Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process is often continuous in nature. We exploit this underlying continuity by developing predictor-corrector algorithms for time-varying stochastic optimizations. We provide error bounds for the iterates, both in presence of pure and noisy access to the queries from the relevant derivatives of the loss function. Furthermore, we show (theoretically and empirically in several examples) that our method outperforms non-predictor corrector methods that do not exploit the underlying continuous process.

翻译：时变随机优化问题在机器学习实践中频繁出现（如渐进域漂移、目标跟踪、策略分类）。尽管多数问题在离散时间框架下求解，但其底层过程本质上常具有连续性。我们通过开发针对时变随机优化的预测-校正算法来利用这一底层连续性。我们给出了迭代过程的误差界，涵盖损失函数相关导数的纯查询与含噪查询两种情况。进一步地，我们通过理论分析与多组实证案例证明，相较于未利用底层连续过程的非预测-校正方法，本方法具有显著优越性。