The Congestion Control (CC) module plays a critical role in the Transmission Control Protocol (TCP), ensuring the stability and efficiency of network data transmission. The CC approaches that are commonly used these days employ heuristics-based rules to adjust the sending rate. Due to their heuristics-based nature, these approaches are not only unable to adapt to changing network conditions but are also agnostic to the diverse requirements that different applications often have. Recently, several learning-based CC approaches have been proposed to adapt to changing network conditions. Unfortunately, they are not designed to take application requirements into account. Prior heuristics-based as well as learning-based CC approaches focus on achieving a singular objective, which is often to maximize throughput, even though a lot of applications care more about latency, packet losses, jitter, and different combinations of various network metrics. Motivated by this, we propose a Deep Reinforcement Learning (DRL) based CC framework, namely ASC, which allows any application to specify any arbitrary objectives that the network traffic of that application should achieve and is able to swiftly adapt to the changes in the objectives of the applications as well as to the changes in the network conditions. Our ASC framework further employs a client-server architecture that serves two purposes: 1) it makes ASC highly scalable in terms of the arrival and departure of TCP connections, and 2) it makes ASC very lightweight for the nodes maintaining the TCP connections. We implemented and extensively evaluated ASC in a variety of settings. Our results show that it can not only achieve various objectives but also outperforms prior approaches even in the specific objectives that those approaches were designed to achieve.