Coordination-Free Byzantine Replication with Minimal Communication Costs

State-of-the-art fault-tolerant and federated data management systems rely on fully-replicated designs in which all participants have equivalent roles. Consequently, these systems have only limited scalability and are ill-suited for high-performance data management. As an alternative, we propose a hierarchical design in which a Byzantine cluster manages data, while an arbitrary number of learners can reliable learn these updates and use the corresponding data. To realize our design, we propose the delayed-replication algorithm, an efficient solution to the Byzantine learner problem that is central to our design. The delayed-replication algorithm is coordination-free, scalable, and has minimal communication cost for all participants involved. In doing so, the delayed-broadcast algorithm opens the door to new high-performance fault-tolerant and federated data management systems. To illustrate this, we show that the delayed-replication algorithm is not only useful to support specialized learners, but can also be used to reduce the overall communication cost of permissioned blockchains and to improve their storage scalability

Byzantine Stochastic Gradient Descent

This paper studies the problem of distributed stochastic optimization in an adversarial setting where, out of the $m$ machines which allegedly compute stochastic gradients every iteration, an $\alpha$-fraction are Byzantine, and can behave arbitrarily and adversarially. Our main result is a variant of stochastic gradient descent (SGD) which finds $\varepsilon$-approximate minimizers of convex functions in $T = \tilde{O}\big( \frac{1}{\varepsilon^2 m} + \frac{\alpha^2}{\varepsilon^2} \big)$ iterations. In contrast, traditional mini-batch SGD needs $T = O\big( \frac{1}{\varepsilon^2 m} \big)$ iterations, but cannot tolerate Byzantine failures. Further, we provide a lower bound showing that, up to logarithmic factors, our algorithm is information-theoretically optimal both in terms of sampling complexity and time complexity

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 $\frac{1}{3}$ Byzantine parameter servers and $\frac{1}{3}$ 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