Adapting to Linear Separable Subsets with Large-Margin in Differentially Private Learning

• URL: http://arxiv.org/abs/2505.24737v1
• Date: Fri, 30 May 2025 15:56:58 GMT
• Title: Adapting to Linear Separable Subsets with Large-Margin in Differentially Private Learning
• Authors: Erchi Wang, Yuqing Zhu, Yu-Xiang Wang,
• Abstract summary: This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification.<n>We obtain an efficient $(varepsilon,delta)$-DP algorithm with an empirical zero-one risk bound.<n>Our algorithm is highly adaptive because it does not require knowing the margin parameter $gamma$ or outlier subset $S_mathrmout$.
• Score: 15.042594878446574
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification. We obtain an efficient $(\varepsilon,\delta)$-DP algorithm with an empirical zero-one risk bound of $\tilde{O}\left(\frac{1}{\gamma^2\varepsilon n} + \frac{|S_{\mathrm{out}}|}{\gamma n}\right)$ where $n$ is the number of data points, $S_{\mathrm{out}}$ is an arbitrary subset of data one can remove and $\gamma$ is the margin of linear separation of the remaining data points (after $S_{\mathrm{out}}$ is removed). Here, $\tilde{O}(\cdot)$ hides only logarithmic terms. In the agnostic case, we improve the existing results when the number of outliers is small. Our algorithm is highly adaptive because it does not require knowing the margin parameter $\gamma$ or outlier subset $S_{\mathrm{out}}$. We also derive a utility bound for the advanced private hyperparameter tuning algorithm.

Related papers

• Guessing Efficiently for Constrained Subspace Approximation [49.83981776254246]
  We introduce a general framework for constrained subspace approximation.<n>We show it provides new algorithms for partition-constrained subspace approximation with applications to $k$-means clustering, and projected non-negative matrix factorization.
  arXiv  Detail & Related papers  (2025-04-29T15:56:48Z)
• Sample and Computationally Efficient Robust Learning of Gaussian Single-Index Models [37.42736399673992]
  A single-index model (SIM) is a function of the form $sigma(mathbfwast cdot mathbfx)$, where $sigma: mathbbR to mathbbR$ is a known link function and $mathbfwast$ is a hidden unit vector. We show that a proper learner attains $L2$-error of $O(mathrmOPT)+epsilon$, where $
  arXiv  Detail & Related papers  (2024-11-08T17:10:38Z)
• Distribution-Independent Regression for Generalized Linear Models with Oblivious Corruptions [49.69852011882769]
  We show the first algorithms for the problem of regression for generalized linear models (GLMs) in the presence of additive oblivious noise. We present an algorithm that tackles newthis problem in its most general distribution-independent setting. This is the first newalgorithmic result for GLM regression newwith oblivious noise which can handle more than half the samples being arbitrarily corrupted.
  arXiv  Detail & Related papers  (2023-09-20T21:41:59Z)
• Differentially Private Stochastic Gradient Descent with Low-Noise [49.981789906200035]
  Modern machine learning algorithms aim to extract fine-grained information from data to provide accurate predictions, which often conflicts with the goal of privacy protection. This paper addresses the practical and theoretical importance of developing privacy-preserving machine learning algorithms that ensure good performance while preserving privacy.
  arXiv  Detail & Related papers  (2022-09-09T08:54:13Z)
• Best Policy Identification in Linear MDPs [70.57916977441262]
  We investigate the problem of best identification in discounted linear Markov+Delta Decision in the fixed confidence setting under a generative model. The lower bound as the solution of an intricate non- optimization program can be used as the starting point to devise such algorithms.
  arXiv  Detail & Related papers  (2022-08-11T04:12:50Z)
• Sketching Algorithms and Lower Bounds for Ridge Regression [65.0720777731368]
  We give a sketching-based iterative algorithm that computes $1+varepsilon$ approximate solutions for the ridge regression problem. We also show that this algorithm can be used to give faster algorithms for kernel ridge regression.
  arXiv  Detail & Related papers  (2022-04-13T22:18:47Z)
• The Curse of Passive Data Collection in Batch Reinforcement Learning [82.6026077420886]
  In high stake applications, active experimentation may be considered too risky and thus data are often collected passively. While in simple cases, such as in bandits, passive and active data collection are similarly effective, the price of passive sampling can be much higher when collecting data from a system with controlled states.
  arXiv  Detail & Related papers  (2021-06-18T07:54:23Z)
• Infinite-Horizon Offline Reinforcement Learning with Linear Function Approximation: Curse of Dimensionality and Algorithm [46.36534144138337]
  In this paper, we investigate the sample complexity of policy evaluation in offline reinforcement learning. Under the low distribution shift assumption, we show that there is an algorithm that needs at most $Oleft(maxleft fracleftVert thetapirightVert _24varepsilon4logfracddelta,frac1varepsilon2left(d+logfrac1deltaright)right right)$ samples to approximate the
  arXiv  Detail & Related papers  (2021-03-17T18:18:57Z)
• Private Stochastic Convex Optimization: Optimal Rates in $\ell_1$ Geometry [69.24618367447101]
  Up to logarithmic factors the optimal excess population loss of any $(varepsilon,delta)$-differently private is $sqrtlog(d)/n + sqrtd/varepsilon n.$ We show that when the loss functions satisfy additional smoothness assumptions, the excess loss is upper bounded (up to logarithmic factors) by $sqrtlog(d)/n + (log(d)/varepsilon n)2/3.
  arXiv  Detail & Related papers  (2021-03-02T06:53:44Z)
• Non-Convex Compressed Sensing with Training Data [0.0]
  We find the solution of the original problem $Ax = b$ with high probability in the range of a one layer linear neural network with comparatively few assumptions on the matrix $A$. In this paper, we consider an alternative, where instead of suitable initial values we are provided with extra training problems $Ax = B_l$, $l=1, dots, p$ that are related to our compressed sensing problem.
  arXiv  Detail & Related papers  (2021-01-20T20:30:59Z)
• Subspace approximation with outliers [6.186553186139257]
  We show how to extend dimension reduction techniques and bi-criteria approximations based on sampling to the problem of subspace approximation with outliers. Our results hold even when the fraction of outliers $alpha$ is large, as long as the obvious condition $0 delta leq 1 - alpha$ is satisfied.
  arXiv  Detail & Related papers  (2020-06-30T07:22:33Z)
• $Q$-learning with Logarithmic Regret [60.24952657636464]
  We prove that an optimistic $Q$-learning enjoys a $mathcalOleft(fracSAcdot mathrmpolyleft(Hright)Delta_minlogleft(SATright)right)$ cumulative regret bound, where $S$ is the number of states, $A$ is the number of actions, $H$ is the planning horizon, $T$ is the total number of steps, and $Delta_min$ is the minimum sub-optimality gap.
  arXiv  Detail & Related papers  (2020-06-16T13:01:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.