Function approximation has experienced significant success in the field of reinforcement learning (RL). Despite a handful of progress on developing theory for nonstationary RL with function approximation under structural assumptions, existing work for nonstationary RL with general function approximation is still limited. In this work, we investigate two different approaches for nonstationary RL with general function approximation: confidence-set based algorithm and UCB-type algorithm. For the first approach, we introduce a new complexity measure called dynamic Bellman Eluder (DBE) for nonstationary MDPs, and then propose a confidence-set based algorithm SW-OPEA based on the complexity metric. SW-OPEA features the sliding window mechanism and a novel confidence set design for nonstationary MDPs. For the second approach, we propose a UCB-type algorithm LSVI-Nonstationary following the popular least-square-value-iteration (LSVI) framework, and mitigate the computational efficiency challenge of the confidence-set based approach. LSVI-Nonstationary features the restart mechanism and a new design of the bonus term to handle nonstationarity. The two proposed algorithms outperform the existing algorithms for nonstationary linear and tabular MDPs in the small variation budget setting. To the best of our knowledge, the two approaches are the first confidence-set based algorithm and UCB-type algorithm in the context of nonstationary MDPs.
{"title":"Toward General Function Approximation in Nonstationary Reinforcement Learning","authors":"Songtao Feng;Ming Yin;Ruiquan Huang;Yu-Xiang Wang;Jing Yang;Yingbin Liang","doi":"10.1109/JSAIT.2024.3381818","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3381818","url":null,"abstract":"Function approximation has experienced significant success in the field of reinforcement learning (RL). Despite a handful of progress on developing theory for nonstationary RL with function approximation under structural assumptions, existing work for nonstationary RL with general function approximation is still limited. In this work, we investigate two different approaches for nonstationary RL with general function approximation: confidence-set based algorithm and UCB-type algorithm. For the first approach, we introduce a new complexity measure called dynamic Bellman Eluder (DBE) for nonstationary MDPs, and then propose a confidence-set based algorithm SW-OPEA based on the complexity metric. SW-OPEA features the sliding window mechanism and a novel confidence set design for nonstationary MDPs. For the second approach, we propose a UCB-type algorithm LSVI-Nonstationary following the popular least-square-value-iteration (LSVI) framework, and mitigate the computational efficiency challenge of the confidence-set based approach. LSVI-Nonstationary features the restart mechanism and a new design of the bonus term to handle nonstationarity. The two proposed algorithms outperform the existing algorithms for nonstationary linear and tabular MDPs in the small variation budget setting. To the best of our knowledge, the two approaches are the first confidence-set based algorithm and UCB-type algorithm in the context of nonstationary MDPs.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"5 ","pages":"190-206"},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140820417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-27DOI: 10.1109/JSAIT.2024.3381195
Hyun-Young Park;Seung-Hyun Nam;Si-Hyeon Lee
In this paper, we propose a new class of local differential privacy (LDP) schemes based on combinatorial block designs for discrete distribution estimation. This class not only recovers many known LDP schemes in a unified framework of combinatorial block design, but also suggests a novel way of finding new schemes achieving the exactly optimal (or near-optimal) privacy-utility trade-off with lower communication costs. Indeed, we find many new LDP schemes that achieve the exactly optimal privacy-utility trade-off, with the minimum communication cost among all the unbiased or consistent schemes, for a certain set of input data size and LDP constraint. Furthermore, to partially solve the sparse existence issue of block design schemes, we consider a broader class of LDP schemes based on regular and pairwise-balanced designs, called RPBD schemes, which relax one of the symmetry requirements on block designs. By considering this broader class of RPBD schemes, we can find LDP schemes achieving near-optimal privacy-utility trade-off with reasonably low communication costs for a much larger set of input data size and LDP constraint.
