Completely Uncoupled Algorithms for Network Utility Maximization
TL;DR: This paper presents an algorithm that can be applied for general non-concave utilities and induces a perturbed Markov chain, whose stochastically stable states are the set of actions that maximize the sum utility.
Abstract: In this paper, we present two completely uncoupled algorithms for utility maximization In the first part, we present an algorithm that can be applied for general non-concave utilities We show that this algorithm induces a perturbed (by ${\epsilon }$ ) Markov chain, whose stochastically stable states are the set of actions that maximize the sum utility In the second part, we present an approximate sub-gradient algorithm for concave utilities, which is considerably faster and requires lesser memory We study the performance of the sub-gradient algorithm for decreasing and fixed step sizes We show that, for decreasing step sizes, the Cesaro averages of the utilities converges to a neighborhood of the optimal sum utility For constant step size, we show that the time average utility converges to a neighborhood of the optimal sum utility Our main contribution is the expansion of the achievable rate region, which has not been considered in the previous paper on completely uncoupled algorithms for utility maximization This expansion aids in allocating a fair share of resources to the nodes, which is important in applications like channel selection, user association, and power control
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06 Jul 2020
TL;DR: Traditional Network Utility Maximization based solutions are inadequate for RDMA due to three challenges: 1) The standard NUM-oriented algorithm cannot deal with coupling variables introduced by multiple dependent RDMA operations; 2) The stringent constraint of RDMA on-board resources complicates the standard NUM by bringing extra optimization dimensions.
Abstract: Remote Direct Memory Access (RDMA) suffers from unfairness issues and performance degradation when multiple applications share RDMA network resources. Hence, an efficient resource scheduling mechanism is urged to optimally allocates RDMA resources among applications. However, traditional Network Utility Maximization (NUM) based solutions are inadequate for RDMA due to three challenges: 1) The standard NUM-oriented algorithm cannot deal with coupling variables introduced by multiple dependent RDMA operations; 2) The stringent constraint of RDMA on-board resources complicates the standard NUM by bringing extra optimization dimensions; 3) Naively applying traditional algorithms for NUM suffers from scalability and convergence issues in solving a large-scale RDMA resource scheduling problem.
3 citations
Cites methods from "Completely Uncoupled Algorithms for..."
...Theoretically, the network resource scheduling optimization was modeled as a NUM problem [9, 11, 12]....
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TL;DR: Zhang et al. as mentioned in this paper developed a novel formal model to characterize the dynamic process of knowledge diffusion in the autonomous learning under multiple networks and proposed an effective algorithm (ERAA) to allocate educational resources.
Abstract: Learners’ autonomous learning is at the heart of modern education, and the convenient network brings new opportunities for it. We notice that learners mainly use the combination of online and offline learning methods to complete the entire autonomous learning process, but most of the existing models cannot effectively describe the complex process of knowledge diffusion under the multinetworks framework. By analyzing the relationship between online learning and offline learning in the autonomous learning, we develop a novel formal model to characterize the dynamic process of knowledge diffusion in the autonomous learning under multiple networks. To guide learners to learn independently and effectively expand the scope of knowledge through hybrid online learning, we then introduce the personalized needs of learners and the guidance of educators and further propose an effective algorithm (ERAA) to allocate educational resources. Through the experiments, we verify the effectiveness of the model and analyze the efficiency of the proposed algorithm. Then, we compare the proposed algorithm with the existing four algorithms and the results show that the proposed algorithm improves performance by 38%. This article provides highly realistic significance for education administrators to analyze the practice, develop autonomous learning strategy and put online educational resources.
2 citations
Posted Content•
TL;DR: This work studies a distributed user association algorithm for a heterogeneous wireless network with the objective of maximizing the sum of the utilities (on the received throughput of wireless users) using the theory of perturbed Markov chains.
Abstract: We study a distributed user association algorithm for a heterogeneous wireless network with the objective of maximizing the sum of the utilities (on the received throughput of wireless users). We consider a state dependent wireless network, where the rate achieved by the users are a function of their user associations as well as the state of the system. We consider three different scenarios depending on the state evolution and the users$\text{'}$ knowledge of the system state. In this context, we present completely uncoupled user association algorithms for utility maximization where the users$\text{'}$ association is entirely a function of its past associations and its received throughput. In particular, the user is oblivious to the association of the other users in the network. Using the theory of perturbed Markov chains, we show the optimality of our algorithms under appropriate scenarios.
