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Pré-Publication, Document De Travail Année : 2023

Online Learning with Adversaries: A Differential Inclusion Analysis

Swetha Ganesh
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Gugan Thoppe
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Résumé

We consider the measurement model Y = AX, where X and, hence, Y are random variables and A is an a priori known tall matrix. At each time instance, a sample of one of Y 's coordinates is available, and the goal is to estimate µ := E[X] via these samples. However, the challenge is that a small but unknown subset of Y 's coordinates are controlled by adversaries with infinite power: they can return any real number each time they are queried for a sample. For such an adversarial setting, we propose the first asynchronous online algorithm that converges to µ almost surely. We prove this result using a novel differential inclusion based two-timescale analysis. Two key highlights of our proof include: (a) the use of a novel Lyapunov function for showing that µ is the unique global attractor for our algorithm's limiting dynamics, and (b) the use of martingale and stopping time theory to show that our algorithm's iterates are almost surely bounded.
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Dates et versions

hal-04158714 , version 1 (11-07-2023)

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  • HAL Id : hal-04158714 , version 1

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Swetha Ganesh, Alexandre Reiffers-Masson, Gugan Thoppe. Online Learning with Adversaries: A Differential Inclusion Analysis. 2023. ⟨hal-04158714⟩
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