{"title":"Exactly Optimal and Communication-Efficient Private Estimation via Block Designs","authors":"Hyun-Young Park;Seung-Hyun Nam;Si-Hyeon Lee","doi":"10.1109/JSAIT.2024.3381195","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3381195","url":null,"abstract":"In this paper, we propose a new class of local differential privacy (LDP) schemes based on combinatorial block designs for discrete distribution estimation. This class not only recovers many known LDP schemes in a unified framework of combinatorial block design, but also suggests a novel way of finding new schemes achieving the exactly optimal (or near-optimal) privacy-utility trade-off with lower communication costs. Indeed, we find many new LDP schemes that achieve the exactly optimal privacy-utility trade-off, with the minimum communication cost among all the unbiased or consistent schemes, for a certain set of input data size and LDP constraint. Furthermore, to partially solve the sparse existence issue of block design schemes, we consider a broader class of LDP schemes based on regular and pairwise-balanced designs, called RPBD schemes, which relax one of the symmetry requirements on block designs. By considering this broader class of RPBD schemes, we can find LDP schemes achieving near-optimal privacy-utility trade-off with reasonably low communication costs for a much larger set of input data size and LDP constraint.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"5 ","pages":"123-134"},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140621268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-26DOI: 10.1109/JSAIT.2024.3381869
Alireza Sadeghi;Gang Wang;Georgios B. Giannakis
Successful training of data-intensive deep neural networks critically rely on vast, clean, and high-quality datasets. In practice however, their reliability diminishes, particularly with noisy, outlier-corrupted data samples encountered in testing. This challenge intensifies when dealing with anonymized, heterogeneous data sets stored across geographically distinct locations due to, e.g., privacy concerns. This present paper introduces robust learning frameworks tailored for centralized and federated learning scenarios. Our goal is to fortify model resilience with a focus that lies in (i) addressing distribution shifts from training to inference time; and, (ii) ensuring test-time robustness, when a trained model may encounter outliers or adversarially contaminated test data samples. To this aim, we start with a centralized setting where the true data distribution is considered unknown, but residing within a Wasserstein ball centered at the empirical distribution. We obtain robust models by minimizing the worst-case expected loss within this ball, yielding an intractable infinite-dimensional optimization problem. Upon leverage the strong duality condition, we arrive at a tractable surrogate learning problem. We develop two stochastic primal-dual algorithms to solve the resultant problem: one for $epsilon $ -accurate convex sub-problems and another for a single gradient ascent step. We further develop a distributionally robust federated learning framework to learn robust model using heterogeneous data sets stored at distinct locations by solving per-learner’s sub-problems locally, offering robustness with modest computational overhead and considering data distribution. Numerical tests corroborate merits of our training algorithms against distributional uncertainties and adversarially corrupted test data samples.
{"title":"Learning Robust to Distributional Uncertainties and Adversarial Data","authors":"Alireza Sadeghi;Gang Wang;Georgios B. Giannakis","doi":"10.1109/JSAIT.2024.3381869","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3381869","url":null,"abstract":"Successful training of data-intensive deep neural networks critically rely on vast, clean, and high-quality datasets. In practice however, their reliability diminishes, particularly with noisy, outlier-corrupted data samples encountered in testing. This challenge intensifies when dealing with anonymized, heterogeneous data sets stored across geographically distinct locations due to, e.g., privacy concerns. This present paper introduces robust learning frameworks tailored for centralized and federated learning scenarios. Our goal is to fortify model resilience with a focus that lies in (i) addressing distribution shifts from training to inference time; and, (ii) ensuring test-time robustness, when a trained model may encounter outliers or adversarially contaminated test data samples. To this aim, we start with a centralized setting where the true data distribution is considered unknown, but residing within a Wasserstein ball centered at the empirical distribution. We obtain robust models by minimizing the worst-case expected loss within this ball, yielding an intractable infinite-dimensional optimization problem. Upon leverage the strong duality condition, we arrive at a tractable surrogate learning problem. We develop two stochastic primal-dual algorithms to solve the resultant problem: one for \u0000<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>\u0000-accurate convex sub-problems and another for a single gradient ascent step. We further develop a distributionally robust federated learning framework to learn robust model using heterogeneous data sets stored at distinct locations by solving per-learner’s sub-problems locally, offering robustness with modest computational overhead and considering data distribution. Numerical tests corroborate merits of our training algorithms against distributional uncertainties and adversarially corrupted test data samples.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"5 ","pages":"105-122"},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140619580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-22DOI: 10.1109/JSAIT.2024.3380598
Ruida Zhou;Chao Tian;Tie Liu
We provide a new information-theoretic generalization error bound that is exactly tight (i.e., matching even the constant) for the canonical quadratic Gaussian (location) problem. Most existing bounds are order-wise loose in this setting, which has raised concerns about the fundamental capability of information-theoretic bounds in reasoning the generalization behavior for machine learning. The proposed new bound adopts the individual-sample-based approach proposed by Bu et al., but also has several key new ingredients. Firstly, instead of applying the change of measure inequality on the loss function, we apply it to the generalization error function itself; secondly, the bound is derived in a conditional manner; lastly, a reference distribution is introduced. The combination of these components produces a KL-divergence-based generalization error bound. We show that although the latter two new ingredients can help make the bound exactly tight, removing them does not significantly degrade the bound, leading to an asymptotically tight mutual-information-based bound. We further consider the vector Gaussian setting, where a direct application of the proposed bound again does not lead to tight bounds except in special cases. A refined bound is then proposed by a decomposition of loss functions, leading to a tight bound for the vector setting.
