Section: New Results
Online resource allocation in dynamic wireless networks
The vast majority of works on wireless resource allocation (spectrum, power, etc.) has focused on two limit cases: In the static regime, the attributes of the network are assumed effectively static and the system's optimality analysis relies on techniques from (static) optimization. On the other hand, in the so-called stochastic regime, the network is assumed to evolve randomly following some fixed probability law, and the allocation of wireless resources is optimized using tools from stochastic optimization and control. In practical wireless networks however, both assumptions fail because of factors that introduce an unpredictable variability to the system (such as user mobility, users going arbitrarily on- and off-line, etc.).
The works , ,  treat this problem by providing no-regret learning algorithms for single-user rate maximization and power control in multi-carrier cognitive radio and Internet of Things networks. The extension of these works to multi-antenna systems was carried out in , where we derived a matrix exponential learning algorithm for dynamic power allocation and control in time-varying MIMO systems. Building on this, we also showed in  that regret minimization techniques can also be applied to the much more challenging problem of energy efficiency maximization in dynamic networks – i.e. the maximization of successfully received bits per Watt of transmitted power in environments that fluctuate unpredictably over time. Finally, as was shown in , , , these unilateral performance gains also extend to large networks comprising hundreds (or even thousands) of users: there, the proposed matrix exponential learning algorithm converges to a stable state within a few iterations, even for very large of antennas and subcarriers.