Monoculture Robust Learning

We introduce a notion of monoculture robustness in Probably Approximately Correct (PAC) learning, as a way to mitigate the problem of *algorithmic monoculture* (Kleinberg & Raghavan, 2021): the tendency of models sharing the same components (e.g., training data) to fail on the same inputs. Specifically, we ask whether a learner with access to a single dataset can output $k$ individually accurate hypotheses whose joint failure probability is comparable to training on $k$ independent datasets. We say that such a learning procedure achieves *monoculture robustness*, and we quantify this by bounding the *conjunctive error* that all $k$ hypotheses misclassify points in an individual sense. We design methods for achieving this type of guarantee by drawing a surprising connection between replicability (Impagliazzo et al., 2022) and monoculture robustness. Specifically, we show that if the base learner is $\rho$-replicable, then running it independently $k$ times on the same sample yields individual monoculture error that shrinks exponentially with $k$, controlled by the single-run error of the base learner at the point and $\rho$. We complement these positive results with a lower bound: for individual monoculture robustness, we prove a worst-case lower bound showing that, for learners, driving the individual conjunctive error down to $\gamma$ can require a sample-size multiplier of $t = \Omega(\log(1/\gamma))$.