Semantic-aware Sampling and Transmission in Energy Harvesting Systems: A POMDP Approach

We study real-time tracking problem in an energy harvesting system with a Markov source under an imperfect channel. We consider both sampling and transmission costs and different from most prior studies that assume the source is fully observable, the sampling cost renders the source unobservable. The goal is to jointly optimize sampling and transmission policies for three semantic-aware metrics: i) the age of information (AoI), ii) general distortion, and iii) the age of incorrect information (AoII). To this end, we formulate and solve a stochastic control problem. Specifically, for the AoI metric, we cast a Markov decision process (MDP) problem and solve it using relative value iteration (RVI). For the distortion and AoII metrics, we utilize the partially observable MDP (POMDP) modeling and leverage the notion of belief MDP formulation of POMDP to find optimal policies. For the distortion metric and the AoII metric under the perfect channel setup, we effectively truncate the corresponding belief space and solve an MDP problem using RVI. For the general setup, a deep reinforcement learning policy is proposed. Through simulations, we demonstrate significant performance improvements achieved by the derived policies. The results reveal various switching-type structures of optimal policies and show that a distortion-optimal policy is also AoII optimal.