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In this paper, we explore a novel approach to end-to-end round-trip time (RTT) estimation using a machine-learning technique known as the Experts Framework. In our proposal, each of several "experts" guesses a fixed value. The weighted average of these guesses estimates the RTT, with the weights updated after every RTT measurement based on the difference between the estimated and actual RTT. Through extensive simulations we show that the proposed machine-learning algorithm adapts very quickly to changes in the RTT. Our results show a considerable reduction in the number of retransmitted packets and a increase in goodput, in particular on more heavily congested scenarios. We corroborate our results through "live" experiments using an implementation of the proposed algorithm in the Linux kernel. These experiments confirm the higher accuracy of the machine learning approach with more than 40% improvement, not only over the standard TCP, but also over the well known Eifel RTT estimator.