Learning Statistically Accurate Resource Allocations in Non-Stationary Wireless Systems

Abstract

This paper considers the resource allocation problem in wireless systems over an unknown time-varying non-stationary channel. The goal is to maximize a utility function, such as a capacity function, over a set of wireless nodes while satisfying a set of resource constraints. To bypass the need for a model for channel distribution as it varies over time, samples of the channel are taken at every time epoch to estimate the channel. The resulting stochastic optimization problem is converted in its Lagrange dual problem, where the resulting stochastic optimization problem can viewed equivalently as minimizing a certain empirical risk measure, a well-studied problem in machine learning. The second order Newton's method is used to quickly learn statistically approximated optimal resource allocation policies over the sampled dual function as the channel evolves over time epochs. The quadratic convergence rate of Newton is used to establish, under certain conditions on the sampling size and rate of channel variation, an instantaneous learning and tracking of these policies. Numerical simulations demonstrate the effectiveness of the learning algorithm on a low-dimensional wireless capacity maximization problem.