This paper presents a data-driven adaptive scheme to adjust the control settings of each wind turbine in a wind farm such that an increase in the total power production of the wind farm is achieved. This is carried out by taking into account the interaction between the turbines through wake effects. The optimization scheme is designed in such a way that it yields fast convergence so that it can adapt to changing wind conditions quickly. The scheme has a distributed architecture in which each wind turbine adapts its control settings through gradient-based optimization, using information that it receives from neighbouring turbines. The novel control method is tested in a simulation of the Princess Amalia Wind Park. It is shown that the distributed gradient-based approach performs the optimization in a more time-efficient manner compared with an existing data-driven wind farm power optimization method that uses a game theoretic approach. Copyright © 2014 John Wiley & Sons, Ltd.