Living systems control cell growth dynamically by processing information from their environment. Although responses to one environmental change have been intensively studied, little is known about how cells react to fluctuating conditions. Here we address this question at the genomic scale by measuring the relative proliferation rate (fitness) of 3,568 yeast gene deletion mutants in out-of-equilibrium conditions: periodic oscillations between two salinity conditions. Fitness and its genetic variance largely depended on the stress period. Surprisingly, dozens of mutants displayed pronounced hyperproliferation at short periods, identifying unexpected controllers of growth under fast dynamics. We validated the implication of the high-affinity cAMP phosphodiesterase and of a regulator of protein translocation to mitochondria in this control. The results illustrate how natural selection acts on mutations in a fluctuating environment, highlighting unsuspected genetic vulnerabilities to periodic stress in molecular processes that are conserved across all eukaryotes.