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Exchange coupled bilayers of soft and hard ferromagnetic thin films show remarkable analogies to conventional antiferromagnetic/ferromagnetic exchange bias heterostructures. Not only do all these ferromagnetic bilayers exhibit a tunable exchange bias effect, they also show a distinct training behavior upon cycling the soft layer through consecutive hysteresis loops. In contrast with conventional exchange bias systems, such all ferromagnetic bilayer structures allow the observation of training induced changes in the bias-setting hardmagnetic layer by means of simple magnetometry. Our experiments show unambiguously that the exchange bias training effect is driven by deviations from equilibrium in the pinning layer. A comparison of our experimental data with predictions from a theory based upon triggered relaxation phenomena shows excellent agreement.