Age-of-information minimization under energy harvesting and non-stationary environment

Abstract

This work focuses on minimizing the age of information for multiple energy harvesting sources that sample data and transmit it to a sink node. At each time, the central scheduler selects one of the sources to probe the quality of its channel to the sink node, and then the assessed channel quality is utilized to determine whether a source will sample and send the packet. For a single source case, we assume that the probed channel quality is known at each time instant, model the problem of AoI minimization as a Markov decision process, and prove the optimal sampling policy threshold structure. We then use this threshold structure and propose an AEC-SW-UCRL2 algorithm to handle unknown and time varying energy harvesting rate and channel statistics, motivated by the popular SWUCRL2 algorithm for non stationary reinforcement learning. This algorithm is applicable when an upper bound is available for the total variation of each of these quantities over a time horizon. Furthermore, in situations where these variation budgets are not accessible, we introduce the AEC-BORL algorithm, motivated by the well known BORL algorithm. For the multiple source case, we demonstrate that the AoI minimization problem can be formulated as a constrained MDP, which can be relaxed using a Lagrange multiplier and decoupled into sub problems across source nodes. We also derive Whittle index based source scheduling policy for probing and an optimal threshold policy for source sampling. We next leverage this Whittle index and threshold structure to develop the WIT-SW-UCRL2 algorithm for unknown time varying energy harvesting rates and channel statistics under their respective variation budgets. Moreover, we also proposed a Whittle index and threshold based bandit over reinforcement learning (WIT-BORL) algorithm for unknown variation budgets. Finally, we numerically demonstrate the efficacy of our algorithms.