Sebastien Rouault

Rachid Guerraoui, Nirupam Gupta, Rafael Pinot et al.

Privacy and Byzantine resilience (BR) are two crucial requirements of modern-day distributed machine learning. The two concepts have been extensively studied individually but the question of how to combine them effectively remains unanswered. This paper contributes to addressing this question by studying the extent to which the distributed SGD algorithm, in the standard parameter-server architecture, can learn an accurate model despite (a) a fraction of the workers being malicious (Byzantine), and (b) the other fraction, whilst being honest, providing noisy information to the server to ensure differential privacy (DP). We first observe that the integration of standard practices in DP and BR is not straightforward. In fact, we show that many existing results on the convergence of distributed SGD under Byzantine faults, especially those relying on $(α,f)$-Byzantine resilience, are rendered invalid when honest workers enforce DP. To circumvent this shortcoming, we revisit the theory of $(α,f)$-BR to obtain an approximate convergence guarantee. Our analysis provides key insights on how to improve this guarantee through hyperparameter optimization. Essentially, our theoretical and empirical results show that (1) an imprudent combination of standard approaches to DP and BR might be fruitless, but (2) by carefully re-tuning the learning algorithm, we can obtain reasonable learning accuracy while simultaneously guaranteeing DP and BR.

El Mahdi El Mhamdi, Rachid Guerraoui, Sebastien Rouault

With the development of neural networks based machine learning and their usage in mission critical applications, voices are rising against the \textit{black box} aspect of neural networks as it becomes crucial to understand their limits and capabilities. With the rise of neuromorphic hardware, it is even more critical to understand how a neural network, as a distributed system, tolerates the failures of its computing nodes, neurons, and its communication channels, synapses. Experimentally assessing the robustness of neural networks involves the quixotic venture of testing all the possible failures, on all the possible inputs, which ultimately hits a combinatorial explosion for the first, and the impossibility to gather all the possible inputs for the second. In this paper, we prove an upper bound on the expected error of the output when a subset of neurons crashes. This bound involves dependencies on the network parameters that can be seen as being too pessimistic in the average case. It involves a polynomial dependency on the Lipschitz coefficient of the neurons activation function, and an exponential dependency on the depth of the layer where a failure occurs. We back up our theoretical results with experiments illustrating the extent to which our prediction matches the dependencies between the network parameters and robustness. Our results show that the robustness of neural networks to the average crash can be estimated without the need to neither test the network on all failure configurations, nor access the training set used to train the network, both of which are practically impossible requirements.