Numerous applications on the web use transmission control protocol (TCP) as a transport protocol to ensure efficient and fair sharing of network resources among users. With the increased complexity in wired/wireless networks, many end-to-end congestion control (CC) algorithms have been proposed in the literature, offering solutions through their proposed TCP variants. In contrast to this, machine learning has attained great success in tackling end-to-end CC for future networks. This survey investigates the most recent research contributions on learning-based CC in general and deep reinforcement learning (DRL)-based CC in particular for traffic management in multi-path TCP (MPTCP). From the literature, it is observed that DRL is a pivotal domain for learning-based CC algorithms in highly dynamic wireless communication networks. We pinpoint key outcomes, corresponding challenges and unaddressed issues. Moreover, this survey delineates the limitations, research challenges, insights, and future opportunities to advance DRL-based traffic management in MPTCP.