A. Marcastel, E. V. Belmega, P. Mertikopoulos, and I. Fijalkow. IEEE Transactions on Signal Processing, vol. 67, no. 11, pp. 2987-3000, June 2019.
One of the key challenges in Internet of Things (IoT) networks is to connect many different types of autonomous devices while reducing their individual power consumption. This problem is exacerbated by two main factors: a) the fact that these devices operate in and give rise to a highly dynamic and unpredictable environment where existing solutions (e.g., water-filling algorithms) are no longer relevant; and b) the lack of sufficient information at the device end. To address these issues, we propose a regret-based formulation that accounts for arbitrary network dynamics: this allows us to derive an online power control scheme which is provably capable of adapting to such changes, while relying solely on strictly causal feedback. In so doing, we identify an important tradeoff between the amount of feedback available at the transmitter side and the resulting system performance: if the device has access to unbiased gradient observations, the algorithm’s regret after T stages is $\tilde{\mathcal{O}}(T^{−1/2})$; on the other hand, if the device only has access to scalar, utility-based information, this decay rate drops to $\mathcal{O}(T^{−1/4})$. The above is validated by an extensive suite of numerical simulations in realistic channel conditions, which clearly exhibit the gains of the proposed online approach over traditional water-filling methods.