The notion of replicable algorithms was introduced by Impagliazzo, Lei, Pitassi, and Sorrell (STOC’22) to describe randomized algorithms that are stable under the resampling of their inputs. More precisely, a replicable algorithm gives the same output with high probability when its randomness is fixed and it is run on a new i.i.d. sample drawn from the same distribution. Using replicable algorithms for data analysis can facilitate the verification of published results by ensuring that the results of an analysis will be the same with high probability, even when that analysis is performed on a new data set.
In this work, we establish new connections and separations between replicability and standard notions of algorithmic stability. In particular, we give sample-efficient algorithmic reductions between perfect generalization, approximate differential privacy, and replicability for a broad class of statistical problems. Conversely, we show any such equivalence must break down computationally: there exist statistical problems that are easy under differential privacy, but that cannot be solved replicably without breaking public-key cryptography. Furthermore, these results are tight: our reductions are statistically optimal, and we show that any computational separation between DP and replicability must imply the existence of one-way functions.
Our statistical reductions give a new algorithmic framework for translating between notions of stability, which we instantiate to answer several open questions in replicability and privacy. This includes giving sample-efficient replicable algorithms for various PAC learning, distribution estimation, and distribution testing problems, algorithmic amplification of δ in approximate DP, conversions from item-level to user-level privacy, and the existence of private agnostic-to-realizable learning reductions under structured distributions.
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Privacy-Preserving Prediction
Ensuring differential privacy of models learned from sensitive user data is an important goal that has
been studied extensively in recent years. It is now known that for some basic learning problems,
especially those involving high-dimensional data, producing an accurate private model requires
much more data than learning without privacy. At the same time, in many applications it is not
necessary to expose the model itself. Instead users may be allowed to query the prediction model
on their inputs only through an appropriate interface. Here we formulate the problem of ensuring
privacy of individual predictions and investigate the overheads required to achieve it in several
standard models of classification and regression.
We first describe a simple baseline approach based on training several models on disjoint subsets
of data and using standard private aggregation techniques to predict. We show that this approach
has nearly optimal sample complexity for (realizable) PAC learning of any class of Boolean
functions. At the same time, without strong assumptions on the data distribution, the aggregation
step introduces a substantial overhead. We demonstrate that this overhead can be avoided for the
well-studied class of thresholds on a line and for a number of standard settings of convex regression.
The analysis of our algorithm for learning thresholds relies crucially on strong generalization
guarantees that we establish for all differentially private prediction algorithms.
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- Award ID(s):
- 1763665
- NSF-PAR ID:
- 10217355
- Editor(s):
- Bubeck, S; Perchet, V; Rigollet, P
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- Volume:
- 75
- ISSN:
- 2640-3498
- Page Range / eLocation ID:
- 1-10
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
