Minimum-Diameter Averaging#

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

Description#

Apply the Minimum-Diameter Averaging aggregator [1]:

\[\mathrm{MDA}_{f} \ (x_1, \dots, x_n) = \frac{1}{n-f} \sum_{i\in S^\star} x_i\]

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.

  • \[\begin{split}S^\star \in \argmin_{\substack{S \subset \{1,\dots,n\} \\ |S|=n-f}} \left\{\max_{i,j \in S} \big|\big|x_i - x_j\big|\big|_2\right\}.\end{split}\]
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.MDA(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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