我们为典型二次高斯（位置）问题提供了一种新的信息论泛化误差约束，它是完全严格的（即甚至与常数相匹配）。在这种情况下，现有的大多数约束都是有序宽松的，这引起了人们对信息论约束在推理机器学习泛化行为方面的基本能力的担忧。所提出的新边界采用了 Bu 等人提出的基于单个样本的方法，但也有几个关键的新成分。首先，我们不是在损失函数上应用度量变化不等式，而是将其应用于泛化误差函数本身；其次，约束是以条件方式导出的；最后，引入了参考分布。这些部分的组合产生了基于 KL-发散的广义误差约束。我们的研究表明，虽然后两个新成分有助于使约束精确严密，但去掉它们并不会明显降低约束，从而得到一个渐近严密的基于相互信息的约束。我们进一步考虑了矢量高斯设置，在这种情况下，除了特殊情况，直接应用所提出的约束也不会导致严格约束。然后，我们通过对损失函数进行分解，提出了一个细化的约束，从而得出了矢量环境下的严密约束。
{"title":"Exactly Tight Information-Theoretic Generalization Error Bound for the Quadratic Gaussian Problem","authors":"Ruida Zhou;Chao Tian;Tie Liu","doi":"10.1109/JSAIT.2024.3380598","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3380598","url":null,"abstract":"We provide a new information-theoretic generalization error bound that is exactly tight (i.e., matching even the constant) for the canonical quadratic Gaussian (location) problem. Most existing bounds are order-wise loose in this setting, which has raised concerns about the fundamental capability of information-theoretic bounds in reasoning the generalization behavior for machine learning. The proposed new bound adopts the individual-sample-based approach proposed by Bu et al., but also has several key new ingredients. Firstly, instead of applying the change of measure inequality on the loss function, we apply it to the generalization error function itself; secondly, the bound is derived in a conditional manner; lastly, a reference distribution is introduced. The combination of these components produces a KL-divergence-based generalization error bound. We show that although the latter two new ingredients can help make the bound exactly tight, removing them does not significantly degrade the bound, leading to an asymptotically tight mutual-information-based bound. We further consider the vector Gaussian setting, where a direct application of the proposed bound again does not lead to tight bounds except in special cases. A refined bound is then proposed by a decomposition of loss functions, leading to a tight bound for the vector setting.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"5 ","pages":"94-104"},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140606029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-21DOI: 10.1109/JSAIT.2024.3403811
Zinan Lin;Shuaiqi Wang;Vyas Sekar;Giulia Fanti
We study a setting where a data holder wishes to share data with a receiver, without revealing certain summary statistics of the data distribution (e.g., mean, standard deviation). It achieves this by passing the data through a randomization mechanism. We propose summary statistic privacy, a metric for quantifying the privacy risk of such a mechanism based on the worst-case probability of an adversary guessing the distributional secret within some threshold. Defining distortion as a worst-case Wasserstein-1 distance between the real and released data, we prove lower bounds on the tradeoff between privacy and distortion. We then propose a class of quantization mechanisms that can be adapted to different data distributions. We show that the quantization mechanism’s privacy-distortion tradeoff matches our lower bounds under certain regimes, up to small constant factors. Finally, we demonstrate on real-world datasets that the proposed quantization mechanisms achieve better privacy-distortion tradeoffs than alternative privacy mechanisms.
