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Large-Scale Network Utility Maximization: Countering Exponential Growth with Exponentiated Gradients

Network utility maximization (NUM) is an iconic problem in network traffic management which is at the core of many current and emerging network design paradigms – and, in particular, software-defined networks (SDNs). Thus, given the exponential growth of modern-day networks (in both size and complexity), it is crucial to develop scalable algorithmic tools that are capable of providing efficient solutions in time which is dimension-free, i.e., independent–or nearly-independent–on the size of the system. To do so, we leverage a suite of modified gradient methods known as “mirror descent” and we derive a scalable and efficient algorithm for the NUM problem based on gradient exponentiation. We show that the convergence speed of the proposed algorithm only carries a logarithmic dependence on the size of the network, so it can be implemented reliably and efficiently in massively large networks where traditional gradient methods are prohibitively slow. These theoretical results are sub-sequently validated by extensive numerical simulations showing an improvement of several order of magnitudes over standard gradient methods in large-scale networks.