Adaptive Robust Clipping (ARC)#

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

Bases: object

Description#

Apply the Adaptive Robust Clipping pre-aggregation rule [1]:

\[\mathrm{ARC}_{f} \ (x_1, \dots, x_n) = \left( \min\left\{1, \frac{x_{\pi(k)}}{\big|\big|x_1\big|\big|_2}\right\} x_1 \ \ , \ \dots \ ,\ \ \min\left\{1, \frac{x_{\pi(k)}}{\big|\big|x_n\big|\big|_2}\right\} x_n \right)\]

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.

  • \(k = \lfloor 2 \cdot \frac{f}{n} \cdot (n - f) \rfloor\).

  • \(\pi\) denotes a permutation on \(\big[n\big]\) that sorts the \(\ell_2\)-norm of the input vectors in non-increasing order. This sorting is expressed as: \(\big|\big|x_{\pi(1)}\big|\big|_2 \leq \ldots \leq \big|\big|x_{\pi(n)}\big|\big|_2\).

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.ARC(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([[1.        , 2.        , 3.        ],
        [4.        , 5.        , 6.        ],
        [4.41004009, 5.04004582, 5.67005155]])

Using torch tensors

>>> import torch
>>> x = torch.tensor([[1., 2., 3.],   # torch.tensor
>>>                   [4., 5., 6.],
>>>                   [7., 8., 9.]])
>>> agg(x)
tensor([[1.0000, 2.0000, 3.0000],
        [4.0000, 5.0000, 6.0000],
        [4.4100, 5.0400, 5.6701]])

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([[1.        , 2.        , 3.        ],
        [4.        , 5.        , 6.        ],
        [4.41004009, 5.04004582, 5.67005155]])

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([[1.0000, 2.0000, 3.0000],
        [4.0000, 5.0000, 6.0000],
        [4.4100, 5.0400, 5.6701]])

References

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