Decentralized optimization is gaining increased traction due to its widespread applications in large-scale machine learning and multi-agent systems. The same mechanism that enables its success, i.e., information sharing among participating agents, however, also leads to the disclosure of individual agents' private information, which is unacceptable when sensitive data are involved. As differential privacy is becoming a de facto standard for privacy preservation, recently results have emerged integrating differential privacy with distributed optimization. However, directly incorporating differential privacy design in existing distributed optimization approaches significantly compromises optimization accuracy. In this paper, we propose to redesign and tailor gradient methods for differentially-private distributed optimization, and propose two differential-privacy oriented gradient methods that can ensure both rigorous epsilon-differential privacy and optimality. The first algorithm is based on static-consensus based gradient methods, and the second algorithm is based on dynamic-consensus (gradient-tracking) based distributed optimization methods and, hence, is applicable to general directed interaction graph topologies. Both algorithms can simultaneously ensure almost sure convergence to an optimal solution and a finite privacy budget, even when the number of iterations goes to infinity. To our knowledge, this is the first time that both goals are achieved simultaneously. Numerical simulations using a distributed estimation problem and experimental results on a benchmark dataset confirm the effectiveness of the proposed approaches.
相關內容
Motivated by privacy concerns in long-term longitudinal studies in medical and social science research, we study the problem of continually releasing differentially private synthetic data. We introduce a model where, in every time step, each individual reports a new data element, and the goal of the synthesizer is to incrementally update a synthetic dataset to capture a rich class of statistical properties. We give continual synthetic data generation algorithms that preserve two basic types of queries: fixed time window queries and cumulative time queries. We show nearly tight upper bounds on the error rates of these algorithms and demonstrate their empirical performance on realistically sized datasets from the U.S. Census Bureau's Survey of Income and Program Participation.
In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the boundary control acts on the system. This peculiar formulation might benefit from model order reduction. Indeed, fast and reliable simulations of this model can be of utmost usefulness in many applied fields, such as geophysics and energy engineering. However, varying boundary control features very complicated and diversified parametric behaviour for the state and adjoint variables. The state solution, for example, changing the boundary control parameter, might feature transport phenomena. Moreover, the problem loses its affine structure. It is well known that classical model order reduction techniques fail in this setting, both in accuracy and in efficiency. Thus, we propose reduced approaches inspired by the ones used when dealing with wave-like phenomena. Indeed, we compare standard proper orthogonal decomposition with two tailored strategies: geometric recasting and local proper orthogonal decomposition. Geometric recasting solves the optimization system in a reference domain simplifying the problem at hand avoiding hyper-reduction, while local proper orthogonal decomposition builds local bases to increase the accuracy of the reduced solution in very general settings (where geometric recasting is unfeasible). We compare the various approaches on two different numerical experiments based on geometries of increasing complexity.
We present a distribution optimization framework that significantly improves confidence bounds for various risk measures compared to previous methods. Our framework encompasses popular risk measures such as the entropic risk measure, conditional value at risk (CVaR), spectral risk measure, distortion risk measure, equivalent certainty, and rank-dependent expected utility, which are well established in risk-sensitive decision-making literature. To achieve this, we introduce two estimation schemes based on concentration bounds derived from the empirical distribution, specifically using either the Wasserstein distance or the supremum distance. Unlike traditional approaches that add or subtract a confidence radius from the empirical risk measures, our proposed schemes evaluate a specific transformation of the empirical distribution based on the distance. Consequently, our confidence bounds consistently yield tighter results compared to previous methods. We further verify the efficacy of the proposed framework by providing tighter problem-dependent regret bound for the CVaR bandit.
Privacy is a central challenge for systems that learn from sensitive data sets, especially when a system's outputs must be continuously updated to reflect changing data. We consider the achievable error for the differentially private continual release of a basic statistic -- the number of distinct items -- in a stream where items may be both inserted and deleted (the turnstile model). With only insertions, existing algorithms have additive error just polylogarithmic in the length of the stream $T$. We uncover a much richer landscape in the turnstile model, even without considering memory restrictions. We show that any differentially private mechanism that handles insertions and deletions has worst-case additive error at least $T^{1/4}$ even under a relatively weak, event-level privacy definition. Then, we identify a property of the input stream, its maximum flippancy, that is low for natural data streams and for which one can give tight parameterized error guarantees. Specifically, the maximum flippancy is the largest number of times the count of a single item changes from a positive number to zero over the course of the stream. We present an item-level differentially private mechanism that, for all turnstile streams with maximum flippancy $w$, continually outputs the number of distinct elements with an $O(\sqrt{w} \cdot \mathsf{poly}\log T)$ additive error, without requiring prior knowledge of $w$. This is the best achievable error bound that depends only on $w$, for a large range of values of $w$. When $w$ is small, our mechanism provides similar error guarantees to the polylogarithmic in $T$ guarantees in the insertion-only setting, bypassing the hardness in the turnstile model.
Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in \mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional independence testing under the constraint of differential privacy. We design two private CI testing procedures: one based on the generalized covariance measure of Shah and Peters (2020) and another based on the conditional randomization test of Cand\`es et al. (2016) (under the model-X assumption). We provide theoretical guarantees on the performance of our tests and validate them empirically. These are the first private CI tests that work for the general case when $Z$ is continuous.
