fedlib.aggregators.GeoMed

class GeoMed(maxiter: Optional[int] = 100, eps: Optional[float] = 1e-06, ftol: Optional[float] = 1e-10)[source]

Bases: object

A robust aggregator from paper “Distributed Statistical Machine Learning in Adversarial Settings: Byzantine Gradient Descent”. GeoMed aims to find a vector that minimizes the sum of its Euclidean distances to all the update vectors:

\[GeoMed := \arg\min_{\boldsymbol{z}} \sum_{k \in [K]} \lVert \boldsymbol{z} - {\Delta}_i \rVert.\]

There is no closed-form solution to the GeoMed problem. It is approximately solved using Weiszfeld’s algorithm in this implementation to.

Parameters:

  • maxiter – Maximum number of Weiszfeld iterations. Default 100

  • eps – Smallest allowed value of denominator, to avoid divide by zero.

Equivalently, this is a smoothing parameter. Default 1e-6. :param ftol: If objective value does not improve by at least this ftol fraction,

terminate the algorithm, default 1e-10.