1 citations
Cites background or methods from "Completely Uncoupled Algorithms for..."
...We conclude by noting that, with modifications as considered in this paper, we could extend the subgradient algorithm in [22] to a state based model as well....
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...In our earlier work [22], we have presented a completely uncoupled subgradient algorithm for maximizing concave utilities....
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References
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TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.
41,772 citations
TL;DR: A model is developed based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game to show how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established.
Abstract: Cooperation in organisms, whether bacteria or primates, has been a difficulty for evolutionary theory since Darwin. On the assumption that interactions between pairs of individuals occur on a probabilistic basis, a model is developed based on the concept of an evolutionarily stable strategy in the context of the Prisoner's Dilemma game. Deductions from the model, and the results of a computer tournament show how cooperation based on reciprocity can get started in an asocial world, can thrive while interacting with a wide range of other strategies, and can resist invasion once fully established. Potential applications include specific aspects of territoriality, mating, and disease.
10,675 citations
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TL;DR: This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.
Abstract: What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.
7,139 citations
"Completely Uncoupled Algorithms for..." refers background in this paper
...With the advances in 5G wireless systems, it is predicted that there will be a phenomenal increase in the number of access points [2]....
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Book•
01 Jan 1984
TL;DR: In this article, the authors introduce the concept of random perturbations in Dynamical Systems with a Finite Time Interval (FTI) and the Averaging Principle.
Abstract: 1.Random Perturbations.- 2.Small Random Perturbations on a Finite Time Interval.- 3.Action Functional.- 4.Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point.- 5.Perturbations Leading to Markov Processes.- 6.Markov Perturbations on Large Time Intervals.- 7.The Averaging Principle. Fluctuations in Dynamical Systems with Averaging.- 8.Random Perturbations of Hamiltonian Systems.- 9. The Multidimensional Case.- 10.Stability Under Random Perturbations.- 11.Sharpenings and Generalizations.- References.- Index.
4,070 citations
"Completely Uncoupled Algorithms for..." refers methods in this paper
...f the joint action profile. A completely uncoupled algorithm to reach efficient Nash equilibrium was proposed by Pradelski et al in [4]. The algorithm was based on the theory of perturbed Markov chains [29],[30]. With similar ideas, Marden et al proposed algorithms to achieve maximum sum payoff in [5]. These algorithms were adapted to wireless networks in [31],[32]. In [33], Borowski et al proposed dist...
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...is of G-NUM In this section, we discuss the optimality of G-NUM. We characterize the performance of G-NUM as t!1and !0. To analyze the performance of G-NUM, we use tools from perturbed Markov chains [29], [30]. We first show that GNUM induces a perturbed Markov chain (perturbed by ). In Theorem 1, we show that the stochastically stable states (See Definition 2) of the Markov chain induced by G-NUM are...
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...terest. VIII. APPENDIX A. Proof of Theorem 1: To prove theorem 1, we need to characterize the stationary distribution of X (t) for small . For such a characterization, we shall use the results from [29],[30] on perturbed Markov chains. Let P (x;y) denote the transition probability of the Markov chain X from state xto state y. Consider the directed graph Gwith the states of the Markov chain as vert...
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TL;DR: The stability of a queueing network with interdependent servers is considered and a policy is obtained which is optimal in the sense that its Stability Region is a superset of the stability region of every other scheduling policy, and this stability region is characterized.
Abstract: The stability of a queueing network with interdependent servers is considered. The dependency among the servers is described by the definition of their subsets that can be activated simultaneously. Multihop radio networks provide a motivation for the consideration of this system. The problem of scheduling the server activation under the constraints imposed by the dependency among servers is studied. The performance criterion of a scheduling policy is its throughput that is characterized by its stability region, that is, the set of vectors of arrival and service rates for which the system is stable. A policy is obtained which is optimal in the sense that its stability region is a superset of the stability region of every other scheduling policy, and this stability region is characterized. The behavior of the network is studied for arrival rates that lie outside the stability region. Implications of the results in certain types of concurrent database and parallel processing systems are discussed. >
3,018 citations
"Completely Uncoupled Algorithms for..." refers background in this paper
...Related Literature Tassiulas and Ephremides proposed the Max-weight algorithm in [7]....
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...The main drawback of the Max-weight algorithm, used in [7]–[9], is its complexity and centralized nature....
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...The Max-weight algorithm can stabilize any arrival rate within the rate region [7]....
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