{"title":"Summary Statistic Privacy in Data Sharing","authors":"Zinan Lin;Shuaiqi Wang;Vyas Sekar;Giulia Fanti","doi":"10.1109/JSAIT.2024.3403811","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3403811","url":null,"abstract":"We study a setting where a data holder wishes to share data with a receiver, without revealing certain summary statistics of the data distribution (e.g., mean, standard deviation). It achieves this by passing the data through a randomization mechanism. We propose summary statistic privacy, a metric for quantifying the privacy risk of such a mechanism based on the worst-case probability of an adversary guessing the distributional secret within some threshold. Defining distortion as a worst-case Wasserstein-1 distance between the real and released data, we prove lower bounds on the tradeoff between privacy and distortion. We then propose a class of quantization mechanisms that can be adapted to different data distributions. We show that the quantization mechanism’s privacy-distortion tradeoff matches our lower bounds under certain regimes, up to small constant factors. Finally, we demonstrate on real-world datasets that the proposed quantization mechanisms achieve better privacy-distortion tradeoffs than alternative privacy mechanisms.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"5 ","pages":"369-384"},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141422569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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 and for image classification using the MNIST and CIFAR-10 datasets.
{"title":"Straggler-Resilient Differentially Private Decentralized Learning","authors":"Yauhen Yakimenka;Chung-Wei Weng;Hsuan-Yin Lin;Eirik Rosnes;Jörg Kliewer","doi":"10.1109/JSAIT.2024.3400995","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3400995","url":null,"abstract":"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 and for image classification using the MNIST and CIFAR-10 datasets.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"5 ","pages":"407-423"},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141495176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
There is an emerging interest in generating robust algorithmic recourse that would remain valid if the model is updated or changed even slightly. Towards finding robust algorithmic recourse (or counterfactual explanations), existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., $|text {Params}(M){-}text {Params}(m)|{lt }Delta $ . However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure – that we call Stability – to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential “naturally-occurring” model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine estimators of our proposed measure and derive a fundamental lower bound on the sample size required to have a precise estimate. We explore methods of using stability measures to generate robust counterfactuals that are close, realistic, and remain valid after potential model changes. This work also has interesting connections with model multiplicity, also known as the Rashomon effect.
人们对产生稳健算法追索权的兴趣日渐浓厚，即使模型更新或稍有改变，这种追索权仍然有效。为了找到稳健的算法追索（或反事实解释），现有文献通常假定原始模型 m 和新模型 M 在参数空间中是有界的，即 $|text {Params}(M){-}text {Params}(m)|{lt }Delta $ 。 然而，模型通常会在参数空间中发生显著变化，而其对给定数据集的预测或准确性却几乎没有变化。在这项工作中，我们引入了一种数学抽象，称为自然发生的模型变化，它允许参数空间的任意变化，从而限制了对位于数据流形上的点的预测变化。接下来，我们提出了一种测量方法--我们称之为 "稳定性"--来量化反事实对可微分模型（如神经网络）潜在模型变化的稳健性。我们的主要贡献在于证明，根据我们的测量方法，具有足够高稳定性值的反事实在潜在的 "自然发生的 "模型变化后将以很高的概率保持有效（利用独立高斯的 Lipschitz 函数的集中边界）。由于我们的量化方法取决于数据点周围的局部 Lipschitz 常量，而该常量并不总是可用的，因此我们还研究了我们提出的测量方法的估计值，并得出了精确估计所需的样本量的基本下限。我们探讨了使用稳定性测量方法生成稳健的反事实的方法，这些反事实是接近的、现实的，并且在潜在的模型变化后仍然有效。这项工作还与模型多重性（又称罗生门效应）有着有趣的联系。
