| % This paper studies sample delivery in a multi-hop network where a power beacon charges devices via radio frequency (RF) signals. Devices forward samples with a deadline from a source to a sink. % The goal is to minimize the power beacon's transmit power and guarantee that samples arrive at the sink with probability $(1-\epsilon)$ by their deadline, where $\epsilon$ is a given probability of failure. % A key challenge is that the power beacon does not have instantaneous channel gains information to devices and also between devices; i.e., it does not know the energy level of devices. % To this end, we formulate a chance-constrained stochastic program for the problem at hand, and employ the sample-average approximation (SAA) method to compute a solution. We also outline two novel approximation methods: Sampling based Probabilistic Optimal Power Allocation (S-POPA) and Bayesian Optimization based Probabilistic Optimal Power Allocation (BO-POPA). % Briefly, S-POPA generates a set of candidate solutions and iteratively learns the solution that returns a high probability of success. On the other hand, BO-POPA applies the Bayesian optimization framework to construct a surrogate model to predict the reward value of transmit power allocations. % Numerical results show that the performance of S-POPA and BO-POPA achieves on average 86.91\% and 79.25\% of the transmit power computed by SAA. % |