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# Licensed under the Apache License, Version 2.0 (the "License");
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# ==============================================================================
"""Machine Learning with Adversaries: Byzantine Tolerant Gradient Descent.
[Blanchard et al., 2017].
Paper: proceedings.neurips.cc/paper/2017/file/f4b9ec30ad9f68f89b29639786cb62ef-Paper.pdf
"""
from collections.abc import Iterable
from logging import INFO
from typing import Callable, Optional, cast
import numpy as np
from flwr.common import ArrayRecord, Message, MetricRecord, NDArray, RecordDict, log
from .fedavg import FedAvg
from .strategy_utils import aggregate_arrayrecords
# pylint: disable=too-many-instance-attributes
[docs]
class MultiKrum(FedAvg):
"""MultiKrum [Blanchard et al., 2017] strategy.
Implementation based on https://arxiv.org/abs/1703.02757
Parameters
----------
fraction_train : float (default: 1.0)
Fraction of nodes used during training. In case `min_train_nodes`
is larger than `fraction_train * total_connected_nodes`, `min_train_nodes`
will still be sampled.
fraction_evaluate : float (default: 1.0)
Fraction of nodes used during validation. In case `min_evaluate_nodes`
is larger than `fraction_evaluate * total_connected_nodes`,
`min_evaluate_nodes` will still be sampled.
min_train_nodes : int (default: 2)
Minimum number of nodes used during training.
min_evaluate_nodes : int (default: 2)
Minimum number of nodes used during validation.
min_available_nodes : int (default: 2)
Minimum number of total nodes in the system.
num_malicious_nodes : int (default: 0)
Number of malicious nodes in the system. Defaults to 0.
num_nodes_to_select : int (default: 1)
Number of nodes to select before averaging.
weighted_by_key : str (default: "num-examples")
The key within each MetricRecord whose value is used as the weight when
computing weighted averages for both ArrayRecords and MetricRecords.
arrayrecord_key : str (default: "arrays")
Key used to store the ArrayRecord when constructing Messages.
configrecord_key : str (default: "config")
Key used to store the ConfigRecord when constructing Messages.
train_metrics_aggr_fn : Optional[callable] (default: None)
Function with signature (list[RecordDict], str) -> MetricRecord,
used to aggregate MetricRecords from training round replies.
If `None`, defaults to `aggregate_metricrecords`, which performs a weighted
average using the provided weight factor key.
evaluate_metrics_aggr_fn : Optional[callable] (default: None)
Function with signature (list[RecordDict], str) -> MetricRecord,
used to aggregate MetricRecords from training round replies.
If `None`, defaults to `aggregate_metricrecords`, which performs a weighted
average using the provided weight factor key.
Notes
-----
MultiKrum is a generalization of Krum. If `num_nodes_to_select` is set to 1,
MultiKrum will reduce to classical Krum.
"""
# pylint: disable=too-many-arguments,too-many-positional-arguments
def __init__(
self,
fraction_train: float = 1.0,
fraction_evaluate: float = 1.0,
min_train_nodes: int = 2,
min_evaluate_nodes: int = 2,
min_available_nodes: int = 2,
num_malicious_nodes: int = 0,
num_nodes_to_select: int = 1,
weighted_by_key: str = "num-examples",
arrayrecord_key: str = "arrays",
configrecord_key: str = "config",
train_metrics_aggr_fn: Optional[
Callable[[list[RecordDict], str], MetricRecord]
] = None,
evaluate_metrics_aggr_fn: Optional[
Callable[[list[RecordDict], str], MetricRecord]
] = None,
) -> None:
super().__init__(
fraction_train=fraction_train,
fraction_evaluate=fraction_evaluate,
min_train_nodes=min_train_nodes,
min_evaluate_nodes=min_evaluate_nodes,
min_available_nodes=min_available_nodes,
weighted_by_key=weighted_by_key,
arrayrecord_key=arrayrecord_key,
configrecord_key=configrecord_key,
train_metrics_aggr_fn=train_metrics_aggr_fn,
evaluate_metrics_aggr_fn=evaluate_metrics_aggr_fn,
)
self.num_malicious_nodes = num_malicious_nodes
self.num_nodes_to_select = num_nodes_to_select
[docs]
def summary(self) -> None:
"""Log summary configuration of the strategy."""
