This paper presents a supervised learning based dynamic power management (DPM) framework for a multicore processor, where a power manager (PM) learns to predict the system performance state from some readily available input features (such as the state of service queue occupancy and the task arrival rate) and then uses this predicted state to look up the optimal power management action from a pre-computed policy lookup table. The motivation for utilizing supervised learning in the form of a Bayesian classifier is to reduce overhead of the PM which has to recurrently determine and issue voltage-frequency setting commands to each processor core in the system. Experimental results reveal that the proposed Bayesian classification based DPM technique ensures system-wide energy savings under rapidly and widely varying workloads.