(12) Finally, the theorem follows by substituting the above expression into E[G T ] = 1 T TX i=1 E h ∥wT −w ⋆ i ∥2 i

+ 2bt (w⋆ t −w ⋆ i )⊤ (w0 −w ⋆ 1) + tX k=2 tX k′=2 at−max(k,k′)+1b|k−k′| w⋆ k−1 −w ⋆ k ⊤ w⋆ k′−1 −w ⋆ k′ + 2 tX k=2 bt−k+1 (w⋆ t −w ⋆ i )⊤ w⋆ k−1 −w ⋆ k +∥w ⋆ t −w ⋆ i ∥2

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Optimal L2 Regularization in High-dimensional Continual Linear Regression

cs.LG · 2026-01-20 · unverdicted · novelty 8.0

In high-dimensional continual linear regression, optimal fixed L2 regularization strength scales as T/ln T with the number of tasks and mitigates label noise for arbitrary linear teachers.

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Optimal L2 Regularization in High-dimensional Continual Linear Regression cs.LG · 2026-01-20 · unverdicted · none · ref 32
In high-dimensional continual linear regression, optimal fixed L2 regularization strength scales as T/ln T with the number of tasks and mitigates label noise for arbitrary linear teachers.

(12) Finally, the theorem follows by substituting the above expression into E[G T ] = 1 T TX i=1 E h ∥wT −w ⋆ i ∥2 i

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