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Online Algorithms with Limited Data Retention (Extended Abstract)

Authors Nicole Immorlica, Brendan Lucier, Markus Mobius, James Siderius

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Author Details

Nicole Immorlica
  • Microsoft Research, Cambridge, MA, USA
Brendan Lucier
  • Microsoft Research, Cambridge, MA, USA
Markus Mobius
  • Microsoft Research, Cambridge, MA, USA
James Siderius
  • Tuck School of Business at Dartmouth, Hanover, NH, USA

Funding

  • Siderius, James: This research was initiated while the author was a Research Intern at Microsoft Research.

Acknowledgements

The authors thank Rad Niazadeh, Stefan Bucher, the Simons Institute for the Theory of Computing, participants at the CS and Law conference, seminar participants at the 2024 SIGecom Winter Meetings and the 2022 C3.ai DTI Workshop on Data, Learning, and Markets.

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Nicole Immorlica, Brendan Lucier, Markus Mobius, and James Siderius. Online Algorithms with Limited Data Retention (Extended Abstract). In 5th Symposium on Foundations of Responsible Computing (FORC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 295, pp. 10:1-10:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FORC.2024.10

Abstract

We introduce a model of online algorithms subject to strict constraints on data retention. An online learning algorithm encounters a stream of data points, one per round, generated by some stationary process. Crucially, each data point can request that it be removed from memory m rounds after it arrives. To model the impact of removal, we do not allow the algorithm to store any information or calculations between rounds other than a subset of the data points (subject to the retention constraints). At the conclusion of the stream, the algorithm answers a statistical query about the full dataset. We ask: what level of performance can be guaranteed as a function of m?
We illustrate this framework for multidimensional mean estimation and linear regression problems. We show it is possible to obtain an exponential improvement over a baseline algorithm that retains all data as long as possible. Specifically, we show that m = Poly(d, log(1/ε)) retention suffices to achieve mean squared error ε after observing O(1/ε) d-dimensional data points. This matches the error bound of the optimal, yet infeasible, algorithm that retains all data forever. We also show a nearly matching lower bound on the retention required to guarantee error ε. One implication of our results is that data retention laws are insufficient to guarantee the right to be forgotten even in a non-adversarial world in which firms merely strive to (approximately) optimize the performance of their algorithms. Our approach makes use of recent developments in the multidimensional random subset sum problem to simulate the progression of stochastic gradient descent under a model of adversarial noise, which may be of independent interest.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • online algorithms
  • machine learning
  • data
  • privacy
  • law

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