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We propose a novel approach to distributed multi-radio channel allocation that is based on learning and a protocol following this approach (termed LCAP). Each node in LCAP independently and iteratively learns the channel allocation using a probabilistic adaptation algorithm that ensures network connectivity while reducing interference. Key enabler of the proposed approach is a novel neighbor discovery mechanism that exploits the mesh network deployment model in practice while being compliant to the 802.11 standard. LCAP addresses the limitations of prior work by not placing any restriction on network structure or traffic patterns, while being localized and negotiation-free for scalable operation.