On the Computational Landscape of Replicable Learning

TL;DR

This paper explores the computational aspects of algorithmic replicability in machine learning, revealing both limitations under cryptographic assumptions and new methods for designing replicable learners across different distributions.

Contribution

It demonstrates a separation between replicable and online learnability, introduces a framework for replicable learning under various distributions, and connects differential privacy with replicability.

Findings

Efficient replicable PAC learnability does not imply efficient online learnability under cryptographic assumptions.

Develops a framework for replicable learning under arbitrary distributions, extending previous results.

Shows that differential privacy mechanisms can be transformed into replicable learners.

Abstract

We study computational aspects of algorithmic replicability, a notion of stability introduced by Impagliazzo, Lei, Pitassi, and Sorrell [2022]. Motivated by a recent line of work that established strong statistical connections between replicability and other notions of learnability such as online learning, private learning, and SQ learning, we aim to understand 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 standard cryptographic assumptions, no efficient online learner exists for this class. Subsequently, we design an efficient replicable learner for PAC learning parities when the marginal distribution is far from uniform, making progress on a question posed by Impagliazzo et al. [2022]. To obtain this result, we design a replicable lifting framework inspired by Blanc, Lange, Malik, and Tan [2023] that transforms in a black-box manner efficient replicable PAC learners under the uniform 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 to a replicable one in time polynomial in the accuracy, confidence parameters and exponential in the representation dimension of the underlying hypothesis class.