We use genetic programming (GP) to discover data-driven control laws for the suppression of quasiperiodic oscillations in a prototypical thermoacoustic system. We rank the control laws based on a predefined cost function that accounts for the pressure amplitude and the actuation effort. We then breed subsequent generations of control laws via a tournament process. We find that GP closed-loop control is more effective than GP open-loop control and conventional periodic forcing, producing a similarly high degree of amplitude suppression but with the lowest actuation effort. We also find that GP closed-loop control can identify unforeseen actuation mechanisms, providing new insight into the physical coupling between the heat release rate and pressure fields.