Multi-Krum#

class byzfl.MultiKrum(f=0)[source]#

Description#

Apply the Multi-Krum aggregator [1]:

\[\mathrm{MultiKrum}_{f} \ (x_1, \dots, x_n) = \frac{1}{n-f}\sum_{i = 1}^{n-f} x_{\pi(i)}\]

where

  • \(x_1, \dots, x_n\) are the input vectors, which conceptually correspond to gradients submitted by honest and Byzantine participants during a training iteration.

  • \(f\) conceptually represents the expected number of Byzantine vectors.

  • \(\big|\big|.\big|\big|_2\) denotes the \(\ell_2\)-norm.

  • For any \(i \in \big[n\big]\), \(\mathit{N}_i\) is the set of the \(n - f\) nearest neighbors of \(x_i\) in \(\{x_1, \dots , x_n\}\).

  • \(\pi\) denotes a permutation on \(\big[n\big]\) that sorts the input vectors in non-decreasing order of squared distance to their \(n-f\) nearest neighbors. This sorting is expressed as:

\[\sum_{x \in \mathit{N}_{\pi(1)}} \big|\big|x_{\pi(1)} - x\big|\big|_2^2 \leq \dots \leq \sum_{x \in \mathit{N}_{\pi(n)}} \big|\big|x_{\pi(n)} - x\big|\big|_2^2\]
Initialization parameters:

f (int, optional) – Number of faulty vectors. Set to 0 by default.

Calling the instance

Input parameters:

vectors (numpy.ndarray, torch.Tensor, list of numpy.ndarray or list of torch.Tensor) – A set of vectors, matrix or tensors.

Returns:

numpy.ndarray or torch.Tensor – The data type of the output will be the same as the input.

Examples

>>> import byzfl
>>> agg = byzfl.MultiKrum(1)

Using numpy arrays

>>> import numpy as np
>>> x = np.array([[1., 2., 3.],       # np.ndarray
>>>               [4., 5., 6.],
>>>               [7., 8., 9.]])
>>> agg(x)
array([2.5 3.5 4.5])

Using torch tensors

>>> import torch
>>> x = torch.tensor([[1., 2., 3.],   # torch.tensor
>>>                   [4., 5., 6.],
>>>                   [7., 8., 9.]])
>>> agg(x)
tensor([2.5000, 3.5000, 4.5000])

Using list of numpy arrays

>>> import numpy as np
>>> x = [np.array([1., 2., 3.]),      # list of np.ndarray
>>>      np.array([4., 5., 6.]),
>>>      np.array([7., 8., 9.])]
>>> agg(x)
array([2.5 3.5 4.5])

Using list of torch tensors

>>> import torch
>>> x = [torch.tensor([1., 2., 3.]),  # list of torch.tensor
>>>      torch.tensor([4., 5., 6.]),
>>>      torch.tensor([7., 8., 9.])]
>>> agg(x)
tensor([2.5000, 3.5000, 4.5000])

References

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