We use Monte Carlo and genetic algorithms to train neural-network feedback-control protocols for simulated fluctuating nanosystems. These protocols convert the information obtained by the feedback process into heat or work, allowing the extraction of work from a colloidal particle pulled by an optical trap and the absorption of entropy by an Ising model undergoing magnetization reversal. The learning framework requires no prior knowledge of the system, depends only upon measurements that are accessible experimentally, and scales to systems of considerable complexity. It could be used in the laboratory to learn protocols for fluctuating nanosystems that convert measurement information into stored work or heat.