Antimicrobial resistance was estimated to be associated with 4.95 million deaths worldwide in 2019. It is possible to frame the antimicrobial resistance problem as a feedback-control problem. If we could optimize this feedback-control problem and translate our findings to the clinic, we could slow, prevent or reverse the development of high-level drug resistance. Prior work on this topic has relied on systems where the exact dynamics and parameters were known a priori. In this study, we extend this work using a reinforcement learning (RL) approach capable of learning effective drug cycling policies in a system defined by empirically measured fitness landscapes. Crucially, we show that is possible to learn effective drug cycling policies despite the problems of noisy, limited, or delayed measurement. Given access to a panel of 15 β-lactam antibiotics with which to treat the simulated E. coli population, we demonstrate that RL agents outperform two naive treatment paradigms at minimizing the population fitness over time. We also show that RL agents approach the performance of the optimal drug cycling policy. Even when stochastic noise is introduced to the measurements of population fitness, we show that RL agents are capable of maintaining evolving populations at lower growth rates compared to controls. We further tested our approach in arbitrary fitness landscapes of up to 1024 genotypes. We show that minimization of population fitness using drug cycles is not limited by increasing genome size. Our work represents a proof-of-concept for using AI to control complex evolutionary processes.