{"title":"Robust Algorithmic Recourse Under Model Multiplicity With Probabilistic Guarantees","authors":"Faisal Hamman;Erfaun Noorani;Saumitra Mishra;Daniele Magazzeni;Sanghamitra Dutta","doi":"10.1109/JSAIT.2024.3401407","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3401407","url":null,"abstract":"There is an emerging interest in generating robust algorithmic recourse that would remain valid if the model is updated or changed even slightly. Towards finding robust algorithmic recourse (or counterfactual explanations), existing literature often assumes that the original model \u0000<italic>m</i>\u0000 and the new model \u0000<italic>M</i>\u0000 are bounded in the parameter space, i.e., \u0000<inline-formula> <tex-math>$|text {Params}(M){-}text {Params}(m)|{lt }Delta $ </tex-math></inline-formula>\u0000. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed \u0000<italic>naturally-occurring</i>\u0000 model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure – that we call \u0000<italic>Stability</i>\u0000 – to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of \u0000<italic>Stability</i>\u0000 as defined by our measure will remain valid after potential “naturally-occurring” model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine estimators of our proposed measure and derive a fundamental lower bound on the sample size required to have a precise estimate. We explore methods of using stability measures to generate robust counterfactuals that are close, realistic, and remain valid after potential model changes. This work also has interesting connections with model multiplicity, also known as the Rashomon effect.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"5 ","pages":"357-368"},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141435351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-09DOI: 10.1109/JSAIT.2024.3397305
Shahab Asoodeh;Huanyu Zhang
We investigate the contraction properties of locally differentially private mechanisms. More specifically, we derive tight upper bounds on the divergence between $P{mathsf K}$ and $Q{mathsf K}$ output distributions of an $varepsilon $ -LDP mechanism $mathsf K$ in terms of a divergence between the corresponding input distributions P and Q, respectively. Our first main technical result presents a sharp upper bound on the $chi ^{2}$ -divergence $chi ^{2}(P{mathsf K}|Q{mathsf K})$ in terms of $chi ^{2}(P|Q)$ and $varepsilon $ . We also show that the same result holds for a large family of divergences, including KL-divergence and squared Hellinger distance. The second main technical result gives an upper bound on $chi ^{2}(P{mathsf K}|Q{mathsf K})$ in terms of total variation distance ${textsf {TV}}(P, Q)$ and $varepsilon $ . We then utilize these bounds to establish locally private versions of the van Trees inequality, Le Cam’s, Assouad’s, and the mutual information methods —powerful tools for bounding minimax estimation risks. These results are shown to lead to tighter privacy analyses than the state-of-the-arts in several statistical problems such as entropy and discrete distribution estimation, non-parametric density estimation, and hypothesis testing.
{"title":"Contraction of Locally Differentially Private Mechanisms","authors":"Shahab Asoodeh;Huanyu Zhang","doi":"10.1109/JSAIT.2024.3397305","DOIUrl":"https://doi.org/10.1109/JSAIT.2024.3397305","url":null,"abstract":"We investigate the contraction properties of locally differentially private mechanisms. More specifically, we derive tight upper bounds on the divergence between \u0000<inline-formula> <tex-math>$P{mathsf K}$ </tex-math></inline-formula>\u0000 and \u0000<inline-formula> <tex-math>$Q{mathsf K}$ </tex-math></inline-formula>\u0000 output distributions of an \u0000<inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>\u0000-LDP mechanism \u0000<inline-formula> <tex-math>$mathsf K$ </tex-math></inline-formula>\u0000 in terms of a divergence between the corresponding input distributions P and Q, respectively. Our first main technical result presents a sharp upper bound on the \u0000<inline-formula> <tex-math>$chi ^{2}$ </tex-math></inline-formula>\u0000-divergence \u0000<inline-formula> <tex-math>$chi ^{2}(P{mathsf K}|Q{mathsf K})$ </tex-math></inline-formula>\u0000 in terms of \u0000<inline-formula> <tex-math>$chi ^{2}(P|Q)$ </tex-math></inline-formula>\u0000 and \u0000<inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>\u0000. We also show that the same result holds for a large family of divergences, including KL-divergence and squared Hellinger distance. The second main technical