一种适用于复合问题的具有记忆的加速梯度方法

Mihai I. Florea
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引用次数: 1

摘要

使用内存的梯度方法在运行时存储在先前迭代中获得的部分oracle信息。该模型允许它们在许多情况下优于经典梯度方法。解决与模型相关的内部问题确实会产生开销,但对于目标具有Lipschitz梯度的无约束问题,这种开销已被证明是最小的。本文提出了一种适用于复合问题的具有记忆的加速梯度方法。在我们的方法中,即使对于具有不可微目标的约束问题,模型开销仍然可以忽略不计。虽然内部问题无法精确解决,但我们提出了一个模型,并选择了内部优化方案的起点,以防止误差随着算法的进展而积累。此外,该方法还动态调整了收敛性保证,使其优于快速梯度法。理论预测在图像去模糊问题上得到了数值验证。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An efficient accelerated gradient method with memory applicable to composite problems
Gradient Methods with Memory store at runtime part of the oracle information obtained at previous iterations. This model allows them to outperform classical gradient methods in many situations. Solving the inner problem associated with the model does incur an overhead but, for unconstrained problems where the objective has a Lipschitz gradient, this overhead has been shown to be minimal. In this work we propose an accelerated gradient method with memory applicable to composite problems. In our method the model overhead remains negligible even for constrained problems with non-differentiable objectives. Although the inner problem cannot be solved exactly, we propose a model and choose the starting point of the inner optimization scheme in a way that prevents the accumulation of errors as the algorithm progresses. Moreover, our method dynamically adjusts the convergence guarantees to exceed those of the Fast Gradient Method. The theoretical predictions are confirmed numerically on an image deblurring problem.
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