We study the problem of optimal opportunistic spectrum access with unknown and heterogeneous channel dynamics in cognitive radio networks. There is neither statistic information about the licensed channels nor information exchange among secondary users in the respective systems. We formulate the problem of maximizing network throughput. To achieve the desired optimization, we propose a win-shift lose-stay algorithm based only on rewards. The key point of the algorithm is to make secondary users tend to shift to another channel after receiving rewards from the current channel. The optimality and the convergence of the proposed algorithm are proved. The simulation results show that for both heterogeneous and homogenous systems the proposed win-shift lose-stay algorithm has better performance in terms of throughput and fairness than an existing algorithm.