1,341 research outputs found
Genuinely Distributed Byzantine Machine Learning
Machine Learning (ML) solutions are nowadays distributed, according to the
so-called server/worker architecture. One server holds the model parameters
while several workers train the model. Clearly, such architecture is prone to
various types of component failures, which can be all encompassed within the
spectrum of a Byzantine behavior. Several approaches have been proposed
recently to tolerate Byzantine workers. Yet all require trusting a central
parameter server. We initiate in this paper the study of the ``general''
Byzantine-resilient distributed machine learning problem where no individual
component is trusted.
We show that this problem can be solved in an asynchronous system, despite
the presence of Byzantine parameter servers and
Byzantine workers (which is optimal). We present a new algorithm, ByzSGD, which
solves the general Byzantine-resilient distributed machine learning problem by
relying on three major schemes. The first, Scatter/Gather, is a communication
scheme whose goal is to bound the maximum drift among models on correct
servers. The second, Distributed Median Contraction (DMC), leverages the
geometric properties of the median in high dimensional spaces to bring
parameters within the correct servers back close to each other, ensuring
learning convergence. The third, Minimum-Diameter Averaging (MDA), is a
statistically-robust gradient aggregation rule whose goal is to tolerate
Byzantine workers. MDA requires loose bound on the variance of non-Byzantine
gradient estimates, compared to existing alternatives (e.g., Krum).
Interestingly, ByzSGD ensures Byzantine resilience without adding communication
rounds (on a normal path), compared to vanilla non-Byzantine alternatives.
ByzSGD requires, however, a larger number of messages which, we show, can be
reduced if we assume synchrony.Comment: This is a merge of arXiv:1905.03853 and arXiv:1911.07537;
arXiv:1911.07537 will be retracte
Dynamic Resilient Containment Control in Multirobot Systems
In this article, we study the dynamic resilient containment control problem for continuous-time multirobot systems (MRSs), i.e., the problem of designing a local interaction protocol that drives a set of robots, namely the followers, toward a region delimited by the positions of another set of robots, namely the leaders, under the presence of adversarial robots in the network. In our setting, all robots are anonymous, i.e., they do not recognize the identity or class of other robots. We consider as adversarial all those robots that intentionally or accidentally try to disrupt the objective of the MRS, e.g., robots that are being hijacked by a cyber–physical attack or have experienced a fault. Under specific topological conditions defined by the notion of (r,s)-robustness, our control strategy is proven to be successful in driving the followers toward the target region, namely a hypercube, in finite time. It is also proven that the followers cannot escape the moving containment area despite the persistent influence of anonymous adversarial robots. Numerical results with a team of 44 robots are provided to corroborate the theoretical findings
Resilient Multi-Dimensional Consensus in Adversarial Environment
This paper considers the multi-dimensional consensus in networked systems,
where some of the agents might be misbehaving (or faulty). Despite the
influence of these misbehaviors, the healthy agents aim to reach an agreement
within the convex hull of their initial states. Towards this end, this paper
develops a resilient consensus algorithm, where each healthy agent sorts its
received values on one dimension, computes two "middle points" based on the
sorted values, and moves its state toward these middle points. We further show
that the computation of middle points can be efficiently achieved by linear
programming. Compared with the existing works, this approach has lower
computational complexity. Assuming that the number of malicious agents is upper
bounded, sufficient conditions on the network topology are then presented to
guarantee the achievement of resilient consensus. Some numerical examples are
finally provided to verify the theoretical results.Comment: arXiv admin note: substantial text overlap with arXiv:1911.1083
Byzantine-Resilient Distributed Optimization of Multi-Dimensional Functions
The problem of distributed optimization requires a group of agents to reach
agreement on a parameter that minimizes the average of their local cost
functions using information received from their neighbors. While there are a
variety of distributed optimization algorithms that can solve this problem,
they are typically vulnerable to malicious (or "Byzantine") agents that do not
follow the algorithm. Recent attempts to address this issue focus on single
dimensional functions, or provide analysis under certain assumptions on the
statistical properties of the functions at the agents. In this paper, we
propose a resilient distributed optimization algorithm for multi-dimensional
convex functions. Our scheme involves two filtering steps at each iteration of
the algorithm: (1) distance-based and (2) component-wise removal of extreme
states. We show that this algorithm can mitigate the impact of up to F
Byzantine agents in the neighborhood of each regular node, without knowing the
identities of the Byzantine agents in advance. In particular, we show that if
the network topology satisfies certain conditions, all of the regular states
are guaranteed to asymptotically converge to a bounded region that contains the
global minimizer.Comment: 10 pages, 1 figure. To appear in the Proceedings of the 2020 American
Control Conference, 1-3 July 2020, Denver, CO, US
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