On the Computational Landscape of Replicable Learning

We study computational aspects of algorithmic replicability, a notion of stability introduced by Impagliazzo, Lei,Pitassi, and Sorrell [STOC, 2022]. Motivated by a recent line of work that established strong statistical connections betweenreplicability and other notions of learnability such as online learning, private learning, and SQ learning, we aim tounderstand better the computational connections between replicability and these learning paradigms.Our first result shows that there is a concept class that is efficiently replicably PAC learnable, but, under standardcryptographic assumptions, no efficient online learner exists for this class. Subsequently, we design an efficientreplicable learner for PAC learning parities when the marginal distribution is far from uniform, making progress on aquestion posed by Impagliazzo et al. [STOC, 2022]. To obtain this result, we design a replicable lifting framework inspired byBlanc, Lange, Malik, and Tan [STOC, 2023], that transforms in a black-box manner efficient replicable PAC learners under theuniform marginal distribution over the Boolean hypercube to replicable PAC learners under any marginal distribution,with sample and time complexity that depends on a certain measure of the complexity of the distribution. Finally, we show that any pure DP learner can be transformed in a black-box manner to a replicable learner, with time complexity polynomial in the confidence and accuracy parameters, but exponential in the representation dimension of the underlying hypothesis class.