A Non-Monotone Preconditioned Trust-Region Method for Neural Network Training
Training deep neural networks at scale can benefit from domain decomposition, where the network is split into subdomains trained in parallel and coupled by a global trust-region mechanism. Building on the Additively Preconditioned Trust-Region Strategy (APTS), we propose a non-monotone variant with a nonlinear additive Schwarz preconditioner that combines parallel subdomain corrections with global coarse-space directions. A windowed acceptance criterion allows controlled objective increases, avoiding needless rejection of effective coarse steps. The resulting non-monotone APTS (NAPTS) preserves accuracy while reducing CPU time by 30\% and cutting rejected steps to one third of those in APTS.
| Authors | Andrea Angino, Bindi Çapriqi, Shega Likaj et al. |
|---|---|
| Primary category | math.OC |
| Published | 14 May 2026 |
| Last updated at source | 14 May 2026 |
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