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To handle the exponential growth of data-intensive network edge services and automatically solve new challenges in routing management, machine learning is steadily being incorporated into software-defined networking solutions. In this line, the article presents the design of a piecewise-stationary Bayesian multi-armed bandit approach for the online optimum end-to-end dynamic routing of data flows in the context of programmable networking systems. This learning-based approach has been analyzed with simulated and emulated data, showing the proposal’s ability to sequentially and proactively self-discover the end-to-end routing path with minimal delay among a considerable number of alternatives, even when facing abrupt changes in transmission delay distributions due to both variable congestion levels on path network devices and dynamic delays to transmission links.