Abstract:We introduce Prox-ITEM, an optimal proximal gradient method for minimizing $f+g$, where $f$ is smooth and strongly convex, and $g$ is convex, proper, and lower semicontinuous. In the smooth case $g=0$, Prox-ITEM reduces to the information-theoretic exact method (ITEM). We prove an exact distance-to-solution bound for Prox-ITEM with the same distance-convergence rate as ITEM, and show that this rate is minimax optimal among span-based first-order methods using the same number of gradient-oracle calls for $f$ and an arbitrary number of proximal-oracle calls for $g$. We also identify the stationary limit of Prox-ITEM, denoted Prox-TMM, which gives a proximal extension of the triple momentum method (TMM) to the composite setting and achieves the corresponding TMM distance-convergence rate.
From: Manu Upadhyaya [view email]
[v1]
Thu, 21 May 2026 18:06:17 UTC (46 KB)
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