As the scarce spectrum resource is becoming over-crowded, cognitive radios (CRs) indicate great flexibility to improve the spectrum efficiency by opportunistically accessing the authorized frequency bands. One of the critical challenges for operating such radios in a network is how to efficiently allocate transmission powers and frequency resource among the secondary users (SUs) while satisfying the quality-of-service (QoS) constraints of the primary users (PUs). In this paper, we focus on the non-cooperative power allocation problem in cognitive wireless mesh networks (CogMesh) formed by a number of clusters with the consideration of energy efficiency. Due to the SUs' selfish and spontaneous properties, the problem is modeled as a stochastic learning process. We first extend the single-agent Q-learning to a multi-user context, and then propose a conjecture based multi-agent Qlearning algorithm to achieve the optimal transmission strategies with only private and incomplete information. An intelligent SU performs Q-function updates based on the conjecture over the other SUs' stochastic behaviors. This learning algorithm provably converges given certain restrictions that arise during learning procedure. Simulation experiments are used to verify the performance of our algorithm and demonstrate its effectiveness of improving the energy efficiency
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