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The capacities of Internet backbone links have been continuously improving over the last decade, but such improvements have not been fully realized at the application level, particularly in high-performance applications. The complicated and monolithic TCP-AIMD dynamics are responsible to a large degree for low throughputs as a result of the difficulty in optimally configuring its parameters such as buffer sizes, AIMD coefficients, and slow-start transition points. In this paper, we propose a new class of UDP-based transport protocols that utilize a rate control scheme founded on the stochastic approximation method to achieve high throughputs at the application level. These protocols operate around a local maximum of the throughput regression curve by dynamically adjusting the source rate in response to acknowledgements and losses based on the statistical behavior of the network connection. We analytically show that this protocol generates a TCP-friendly flow, and also stochastically converges to the maximum throughput under a monotone loss rate condition. Our implementation achieved very robust performance over diverse Internet connections with different characteristics: it tracked the peak throughput in presence of time-varying cross traffic and consistently achieved 2-5 times the throughput of default TCP without significantly affecting the concurrent regular traffic.