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FOSI: Hybrid First and Second Order Optimization Study at ICLR 2024

Q: How does FOSI handle overfitting compared to base optimizers?

FOSI handles overfitting differently compared to base optimizers by improving convergence rates and optimizing the optimization process without additional tuning. In tasks where the base optimizer tends to overfit, FOSI accelerates convergence, leading to an earlier overfitting point. However, it is important to note that while FOSI may reach the same or superior validation accuracy as the base optimizer, its acceleration of convergence can also lead to an earlier onset of overfitting. This means that while FOSI improves the speed of reaching a target metric, it may also exhibit early signs of overfitting if not carefully monitored.

Q: What are the implications of using Lanczos approximation for curvature information?

Using Lanczos approximation for curvature information in optimization algorithms like FOSI has several implications: Efficient Approximation: The Lanczos algorithm provides an efficient way to estimate extreme eigenvalues and eigenvectors of a symmetric matrix without explicitly computing the entire Hessian. Reduced Computational Complexity: By utilizing Lanczos approximation, computations involving curvature information become more manageable in high-dimensional spaces. Improved Stability: Lanczos approximation helps improve stability during optimization by providing accurate estimates of critical curvature properties without excessive computational overhead. Spectral Analysis: The use of Lanczos allows for spectral analysis which can aid in understanding and optimizing convergence behavior based on eigenvalues and eigenvectors.

Q: How can automatic tuning of parameters like k and ℓ improve the efficiency of FOSI?

Automatic tuning of parameters such as k (number of largest eigenvalues) and ℓ (number smallest eigenvalues) in FOSI can significantly enhance its efficiency: Adaptive Adjustment: Automatic tuning allows for dynamic adjustment based on problem characteristics, ensuring optimal performance across different scenarios. Optimal Condition Number Reduction: Tuning these parameters effectively reduces condition numbers within subspaces defined by extreme eigenvalues, leading to faster convergence rates. Enhanced Convergence Speed: By automatically adjusting k and ℓ according to their impact on effective condition numbers, FOSI becomes more adaptive and efficient in minimizing functions with varying complexities. Reduced Manual Intervention: Automation eliminates manual parameter tweaking efforts, making it easier for users to apply FOSI across diverse optimization tasks seamlessly. These automated adjustments optimize how second-order information is incorporated into first-order optimization processes through meta-algorithms like FOSI efficiently under various conditions without requiring constant manual intervention from users.

Kernekoncepter

FOSI is a novel meta-algorithm that enhances first-order optimizers by incorporating second-order information efficiently.

Resumé

The study introduces FOSI, a meta-optimizer that improves convergence rates of base optimizers by integrating second-order information. FOSI splits the optimization process into two subspaces, utilizing Newton's method on one and the base optimizer on the other. The algorithm demonstrates improved performance over popular first-order methods like Heavy-Ball and Adam, as well as outperforms second-order methods like K-FAC and L-BFGS. The research provides theoretical analysis, empirical evaluations on DNN training tasks, and an open-source implementation of FOSI available on GitHub.

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arxiv.org

Statistik

Published at ICLR 2024
MobileNetV1 trained on AudioSet dataset with 40.4% validation accuracy in 1850 seconds for FOSI-HB.
RNN-based language model trained on Tiny Shakespeare dataset with a loss of 1.71 in 207 seconds for FOSI-HB.
Autoencoder trained on CIFAR-10 dataset with a loss of 1.76 in 219 seconds for FOSI-HB.
Transfer learning from ImageNet to CIFAR-10 reaching 79.0% validation accuracy in 53 seconds for FOSI-HB.
Logistic regression model for MNIST dataset achieving 92.8% validation accuracy in 8 seconds for FOSI-HB.

Citater

"FOSI improves convergence rates of base optimizers by incorporating second-order information efficiently."
"FOSI outperforms both first-order and second-order optimization methods."
"The algorithm splits the optimization process into two orthogonal subspaces to enhance performance."

Vigtigste indsigter udtrukket fra

FOSI

by Hadar Sivan,... kl. arxiv.org 03-08-2024

https://arxiv.org/pdf/2302.08484.pdf

Dybere Forespørgsler

How does FOSI handle overfitting compared to base optimizers?

FOSI handles overfitting differently compared to base optimizers by improving convergence rates and optimizing the optimization process without additional tuning. In tasks where the base optimizer tends to overfit, FOSI accelerates convergence, leading to an earlier overfitting point. However, it is important to note that while FOSI may reach the same or superior validation accuracy as the base optimizer, its acceleration of convergence can also lead to an earlier onset of overfitting. This means that while FOSI improves the speed of reaching a target metric, it may also exhibit early signs of overfitting if not carefully monitored.

What are the implications of using Lanczos approximation for curvature information?

Using Lanczos approximation for curvature information in optimization algorithms like FOSI has several implications:

Efficient Approximation: The Lanczos algorithm provides an efficient way to estimate extreme eigenvalues and eigenvectors of a symmetric matrix without explicitly computing the entire Hessian.
Reduced Computational Complexity: By utilizing Lanczos approximation, computations involving curvature information become more manageable in high-dimensional spaces.
Improved Stability: Lanczos approximation helps improve stability during optimization by providing accurate estimates of critical curvature properties without excessive computational overhead.
Spectral Analysis: The use of Lanczos allows for spectral analysis which can aid in understanding and optimizing convergence behavior based on eigenvalues and eigenvectors.

How can automatic tuning of parameters like k and ℓ improve the efficiency of FOSI?

Automatic tuning of parameters such as k (number of largest eigenvalues) and ℓ (number smallest eigenvalues) in FOSI can significantly enhance its efficiency:

Adaptive Adjustment: Automatic tuning allows for dynamic adjustment based on problem characteristics, ensuring optimal performance across different scenarios.
Optimal Condition Number Reduction: Tuning these parameters effectively reduces condition numbers within subspaces defined by extreme eigenvalues, leading to faster convergence rates.
Enhanced Convergence Speed: By automatically adjusting k and ℓ according to their impact on effective condition numbers, FOSI becomes more adaptive and efficient in minimizing functions with varying complexities.
Reduced Manual Intervention: Automation eliminates manual parameter tweaking efforts, making it easier for users to apply FOSI across diverse optimization tasks seamlessly.

These automated adjustments optimize how second-order information is incorporated into first-order optimization processes through meta-algorithms like FOSI efficiently under various conditions without requiring constant manual intervention from users.