VALID: a Validated Algorithm for Learning in Decentralized Networks with Possible Adversarial Presence

We introduce the paradigm of validated decentralized learning for undirected networks with heterogeneous data and possible adversarial infiltration. We require (a) convergence to a global empirical loss minimizer when adversaries are absent, and (b) either detection of adversarial presence of convergence to an admissible consensus irrespective of the adversarial configuration. To this end, we propose the VALID protocol which, to the best of our knowledge, is the first to achieve a validated learning guarantee. Moreover, VALID offers an O(1/T) convergence rate (under pertinent regularity assumptions), and computational and communication complexities comparable to non-adversarial distributed stochastic gradient descent. Remarkably, VALID retains optimal performance metrics in adversary-free environments, sidestepping the robustness penalties observed in prior byzantine-robust methods. A distinctive aspect of our study is a heterogeneity metric based on the norms of individual agents' gradients computed at the global empirical loss minimizer. This not only provides a natural statistic for detecting significant byzantine disruptions but also allows us to prove the optimality of VALID in wide generality. Lastly, our numerical results reveal that, in the absence of adversaries, VALID converges faster than state-of-the-art byzantine robust algorithms, while when adversaries are present, VALID terminates with each honest either converging to an admissible consensus of declaring adversarial presence in the network.

Straggler-Resilient Differentially-Private Decentralized Learning

We consider the straggler problem in decentralized learning over a logical ring while preserving user data privacy. Especially, we extend the recently proposed framework of differential privacy (DP) amplification by decentralization by Cyffers and Bellet to include overall training latency--comprising both computation and communication latency. Analytical results on both the convergence speed and the DP level are derived for both a skipping scheme (which ignores the stragglers after a timeout) and a baseline scheme that waits for each node to finish before the training continues. A trade-off between overall training latency, accuracy, and privacy, parameterized by the timeout of the skipping scheme, is identified and empirically validated for logistic regression on a real-world dataset.

Generative Adversarial User Privacy in Lossy Single-Server Information Retrieval

We consider the problem of information retrieval from a dataset of files stored on a single server under both a user distortion and a user privacy constraint. Specifically, a user requesting a file from the dataset should be able to reconstruct the requested file with a prescribed distortion, and in addition, the identity of the requested file should be kept private from the server with a prescribed privacy level. The proposed model can be seen as an extension of the well-known concept of private information retrieval by allowing for distortion in the retrieval process and relaxing the perfect privacy requirement. We initiate the study of the tradeoff between download rate, distortion, and user privacy leakage, and show that the optimal rate-distortion-leakage tradeoff is convex and that in the limit of large file sizes this allows for a concise information-theoretical formulation in terms of mutual information. Moreover, we propose a new data-driven framework by leveraging recent advancements in generative adversarial models which allows a user to learn efficient schemes in terms of download rate from the data itself. Learning the scheme is formulated as a constrained minimax game between a user which desires to keep the identity of the requested file private and an adversary that tries to infer which file the user is interested in under a distortion constraint. In general, guaranteeing a certain privacy level leads to a higher rate-distortion tradeoff curve, and hence a sacrifice in either download rate or distortion. We evaluate the performance of the scheme on a synthetic Gaussian dataset as well as on the MNIST and CIFAR-$10$ datasets. For the MNIST dataset, the data-driven approach significantly outperforms a proposed general achievable scheme combining source coding with the download of multiple files, while for CIFAR-$10$ the performances are comparable.