bonding to Contiguous-Resource Batching Task Scheduling

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IEEE-ACM TRANSACTIONS ON NETWORKING 2022年第3期30卷 1245-1254页

作者： Shi, Hehuan Chen, Lin Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510275 Peoples R China

We formulate and analyze a generic task scheduling problem: a set of tasks need to be executed on a pool of continuous resource such as spectrum and memory, each requiring a certain amount of time and contiguous resource;some tasks can be executed simultaneously in batch by sharing the resource, while others requiring exclusive use of the resource. We seek an optimal resource allocation and the related scheduling policy maximizing the overall system utility. This problem, termed as the contiguous-resource batching task scheduling problem, arises in a variety of engineering fields, where communication and storage resources are potential bottlenecks and thus need to be carefully scheduled. Two motivating examples are the spectrum bonding problem in dynamic spectrum access systems and the dynamic storage allocation problem in computer systems. In this paper, we investigate both offline and online scheduling settings. We first establish the NP-hardness of the offline setting and the inapproximability of the online setting in its generic form. Given the theoretical performance limit, we then develop approximation algorithms with mathematically proven performance guarantee in terms of approximation and competitive ratios for the offline and online settings.

关键词： Task analysis Bonding Time-frequency analysis approximation algorithms Resource management Dynamic scheduling Heuristic algorithms Channel bonding batching task scheduling contiguous resource allocation offline and online approximation algorithm design

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Appropriate Learning Rates of Adaptive Learning Rate Optimization algorithms for Training Deep Neural Networks

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第12期52卷 13250-13261页

作者： Iiduka, Hideaki Meiji Univ Dept Comp Sci Tokyo Kanagawa 2148571 Japan

This article deals with nonconvex stochastic optimization problems in deep learning. Appropriate learning rates, based on theory, for adaptive-learning-rate optimization algorithms (e.g., Adam and AMSGrad) to approximate the stationary points of such problems are provided. These rates are shown to allow faster convergence than previously reported for these algorithms. Specifically, the algorithms are examined in numerical experiments on text and image classification and are shown in experiments to perform better with constant learning rates than algorithms using diminishing learning rates.

关键词： Optimization Convergence Stochastic processes Deep learning approximation algorithms Training Heuristic algorithms Adaptive mean square gradient (AMSGrad) adaptive moment estimation (Adam) adaptive-learning-rate optimization algorithm deep neural network learning rate nonconvex stochastic optimization

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