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Efficiently transferring data over long-distance, high-speed networks requires optimal utilization of available network bandwidth. One effective method to achieve this is through the use of parallel TCP streams. This approach allows applications to leverage network parallelism, thereby enhancing transfer throughput. However, determining the ideal number of parallel TCP streams can be challenging due to non-deterministic background traffic sharing the network, as well as non-stationary and partially observable network signals. We present a novel learning-based approach that utilizes deep reinforcement learning (DRL) to determine the optimal number of parallel TCP streams. Our DRL-based algorithm is designed to intelligently utilize available network bandwidth while adapting to different network conditions. Unlike rule-based heuristics, which lack generalization in unknown network scenarios, our DRL-based solution can dynamically adjust the parallel TCP stream numbers to optimize network bandwidth utilization without causing network congestion and ensuring fairness among competing transfers. We conducted extensive experiments to evaluate our DRL-based algorithm’s performance and compared it with several state-of-the-art online optimization algorithms. The results demonstrate that our algorithm can identify nearly optimal solutions 40% faster while achieving up to 15% higher throughput. Furthermore, we show that our solution can prevent network congestion and distribute the available network resources fairly among competing transfers, unlike a discriminatory algorithm.