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Learning-based dynamic power management (DPM) techniques, being able to adapt to varying system conditions and workloads, have attracted a lot of research attention recently. To the best of our knowledge, however, none of the existing learning-based DPM solutions are dedicated to power reduction in multicore processors, although they can be utilized by treating each processor core as a standalone entity and conducting DPM for them separately. In this paper, by including task allocation into our learning-based DPM framework for multicore processors, we are able to manipulate idle periods on processor cores to achieve a better tradeoff between power consumption and system performance. Experimental results show that the proposed solution significantly outperforms existing DPM techniques.