A fundamental theme throughout learning theory and statistics is that "smooth" functions ought to be

In real-world applications, the distribution of the data, and our goals, evolve over time.

Due to statistical lower bounds on the learnability of many function classes under privacy constraints, there has been recent interest in leveraging public data to improve the performance of private learning algorithms. In this model, algorithms must always guarantee differential privacy with respect to the private samples while also ensuring learning guarantees when the private data distribution is sufficiently close to that of the public data. Previous work has demonstrated that when sufficient public, unlabelled data is available, private learning can be made statistically tractable, but the resulting algorithms have all been computationally inefficient. In this work, we present the first computationally efficient, algorithms to provably leverage public data to learn privately whenever a function class is learnable non-privately, where our notion of computational efficiency is with respect to the number of calls to an optimization oracle for the function class. In addition to this general result, we provide specialized algorithms with improved sample complexities in the special cases when the function class is convex or when the task is binary classification.

The replicability crisis is omnipresent in many scientific disciplines including biology, chemistry, and, importantly, AI [Baker, 2016, Pineau et al., 2019].

Table 1: A comparison between sample and oracle complexities (i.e., number of weak learning calls) of the present results and previous works, in each case to achieve