Learned database systems address several weaknesses of traditional cost estimation techniques in query optimization: they learn a model of a database instance, e.g., as queries are executed. However, when the database instance has skew and correlation, it is nontrivial to create an effective training set that anticipates workload shifts, where query structure changes and/or different regions of the data contribute to query answers. Our predictive model may perform poorly with these out-of-distribution inputs. In this paper, we study how the notion of a replay buffer can be managed through online algorithms to build a concise yet representative model of the workload distribution --- allowing for rapid adaptation and effective prediction of cardinalities and costs. We experimentally validate our methods over several data domains.