One of the key challenges in Internet of Things(IoT) networks is to connect many dierent types of autonomousdevices 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 ahighly dynamic and unpredictable environment where existingsolutions (e.g., water-filling algorithms) are no longer relevant;and b) the lack of sucient information at the device end. Toaddress these issues, we propose a regret-based formulationthat accounts for arbitrary network dynamics: this allows usto derive an online power control scheme which is provablycapable of adapting to such changes, while relying solely onstrictly causal feedback. In so doing, we identify an importanttradeo between the amount of feedback available at the transmitterside and the resulting system performance: if the devicehas access to unbiased gradient observations, the algorithm’sregret after T stages is O(T1=2) (up to logarithmic factors); onthe other hand, if the device only has access to scalar, utilitybasedinformation, this decay rate drops toO(T1=4). The aboveis validated by an extensive suite of numerical simulations inrealistic channel conditions, which clearly exhibit the gainsof the proposed online approach over traditional water-fillingmethods.
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