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In a cognitive radio network, opportunistic spectrum access (OSA) to the underutilized spectrum involves not only sensing the spectrum occupancy but also probing the channel quality in order to identify an idle and good channel for data transmission-particularly if a large number of channels is open for secondary spectrum reuse. Although such a joint mechanism, referred to as active sensing, may improve the OSA performance due to diversity, it inevitably incurs additional energy consumption. In this paper, we consider a wideband cognitive radio network with limited available frame energy and treat a fundamental energy allocation problem: how available energy should be optimally allocated for sensing, probing, and data transmission to maximize the achievable average OSA throughput. By casting this problem into the multiarmed bandit framework under probably approximately correct (PAC) learning, we put forth a proactive strategy for determining the optimal sensing cardinality (the number of channels chosen to sense) and probing cardinality (the number of channels chosen to probe) that maximize the average throughput of the secondary user with limited available frame energy. This framework determines the optimal amount of pure exploration for the active sensing OSA bandit problem in which we refine the action (median) elimination algorithm for channel probing to minimize the sample complexity in PAC learning. Numerical results show that the optimal active sensing achieves a significant throughput gain over the (even optimal) sensing alone. Therefore, this work provides an energy allocation policy to optimally balance the available energy between exploration (sensing and probing) and exploitation (data transmission), giving the optimal diversity-energy tradeoff for the average OSA throughput.