发表机构
Johns Hopkins University（约翰·霍普金斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在固定在线计算预算下，半摊销参数优化中离线信息与精度的关系。通过构建非参数预测器分析，给出强凸和满足特定条件凸目标的内存上下界及证明框架，实验验证了内存-计算-精度权衡。
AI 中文摘要
启用学习的决策系统通常使用离线数据或计算来降低在线计算成本。尽管这些方法在经验上取得了成功，但对于在固定的在线计算预算下需要多少离线信息才能达到所需的精度，人们的普遍理解有限。我们通过摊销参数优化的视角来研究这个问题：离线阶段存储已解决问题实例的有限内存，在线阶段通过检索热启动并应用K步投影梯度下降来为新实例生成解决方案。我们使用从存储的离线解决方案构建的非参数预测器，分析了在紧凑域上进行平滑凸参数优化的这种设置。对于μ-强凸目标，我们在固定的在线迭代预算K下，建立了保证ε-精度所需内存的匹配上下界。对于满足β-增长条件（β>2）的凸目标，我们获得了近似匹配的界，并确定了K中的一个相变，超过该相变额外的内存没有益处。我们还提供了一个通用的证明框架，（i）明确量化加速的内存成本——在没有辅助的在线优化器的情况下实现规定加速需要多少离线内存——以及（ii）确定驱动此成本的两个关键量：在线优化器的收敛速度和解决方案映射对问题参数的Lipschitz敏感性。参数化岭回归实验证实了预测的内存-计算-精度权衡。
英文摘要
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 $μ$-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 $β$-growth condition ($β>2$), 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.
