arXiv subjects

Maximilian Egger

Publications and source records attributed to Maximilian Egger.

24 records · Page 2Linked to original sources

arXiv2023

Sparsity and Privacy in Secret Sharing: A Fundamental Trade-Off

This work investigates the design of sparse secret sharing schemes that encode a sparse private matrix into sparse shares. This investigation is motivated by distributed computing, where the multiplication of sparse and private matrices is moved from a computationally weak main node to untrusted worker machines. Classical secret-sharing schemes produce dense shares. However, sparsity can help speed up the computation. We show that, for matrices with i.i.d. entries, sparsity in the shares comes at a fundamental cost of weaker privacy. We derive a fundamental tradeoff between sparsity and privacy and construct optimal sparse secret sharing schemes that produce shares that leak the minimum amount of information for a desired sparsity of the shares. We apply our schemes to distributed sparse and private matrix multiplication schemes with no colluding workers while tolerating stragglers. For the setting of two non-communicating clusters of workers, we design a sparse one-time pad so that no private information is leaked to a cluster of untrusted and colluding workers, and the shares with bounded but non-zero leakage are assigned to a cluster of partially trusted workers. We conclude by discussing the necessity of using permutations for matrices with correlated entries.

cs.CR↗

arXiv2023

Sparse and Private Distributed Matrix Multiplication with Straggler Tolerance

This paper considers the problem of outsourcing the multiplication of two private and sparse matrices to untrusted workers. Secret sharing schemes can be used to tolerate stragglers and guarantee information-theoretic privacy of the matrices. However, traditional secret sharing schemes destroy all sparsity in the offloaded computational tasks. Since exploiting the sparse nature of matrices was shown to speed up the multiplication process, preserving the sparsity of the input matrices in the computational tasks sent to the workers is desirable. It was recently shown that sparsity can be guaranteed at the expense of a weaker privacy guarantee. Sparse secret sharing schemes with only two output shares were constructed. In this work, we construct sparse secret sharing schemes that generalize Shamir's secret sharing schemes for a fixed threshold $t=2$ and an arbitrarily large number of shares. We design our schemes to provide the strongest privacy guarantee given a desired sparsity of the shares under some mild assumptions. We show that increasing the number of shares, i.e., increasing straggler tolerance, incurs a degradation of the privacy guarantee. However, this degradation is negligible when the number of shares is comparably small to the cardinality of the input alphabet.

cs.IT↗

arXiv2023

Fast and Straggler-Tolerant Distributed SGD with Reduced Computation Load

In distributed machine learning, a central node outsources computationally expensive calculations to external worker nodes. The properties of optimization procedures like stochastic gradient descent (SGD) can be leveraged to mitigate the effect of unresponsive or slow workers called stragglers, that otherwise degrade the benefit of outsourcing the computation. This can be done by only waiting for a subset of the workers to finish their computation at each iteration of the algorithm. Previous works proposed to adapt the number of workers to wait for as the algorithm evolves to optimize the speed of convergence. In contrast, we model the communication and computation times using independent random variables. Considering this model, we construct a novel scheme that adapts both the number of workers and the computation load throughout the run-time of the algorithm. Consequently, we improve the convergence speed of distributed SGD while significantly reducing the computation load, at the expense of a slight increase in communication load.

cs.DC↗

arXiv2022

Nested Gradient Codes for Straggler Mitigation in Distributed Machine Learning

We consider distributed learning in the presence of slow and unresponsive worker nodes, referred to as stragglers. In order to mitigate the effect of stragglers, gradient coding redundantly assigns partial computations to the worker such that the overall result can be recovered from only the non-straggling workers. Gradient codes are designed to tolerate a fixed number of stragglers. Since the number of stragglers in practice is random and unknown a priori, tolerating a fixed number of stragglers can yield a sub-optimal computation load and can result in higher latency. We propose a gradient coding scheme that can tolerate a flexible number of stragglers by carefully concatenating gradient codes for different straggler tolerance. By proper task scheduling and small additional signaling, our scheme adapts the computation load of the workers to the actual number of stragglers. We analyze the latency of our proposed scheme and show that it has a significantly lower latency than gradient codes.

cs.IT↗

arXiv2022

Cost-Efficient Distributed Learning via Combinatorial Multi-Armed Bandits

We consider the distributed SGD problem, where a main node distributes gradient calculations among $n$ workers. By assigning tasks to all the workers and waiting only for the $k$ fastest ones, the main node can trade-off the algorithm's error with its runtime by gradually increasing $k$ as the algorithm evolves. However, this strategy, referred to as adaptive $k$-sync, neglects the cost of unused computations and of communicating models to workers that reveal a straggling behavior. We propose a cost-efficient scheme that assigns tasks only to $k$ workers, and gradually increases $k$. We introduce the use of a combinatorial multi-armed bandit model to learn which workers are the fastest while assigning gradient calculations. Assuming workers with exponentially distributed response times parameterized by different means, we give empirical and theoretical guarantees on the regret of our strategy, i.e., the extra time spent to learn the mean response times of the workers. Furthermore, we propose and analyze a strategy applicable to a large class of response time distributions. Compared to adaptive $k$-sync, our scheme achieves significantly lower errors with the same computational efforts and less downlink communication while being inferior in terms of speed.

cs.IT↗

arXiv2022

Efficient Private Storage of Sparse Machine Learning Data

We consider the problem of maintaining sparsity in private distributed storage of confidential machine learning data. In many applications, e.g., face recognition, the data used in machine learning algorithms is represented by sparse matrices which can be stored and processed efficiently. However, mechanisms maintaining perfect information-theoretic privacy require encoding the sparse matrices into randomized dense matrices. It has been shown that, under some restrictions on the storage nodes, sparsity can be maintained at the expense of relaxing the perfect information-theoretic privacy requirement, i.e., allowing some information leakage. In this work, we lift the restrictions imposed on the storage nodes and show that there exists a trade-off between sparsity and the achievable privacy guarantees. We focus on the setting of non-colluding nodes and construct a coding scheme that encodes the sparse input matrices into matrices with the desired sparsity level while limiting the information leakage.

cs.IT↗