Exponential convergence of testing error for stochastic gradient methods
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Abstract (arXiv)
We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing error (classification error) converges exponentially fast if low-noise conditions are assumed.
Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Dec 2017.
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Citing papers per year: 2021: 1; 2022: 6; 2023: 3; 2024: 1; 2025: 1; 2026: 1.
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- 2022Phenomenology of Double Descent in Finite-Width Neural Networkscited by 11
- 2022On the Benefits of Large Learning Rates for Kernel Methodscited by 8
- 2023Convergence and concentration properties of constant step-size SGD through Markov chainscited by 8
- 2023Lower Generalization Bounds for GD and SGD in Smooth Stochastic Convex Optimizationcited by 6
- 2022Multiclass learning with margin: exponential rates with no bias-variance trade-offcited by 5
- 2021Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learningcited by 4
- 2022A Case of Exponential Convergence Rates for SVMcited by 3
- 2022Active Labeling: Streaming Stochastic Gradientscited by 3
- 2024Universal Rates of Empirical Risk Minimizationcited by 3
- 2023Binary Classification with Instance and Label Dependent Label Noisecited by 2
- 2025Universal rates of ERM for agnostic learningcited by 1
- 2022From Weakly Supervised Learning to Active Learningcited by 0
- 2026Generalization Bounds of Stochastic Gradient Descent in Homogeneous Neural Networks26 Feb 2026
- 2025Universal rates of ERM for agnostic learning17 Jun 2025
- 2024Universal Rates of Empirical Risk Minimization3 Dec 2024
- 2023Convergence and concentration properties of constant step-size SGD through Markov chains20 Jun 2023
- 2023Binary Classification with Instance and Label Dependent Label Noise6 Jun 2023
- 2023Lower Generalization Bounds for GD and SGD in Smooth Stochastic Convex Optimization19 Mar 2023
- 2022From Weakly Supervised Learning to Active Learning23 Sep 2022
- 2022Active Labeling: Streaming Stochastic Gradients26 May 2022
- 2022A Case of Exponential Convergence Rates for SVM20 May 2022
- 2022Phenomenology of Double Descent in Finite-Width Neural Networks14 Mar 2022
- 2022On the Benefits of Large Learning Rates for Kernel Methods28 Feb 2022
- 2022Multiclass learning with margin: exponential rates with no bias-variance trade-off3 Feb 2022
- 2022Phenomenology of Double Descent in Finite-Width Neural Networkscited by 11
- 2022On the Benefits of Large Learning Rates for Kernel Methodscited by 8
- 2023Convergence and concentration properties of constant step-size SGD through Markov chainscited by 8
- 2023Lower Generalization Bounds for GD and SGD in Smooth Stochastic Convex Optimizationcited by 6
- 2022Multiclass learning with margin: exponential rates with no bias-variance trade-offcited by 5
- 2021Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learningcited by 4
- 2022A Case of Exponential Convergence Rates for SVMcited by 3
- 2022Active Labeling: Streaming Stochastic Gradientscited by 3
- 2024Universal Rates of Empirical Risk Minimizationcited by 3
- 2023Binary Classification with Instance and Label Dependent Label Noisecited by 2
- 2025Universal rates of ERM for agnostic learningcited by 1
- 2022From Weakly Supervised Learning to Active Learningcited by 0
12 most cited of 13 All 13 (JSON)
- 2026Generalization Bounds of Stochastic Gradient Descent in Homogeneous Neural Networks26 Feb 2026
- 2025Universal rates of ERM for agnostic learning17 Jun 2025
- 2024Universal Rates of Empirical Risk Minimization3 Dec 2024
- 2023Convergence and concentration properties of constant step-size SGD through Markov chains20 Jun 2023
- 2023Binary Classification with Instance and Label Dependent Label Noise6 Jun 2023
- 2023Lower Generalization Bounds for GD and SGD in Smooth Stochastic Convex Optimization19 Mar 2023
- 2022From Weakly Supervised Learning to Active Learning23 Sep 2022
- 2022Active Labeling: Streaming Stochastic Gradients26 May 2022
- 2022A Case of Exponential Convergence Rates for SVM20 May 2022
- 2022Phenomenology of Double Descent in Finite-Width Neural Networks14 Mar 2022
- 2022On the Benefits of Large Learning Rates for Kernel Methods28 Feb 2022
- 2022Multiclass learning with margin: exponential rates with no bias-variance trade-off3 Feb 2022
12 newest of 13 All 13 (JSON)