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This research establishes theoretical bounds on the memory required for amortized parametric optimization, quantifying how offline data storage can reduce online computation costs in learning-enabled decision systems. By identifying phase transitions where additional memory yields diminishing returns, the study provides a rigorous framework for balancing accuracy against resource constraints in convex and strongly convex settings. Experiments on parameterized ridge regression validate these tradeoffs, offering practical guidance for optimizing inference pipelines that rely on warm-starting gradient descent methods.
Memory-Computation Tradeoffs in Semi Amortized Parametric Optimization
arXiv:2607.20769v1 Announce Type: new Abstract: Learning-enabled decision systems often use offline data or computation to reduce online compute cost. Despite the empirical success of such approaches, there is limited general understanding of how much offline information is needed to achieve a desired accuracy under a fixed online computation budget. We study this question through the lens of amortized parametric optimization: an offline phase stores a finite memory of solved problem instances, and an online phase produces a solution to a new instance by retrieving a warm start and applying $K$ steps of projected gradient descent. We analyze this setup for smooth convex parametric optimization over a compact domain, using a nonparametric predictor built from the stored offline solutions. For $\mu$-strongly convex objectives, we establish matching upper and lower bounds on the memory required to guarantee $\varepsilon$-accuracy under a fixed online iteration budget $K$. For convex objectives satisfying a $\beta$-growth condition ($\beta>2$), we obtain near-matching bounds and identify a phase transition in $K$ beyond which additional memory provides no benefit. We further provide a general proof framework that (i) explicitly quantifies the memory cost of acceleration---how much offline memory is required to achieve a prescribed speedup over the unaided online optimizer---and (ii) identifies two key quantities driving this cost: the convergence rate of the online optimizer and the Lipschitz sensitivity of the solution map to the problem parameter. Experiments on parameterized ridge regression confirm the predicted memory--computation--accuracy tradeoffs.
Abstract:Learning-enabled decision systems often use offline data or computation to reduce online compute cost. Despite the empirical success of such approaches, there is limited general understanding of how much offline information is needed to achieve a desired accuracy under a fixed online computation budget. We study this question through the lens of amortized parametric optimization: an offline phase stores a finite memory of solved problem instances, and an online phase produces a solution to a new instance by retrieving a warm start and applying $K$ steps of projected gradient descent. We analyze this setup for smooth convex parametric optimization over a compact domain, using a nonparametric predictor built from the stored offline solutions. For $\mu$-strongly convex objectives, we establish matching upper and lower bounds on the memory required to guarantee $\varepsilon$-accuracy under a fixed online iteration budget $K$. For convex objectives satisfying a $\beta$-growth condition ($\beta>2$), we obtain near-matching bounds and identify a phase transition in $K$ beyond which additional memory provides no benefit. We further provide a general proof framework that (i) explicitly quantifies the memory cost of acceleration---how much offline memory is required to achieve a prescribed speedup over the unaided online optimizer---and (ii) identifies two key quantities driving this cost: the convergence rate of the online optimizer and the Lipschitz sensitivity of the solution map to the problem parameter. Experiments on parameterized ridge regression confirm the predicted memory--computation--accuracy tradeoffs.
Machine Learning (cs.LG)
arXiv:2607.20769 [cs.LG]
(or arXiv:2607.20769v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.20769 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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