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-) by their deadline, where 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.