Distributed stochastic optimization via matrix exponential learning

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria - or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.Comment: 31 pages, 3 figure

Dynamic Multi-Arm Bandit Game Based Multi-Agents Spectrum Sharing Strategy Design

For a wireless avionics communication system, a Multi-arm bandit game is mathematically formulated, which includes channel states, strategies, and rewards. The simple case includes only two agents sharing the spectrum which is fully studied in terms of maximizing the cumulative reward over a finite time horizon. An Upper Confidence Bound (UCB) algorithm is used to achieve the optimal solutions for the stochastic Multi-Arm Bandit (MAB) problem. Also, the MAB problem can also be solved from the Markov game framework perspective. Meanwhile, Thompson Sampling (TS) is also used as benchmark to evaluate the proposed approach performance. Numerical results are also provided regarding minimizing the expectation of the regret and choosing the best parameter for the upper confidence bound