从不精确优化到梯度集中学习
From inexact optimization to learning via gradient concentration
摘要：
机器学习中的优化通常处理由训练数据定义的经验目标的最小化。然而，学习的最终目标是最小化未来数据的错误（测试错误），训练数据仅提供部分信息。在这种观点中，实际可行的优化问题是基于随机性质的不精确量。在本文中，我们将展示如何概率结果，特别是梯度浓度，可以结合不精确优化的结果，以获得尖锐的测试误差保证。通过考虑无约束的目标，我们强调了学习优化的隐式正则化特性。
英文摘要：
Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training data provides only partial information. In this view, the optimization problems that are practically feasible are based on inexact quantities that are stochastic in nature. In this paper, we show how probabilistic results, specifically gradient concentration, can be combined with results from inexact optimization to derive sharp test error guarantees. By considering unconstrained objectives we highlight the implicit regularization properties of optimization for learning.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
