In this paper, we address the problem of joint allocation of transmit and jamming power at the source and destination, respectively, to enhance the long-term cumulative secrecy performance of an energy-harvesting wireless communication system until it stops functioning in the presence of an eavesdropper. The source and destination have energy-harvesting devices with limited battery capacities. The destination also has a full-duplex transceiver to transmit jamming signals for secrecy. We frame the problem as an infinite-horizon Markov decision process (MDP) problem and propose a reinforcement learning (RL)-based optimal joint power allocation (OJPA) algorithm that employs a policy iteration (PI) algorithm. Since the optimal algorithm is computationally expensive, we develop a low-complexity sub-optimal joint power allocation (SJPA) algorithm, namely, reduced state joint power allocation (RSJPA). Two other SJPA algorithms, the greedy algorithm (GA), and the naive algorithm (NA) are implemented as benchmarks. In addition, the OJPA algorithm outperforms the individual power allocation (IPA) algorithms termed individual transmit power allocation (ITPA) and individual jamming power allocation (IJPA), where the transmit and jamming powers, respectively, are optimized individually. The results show that the OJPA algorithm is also more energy efficient.Results also show that the OJPA algorithm significantly improves the secrecy performance compared to all SJPA algorithms. The OJPA algorithm also outperforms the secrecy performance of a genetic algorithm-based RL algorithm and a finite-horizon RL algorithm.The proposed RSJPA algorithm achieves nearly optimal performance with significantly less computational complexity marking it the balanced choice between the complexity and the performance.