In this paper, we study the well-known "Heavy Ball" method for convex and nonconvex optimization introduced by Polyak in 1964, and establish its convergence under a variety of situations. Traditionally, most algorithms use "full-coordinate update," that is, at each step, every component of the argument is updated. However, when the dimension of the argument is very high, it is more efficient to update some but not all components of the argument at each iteration. We refer to this as "batch updating" in this paper. When gradient-based algorithms are used together with batch updating, in principle it is sufficient to compute only those components of the gradient for which the argument is to be updated. However, if a method such as backpropagation is used to compute these components, computing only some components of gradient does not offer much savings over computing the entire gradient. Therefore, to achieve a noticeable reduction in CPU usage at each step, one can use first-order differences to approximate the gradient. The resulting estimates are biased, and also have unbounded variance. Thus some delicate analysis is required to ensure that the HB algorithm converge when batch updating is used instead of full-coordinate updating, and/or approximate gradients are used instead of true gradients. In this paper, we establish the almost sure convergence of the iterations to the stationary point(s) of the objective function under suitable conditions; in addition, we also derive upper bounds on the rate of convergence. To the best of our knowledge, there is no other paper that combines all of these features. This paper is dedicated to the memory of Boris Teodorovich Polyak
This paper presents a personalized graph federated learning (PGFL) framework in which distributedly connected servers and their respective edge devices collaboratively learn device or cluster-specific models while maintaining the privacy of every individual device. The proposed approach exploits similarities among different models to provide a more relevant experience for each device, even in situations with diverse data distributions and disproportionate datasets. Furthermore, to ensure a secure and efficient approach to collaborative personalized learning, we study a variant of the PGFL implementation that utilizes differential privacy, specifically zero-concentrated differential privacy, where a noise sequence perturbs model exchanges. Our mathematical analysis shows that the proposed privacy-preserving PGFL algorithm converges to the optimal cluster-specific solution for each cluster in linear time. It also shows that exploiting similarities among clusters leads to an alternative output whose distance to the original solution is bounded, and that this bound can be adjusted by modifying the algorithm's hyperparameters. Further, our analysis shows that the algorithm ensures local differential privacy for all clients in terms of zero-concentrated differential privacy. Finally, the performance of the proposed PGFL algorithm is examined by performing numerical experiments in the context of regression and classification using synthetic data and the MNIST dataset.
The Internet of Things brings new ways to collect privacy-sensitive data from billions of devices. Well-tailored distributed ledger technologies (DLTs) can provide high transaction processing capacities to IoT devices in a decentralized fashion. However, privacy aspects are often neglected or unsatisfying, with a focus mainly on performance and security. In this paper, we introduce decentralized usage control mechanisms to empower IoT devices to control the data they generate. Usage control defines obligations, i.e., actions to be fulfilled to be granted access, and conditions on the system in addition to data dissemination control. The originality of this paper is to consider the usage control system as a component of distributed ledger networks, instead of an external tool. With this integration, both technologies work in synergy, benefiting their privacy, security and performance. We evaluated the performance improvements of integration using the IOTA technology, particularly suitable due to the participation of small devices in the consensus. The results of the tests on a private network show an approximate 90% decrease of the time needed for the UCS to push a transaction and make its access decision in the integrated setting, regardless of the number of nodes in the network.
Hyperparameter optimization, also known as hyperparameter tuning, is a widely recognized technique for improving model performance. Regrettably, when training private ML models, many practitioners often overlook the privacy risks associated with hyperparameter optimization, which could potentially expose sensitive information about the underlying dataset. Currently, the sole existing approach to allow privacy-preserving hyperparameter optimization is to uniformly and randomly select hyperparameters for a number of runs, subsequently reporting the best-performing hyperparameter. In contrast, in non-private settings, practitioners commonly utilize "adaptive" hyperparameter optimization methods such as Gaussian process-based optimization, which select the next candidate based on information gathered from previous outputs. This substantial contrast between private and non-private hyperparameter optimization underscores a critical concern. In our paper, we introduce DP-HyPO, a pioneering framework for "adaptive" private hyperparameter optimization, aiming to bridge the gap between private and non-private hyperparameter optimization. To accomplish this, we provide a comprehensive differential privacy analysis of our framework. Furthermore, we empirically demonstrate the effectiveness of DP-HyPO on a diverse set of real-world and synthetic datasets.
This paper aims to mitigate straggler effects in synchronous distributed learning for multi-agent reinforcement learning (MARL) problems. Stragglers arise frequently in a distributed learning system, due to the existence of various system disturbances such as slow-downs or failures of compute nodes and communication bottlenecks. To resolve this issue, we propose a coded distributed learning framework, which speeds up the training of MARL algorithms in the presence of stragglers, while maintaining the same accuracy as the centralized approach. As an illustration, a coded distributed version of the multi-agent deep deterministic policy gradient(MADDPG) algorithm is developed and evaluated. Different coding schemes, including maximum distance separable (MDS)code, random sparse code, replication-based code, and regular low density parity check (LDPC) code are also investigated. Simulations in several multi-robot problems demonstrate the promising performance of the proposed framework.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191