One of the most immediate practical applications of quantum information processing is performing precise quantum measurements. Quantum measurement schemes employing adaptive feedback are most effective, since accumulated information from measurements is exploited to maximize the information gain in subsequent measurements. Yet devising such feedback policies is complicated and often involves clever guesswork. Here we present an automated method, based on machine learning, to generate adaptive feedback measurement policies. We apply our technique to adaptive quantum phase measurement, which is important for applications such as atomic clocks and gravitational wave detection. Our algorithm autonomously learns to perform phase estimation based on experimental trial runs, which can be either simulated or performed using a real world experiment.