result gives an upper bound on \u0000<inline-formula> <tex-math>$chi ^{2}(P{mathsf K}|Q{mathsf K})$ </tex-math></inline-formula>\u0000 in terms of total variation distance \u0000<inline-formula> <tex-math>${textsf {TV}}(P, Q)$ </tex-math></inline-formula>\u0000 and \u0000<inline-formula> <tex-math>$varepsilon $ </tex-math></inline-formula>\u0000. We then utilize these bounds to establish locally private versions of the van Trees inequality, Le Cam’s, Assouad’s, and the mutual information methods —powerful tools for bounding minimax estimation risks. These results are shown to lead to tighter privacy analyses than the state-of-the-arts in several statistical problems such as entropy and discrete distribution estimation, non-parametric density estimation, and hypothesis testing.","PeriodicalId":73295,"journal":{"name":"IEEE journal on selected areas in information theory","volume":"5 ","pages":"385-395"},"PeriodicalIF":0.0,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141494817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-09DOI: 10.1109/JSAIT.2024.3397741
Lucas Monteiro Paes;Ananda Theertha Suresh;Alex Beutel;Flavio P. Calmon;Ahmad Beirami
Machine learning (ML) models used in prediction and classification tasks may display performance disparities across population groups determined by sensitive attributes (e.g., race, sex, age). We consider the problem of evaluating the performance of a fixed ML model across population groups defined by multiple sensitive attributes (e.g., race and sex and age). Here, the sample complexity for estimating the worst-case performance gap across groups (e.g., the largest difference in error rates) increases exponentially with the number of group-denoting sensitive attributes. To address this issue, we propose an approach to test for performance disparities based on Conditional Value-at-Risk (CVaR). By allowing a small probabilistic slack on the groups over which a model has approximately equal performance, we show that the sample complexity required for discovering performance violations is reduced exponentially to be at most upper bounded by the square root of the number of groups. As a byproduct of our analysis, when the groups are weighted by a specific prior distribution, we show that Rényi entropy of order 2/3 of the prior distribution captures the sample complexity of the proposed CVaR test algorithm. Finally, we also show that there exists a non-i.i.d. data collection strategy that results in a sample complexity independent of the number of groups.
在预测和分类任务中使用的机器学习（ML）模型可能会在由敏感属性（如种族、性别、年龄）决定的人群中显示出性能差异。我们考虑的问题是，如何评估固定 ML 模型在由多个敏感属性（如种族、性别和年龄）决定的人群中的性能。在这种情况下，估计不同群体间最坏情况下的性能差距（例如，误差率的最大差异）的样本复杂度会随着群体敏感属性的数量呈指数增长。为了解决这个问题，我们提出了一种基于条件风险值（CVaR）的性能差距测试方法。通过允许模型在性能大致相同的组别上有较小的概率松弛，我们证明发现性能违规所需的样本复杂度会以指数形式降低，最多为组别数量平方根的上限。作为我们分析的副产品，当各组由特定的先验分布加权时，我们证明先验分布的 2/3 阶雷尼熵可以捕捉到所提 CVaR 检验算法的样本复杂度。最后，我们还证明，存在一种非 i.i.d. 数据收集策略，其样本复杂度与组数无关。
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Pub Date : 2024-03-06DOI: 10.1109/JSAIT.2024.3397187
Mark Beliaev;Payam Delgosha;Hamed Hassani;Ramtin Pedarsani
Over the past two decades, the rise in adoption of neural networks has surged in parallel with their performance. Concurrently, we have observed the inherent fragility of these prediction models: small changes to the inputs can induce classification errors across entire datasets. In the following study, we examine perturbations constrained by the $ell _{0}$ –norm, a potent attack model in the domains of computer vision, malware detection, and natural language processing. To combat this adversary, we introduce a novel defense technique comprised of two components: “truncation” and “adversarial training”. Subsequently, we conduct a theoretical analysis of the Gaussian mixture setting and establish the asymptotic optimality of our proposed defense. Based on this obtained insight, we broaden the application of our technique to neural networks. Lastly, we empirically validate our results in the domain of computer vision, demonstrating substantial enhancements in the robust classification error of neural networks.
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