Improved Convergence Rates for Distributed Resource Allocation

In this paper, we develop a class of decentralized algorithms for solving a convex resource allocation problem in a network of $n$ agents, where the agent objectives are decoupled while the resource constraints are coupled. The agents communicate over a connected undirected graph, and they want to collaboratively determine a solution to the overall network problem, while each agent only communicates with its neighbors. We first study the connection between the decentralized resource allocation problem and the decentralized consensus optimization problem. Then, using a class of algorithms for solving consensus optimization problems, we propose a novel class of decentralized schemes for solving resource allocation problems in a distributed manner. Specifically, we first propose an algorithm for solving the resource allocation problem with an $o(1/k)$ convergence rate guarantee when the agents' objective functions are generally convex (could be nondifferentiable) and per agent local convex constraints are allowed; We then propose a gradient-based algorithm for solving the resource allocation problem when per agent local constraints are absent and show that such scheme can achieve geometric rate when the objective functions are strongly convex and have Lipschitz continuous gradients. We have also provided scalability/network dependency analysis. Based on these two algorithms, we have further proposed a gradient projection-based algorithm which can handle smooth objective and simple constraints more efficiently. Numerical experiments demonstrates the viability and performance of all the proposed algorithms

Autonomous Algorithms for Centralized and Distributed Interference Coordination: A Virtual Layer Based Approach

Interference mitigation techniques are essential for improving the performance of interference limited wireless networks. In this paper, we introduce novel interference mitigation schemes for wireless cellular networks with space division multiple access (SDMA). The schemes are based on a virtual layer that captures and simplifies the complicated interference situation in the network and that is used for power control. We show how optimization in this virtual layer generates gradually adapting power control settings that lead to autonomous interference minimization. Thereby, the granularity of control ranges from controlling frequency sub-band power via controlling the power on a per-beam basis, to a granularity of only enforcing average power constraints per beam. In conjunction with suitable short-term scheduling, our algorithms gradually steer the network towards a higher utility. We use extensive system-level simulations to compare three distributed algorithms and evaluate their applicability for different user mobility assumptions. In particular, it turns out that larger gains can be achieved by imposing average power constraints and allowing opportunistic scheduling instantaneously, rather than controlling the power in a strict way. Furthermore, we introduce a centralized algorithm, which directly solves the underlying optimization and shows fast convergence, as a performance benchmark for the distributed solutions. Moreover, we investigate the deviation from global optimality by comparing to a branch-and-bound-based solution.Comment: revised versio

Distributed Rate Allocation Policies for Multi-Homed Video Streaming over Heterogeneous Access Networks

We consider the problem of rate allocation among multiple simultaneous video streams sharing multiple heterogeneous access networks. We develop and evaluate an analytical framework for optimal rate allocation based on observed available bit rate (ABR) and round-trip time (RTT) over each access network and video distortion-rate (DR) characteristics. The rate allocation is formulated as a convex optimization problem that minimizes the total expected distortion of all video streams. We present a distributed approximation of its solution and compare its performance against H-infinity optimal control and two heuristic schemes based on TCP-style additive-increase-multiplicative decrease (AIMD) principles. The various rate allocation schemes are evaluated in simulations of multiple high-definition (HD) video streams sharing multiple access networks. Our results demonstrate that, in comparison with heuristic AIMD-based schemes, both media-aware allocation and H-infinity optimal control benefit from proactive congestion avoidance and reduce the average packet loss rate from 45% to below 2%. Improvement in average received video quality ranges between 1.5 to 10.7 dB in PSNR for various background traffic loads and video playout deadlines. Media-aware allocation further exploits its knowledge of the video DR characteristics to achieve a more balanced video quality among all streams.Comment: 12 pages, 22 figure

On Resource Allocation in Fading Multiple Access Channels - An Efficient Approximate Projection Approach

We consider the problem of rate and power allocation in a multiple-access channel. Our objective is to obtain rate and power allocation policies that maximize a general concave utility function of average transmission rates on the information theoretic capacity region of the multiple-access channel. Our policies does not require queue-length information. We consider several different scenarios. First, we address the utility maximization problem in a nonfading channel to obtain the optimal operating rates, and present an iterative gradient projection algorithm that uses approximate projection. By exploiting the polymatroid structure of the capacity region, we show that the approximate projection can be implemented in time polynomial in the number of users. Second, we consider resource allocation in a fading channel. Optimal rate and power allocation policies are presented for the case that power control is possible and channel statistics are available. For the case that transmission power is fixed and channel statistics are unknown, we propose a greedy rate allocation policy and provide bounds on the performance difference of this policy and the optimal policy in terms of channel variations and structure of the utility function. We present numerical results that demonstrate superior convergence rate performance for the greedy policy compared to queue-length based policies. In order to reduce the computational complexity of the greedy policy, we present approximate rate allocation policies which track the greedy policy within a certain neighborhood that is characterized in terms of the speed of fading.Comment: 32 pages, Submitted to IEEE Trans. on Information Theor

A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and several challenges arise in a distributed framework, so that looking for suboptimal solutions is of interest. To achieve this goal, the presence of a linear coupling calls for tailored decomposition approaches. We propose a fully distributed algorithm based on a primal decomposition approach and a suitable tightening of the coupling constraints. Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of an approximate version of the original problem. Based on such allocation vectors, agents are able to (locally) compute a mixed-integer solution, which is guaranteed to be feasible after a sufficiently large time. Asymptotic and finite-time suboptimality bounds are established for the computed solution. Numerical simulations highlight the efficacy of the proposed methodology.Comment: 57th IEEE Conference on Decision and Contro