Median

See also

For a simple mean baseline, see Average. For distance-based selection, see Krum / Multi-Krum.

API Reference

aggregators.median.upper_bound(n: int, f: int, d: int) → float

Compute the theoretical coordinate-wise median robustness bound.

Parameters:

  • n (int) – Total number of workers, including Byzantine workers.

  • f (int) – Expected number of Byzantine workers.

  • d (int) – Gradient dimension. Accepted for compatibility with the GAR metadata interface; the current formula does not depend on it.

  • Returns

  • -------

  • float – Upper bound on the ratio between non-Byzantine standard deviation and gradient norm.

  • Notes

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  • is (The bound formula)

  • math:: (..) – \frac{1}{\sqrt{n - f}}