Cross-Layer Designs in Coded Wireless Fading Networks with Multicast

A cross-layer design along with an optimal resource allocation framework is formulated for wireless fading networks, where the nodes are allowed to perform network coding. The aim is to jointly optimize end-to-end transport layer rates, network code design variables, broadcast link flows, link capacities, average power consumption, and short-term power allocation policies. As in the routing paradigm where nodes simply forward packets, the cross-layer optimization problem with network coding is non-convex in general. It is proved however, that with network coding, dual decomposition for multicast is optimal so long as the fading at each wireless link is a continuous random variable. This lends itself to provably convergent subgradient algorithms, which not only admit a layered-architecture interpretation but also optimally integrate network coding in the protocol stack. The dual algorithm is also paired with a scheme that yields near-optimal network design variables, namely multicast end-to-end rates, network code design quantities, flows over the broadcast links, link capacities, and average power consumption. Finally, an asynchronous subgradient method is developed, whereby the dual updates at the physical layer can be affordably performed with a certain delay with respect to the resource allocation tasks in upper layers. This attractive feature is motivated by the complexity of the physical layer subproblem, and is an adaptation of the subgradient method suitable for network control.Comment: Accepted in IEEE/ACM Transactions on Networking; revision pendin

Unsupervised Learning for Asynchronous Resource Allocation in Ad-hoc Wireless Networks

We consider optimal resource allocation problems under asynchronous wireless network setting. Without explicit model knowledge, we design an unsupervised learning method based on Aggregation Graph Neural Networks (Agg-GNNs). Depending on the localized aggregated information structure on each network node, the method can be learned globally and asynchronously while implemented locally. We capture the asynchrony by modeling the activation pattern as a characteristic of each node and train a policy-based resource allocation method. We also propose a permutation invariance property which indicates the transferability of the trained Agg-GNN. We finally verify our strategy by numerical simulations compared with baseline methods.Comment: 5 pages, 4 figures, conferenc

Network Resource Allocation via Stochastic Subgradient Descent: Convergence Rate

This paper considers a general stochastic resource allocation problem that arises widely in wireless networks, cognitive radio, networks, smart-grid communications, and cross-layer design. The problem formulation involves expectations with respect to a collection of random variables with unknown distributions, representing exogenous quantities such as channel gain, user density, or spectrum occupancy. We consider the constant step-size stochastic dual subgradient descent (SDSD) method that has been widely used for online resource allocation in networks. The problem is solved in dual domain which results in a primal resource allocation subproblem at each time instant. The goal here is to characterize the non-asymptotic behavior of such stochastic resource allocations in an almost sure sense. It is well known that with a step size of $\epsilon$, {SDSD} converges to an $\mathcal{O}(\epsilon)$-sized neighborhood of the optimum. In practice however, there exists a trade-off between the rate of convergence and the choice of $\epsilon$. This paper establishes a convergence rate result for the SDSD algorithm that precisely characterizes this trade-off. {Towards this end, a novel stochastic bound on the gap between the objective function and the optimum is developed. The asymptotic behavior of the stochastic term is characterized in an almost sure sense, thereby generalizing the existing results for the {stochastic subgradient} methods.} For the stochastic resource allocation problem at hand, the result explicates the rate with which the allocated resources become near-optimal. As an application, the power and user-allocation problem in device-to-device networks is formulated and solved using the {SDSD} algorithm. Further intuition on the rate results is obtained from the verification of the regularity conditions and accompanying simulation results

Asynchronous Incremental Stochastic Dual Descent Algorithm for Network Resource Allocation

Stochastic network optimization problems entail finding resource allocation policies that are optimum on an average but must be designed in an online fashion. Such problems are ubiquitous in communication networks, where resources such as energy and bandwidth are divided among nodes to satisfy certain long-term objectives. This paper proposes an asynchronous incremental dual decent resource allocation algorithm that utilizes delayed stochastic {gradients} for carrying out its updates. The proposed algorithm is well-suited to heterogeneous networks as it allows the computationally-challenged or energy-starved nodes to, at times, postpone the updates. The asymptotic analysis of the proposed algorithm is carried out, establishing dual convergence under both, constant and diminishing step sizes. It is also shown that with constant step size, the proposed resource allocation policy is asymptotically near-optimal. An application involving multi-cell coordinated beamforming is detailed, demonstrating the usefulness of the proposed algorithm

Practical Precoding via Asynchronous Stochastic Successive Convex Approximation

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. Such extra-gradient information is not used by SGD, but has been shown to be useful, for instance in the context of stochastic expectation-maximization, stochastic majorization-minimization, and stochastic successive convex approximation (SCA) approaches. By constructing a stochastic strongly convex surrogates of the loss function at every iteration, the stochastic SCA algorithms can exploit the structural properties of the loss function and achieve superior empirical performance as compared to the SGD. 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 surrogates 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