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A Variational Persp...
A Variational Perspective on High-Resolution ODEs
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- Maskan, Hoomaan (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Zygalakis, Konstantinos C. (author)
- University of Edinburgh, United Kingdom
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- Yurtsever, Alp (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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(creator_code:org_t)
- Neural information processing systems foundation, 2023
- 2023
- English.
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In: Advances in Neural Information Processing Systems 36 (NeurIPS 2023). - : Neural information processing systems foundation.
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Abstract
Subject headings
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- We consider unconstrained minimization of smooth convex functions. We propose a novel variational perspective using forced Euler-Lagrange equation that allows for studying high-resolution ODEs. Through this, we obtain a faster convergence rate for gradient norm minimization using Nesterov's accelerated gradient method. Additionally, we show that Nesterov's method can be interpreted as a rate-matching discretization of an appropriately chosen high-resolution ODE. Finally, using the results from the new variational perspective, we propose a stochastic method for noisy gradients. Several numerical experiments compare and illustrate our stochastic algorithm with state of the art methods.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Publication and Content Type
- ref (subject category)
- kon (subject category)
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