We consider the distributed channel selection problem in the context of device-to-device (D2D) communication as an underlay to a cellular network. Underlaid D2D users communicate directly by utilizing the cellular spectrum, but their decisions are not governed by any centralized controller. Selfish D2D users that compete for access to the resources form a distributed system where the transmission performance depends on channel availability and quality. This information, however, is difficult to acquire. Moreover, the adverse effects of D2D users on cellular transmissions should be minimized. In order to overcome these limitations, we propose a network-assisted distributed channel selection approach in which D2D users are only allowed to use vacant cellular channels. This scenario is modeled as a multi-player multi-armed bandit game with side information, for which a distributed algorithmic solution is proposed. The solution is a combination of no-regret learning and calibrated forecasting, and can be applied to a broad class of multi-player stochastic learning problems, in addition to the formulated channel selection problem. Theoretical analysis shows that the proposed approach not only yields vanishing regret in comparison to the global optimal solution but also guarantees that the empirical joint frequencies of the game converge to the set of correlated equilibria.