log(INFO, "\t├──> MultiKrum settings:")
log(INFO, "\t│\t├── Number of malicious nodes: %d", self.num_malicious_nodes)
log(INFO, "\t│\t└── Number of nodes to select: %d", self.num_nodes_to_select)
super().summary()
[docs]
def aggregate_train(
self,
server_round: int,
replies: Iterable[Message],
) -> tuple[Optional[ArrayRecord], Optional[MetricRecord]]:
"""Aggregate ArrayRecords and MetricRecords in the received Messages."""
valid_replies, _ = self._check_and_log_replies(replies, is_train=True)
arrays, metrics = None, None
if valid_replies:
reply_contents = [msg.content for msg in valid_replies]
# Krum or MultiKrum selection
replies_to_aggregate = select_multikrum(
reply_contents,
num_malicious_nodes=self.num_malicious_nodes,
num_nodes_to_select=self.num_nodes_to_select,
)
# Aggregate ArrayRecords
arrays = aggregate_arrayrecords(
replies_to_aggregate,
self.weighted_by_key,
)
# Aggregate MetricRecords
metrics = self.train_metrics_aggr_fn(
replies_to_aggregate,
self.weighted_by_key,
)
return arrays, metrics
def compute_distances(records: list[ArrayRecord]) -> NDArray:
"""Compute squared L2 distances between ArrayRecords.
Parameters
----------
records : list[ArrayRecord]
A list of ArrayRecords (arrays received in replies)
Returns
-------
NDArray
A 2D array representing the distance matrix of squared L2 distances
between input ArrayRecords
"""
# Formula: ||x - y||^2 = ||x||^2 + ||y||^2 - 2 * x.y
# Flatten records and stack them into a matrix
flat_w = np.stack(
[np.concatenate(rec.to_numpy_ndarrays(), axis=None).ravel() for rec in records],
axis=0,
) # shape: (n, d) with n number of records and d the dimension of model
# Compute squared norms of each vector
norms: NDArray = np.square(flat_w).sum(axis=1) # shape (n,)
# Use broadcasting to compute pairwise distances
distance_matrix: NDArray = norms[:, None] + norms[None, :] - 2 * flat_w @ flat_w.T
return distance_matrix
def select_multikrum(
contents: list[RecordDict],
num_malicious_nodes: int,
num_nodes_to_select: int,
) -> list[RecordDict]:
"""Select the set of RecordDicts to aggregate using the Krum or MultiKrum algorithm.
For each node, computes the sum of squared L2 distances to its n-f-2 closest
parameter vectors, where n is the number of nodes and f is the number of
malicious nodes. The node(s) with the lowest score(s) are selected for
aggregation.
Parameters
----------
contents : list[RecordDict]
List of contents from reply messages, where each content is a RecordDict
containing an ArrayRecord of model parameters from a node (client).
num_malicious_nodes : int
Number of malicious nodes in the system.
num_nodes_to_select : int
Number of client updates to select.
- If 1, the algorithm reduces to classical Krum (selecting a single update).
- If >1, Multi-Krum is applied (selecting multiple updates).
Returns
-------
list[RecordDict]
Selected contents following the Krum or Multi-Krum algorithm.
Notes
-----
If `num_nodes_to_select` is set to 1, Multi-Krum reduces to classical Krum
and only a single RecordDict is selected.
"""
# Construct list of ArrayRecord objects from replies
record_key = list(contents[0].array_records.keys())[0]
# Recall aggregate_train first ensures replies only contain one ArrayRecord
array_records = [cast(ArrayRecord, reply[record_key]) for reply in contents]
distance_matrix = compute_distances(array_records)
# For each node, take the n-f-2 closest parameters vectors
num_closest = max(1, len(array_records) - num_malicious_nodes - 2)
closest_indices = []
for distance in distance_matrix:
closest_indices.append(
np.argsort(distance)[1 : num_closest + 1].tolist() # noqa: E203
)
# Compute the score for each node, that is the sum of the distances
# of the n-f-2 closest parameters vectors
scores = [
np.sum(distance_matrix[i, closest_indices[i]])
for i in range(len(distance_matrix))
]
# Choose the num_nodes_to_select lowest-scoring nodes (MultiKrum)
# and return their updates
best_indices = np.argsort(scores)[:num_nodes_to_select]
return [contents[i] for i in best_indices]