论文标题
解决随机组成优化几乎与解决随机优化一样容易
Solving Stochastic Compositional Optimization is Nearly as Easy as Solving Stochastic Optimization
论文作者
论文摘要
随机组成优化将经典（非组成）随机优化推广到功能组成的最小化。每个组合可能会引入额外的期望。一系列期望可能是嵌套的。随机组成优化在诸如增强学习和元学习之类的应用中越来越受欢迎。本文提出了一种新的随机校正的随机组成梯度法（SCSC）。 SCSC以单个环的单个尺度运行，使用固定的批次大小，并保证以与随机梯度下降（SGD）方法相同的速率进行非复合随机优化的速度收敛。这是通过仔细改进流行的随机组成梯度方法来实现的。将SGD改善技术应用于加速SCSC很容易。这有助于SCSC实现随机组成优化的最新性能。特别是，我们将ADAM应用于SCSC，并且表现出的收敛速率与非组成随机优化的原始Adam的收敛速率相匹配。我们使用投资组合管理和模型不合时宜的元学习任务来测试SCSC。
Stochastic compositional optimization generalizes classic (non-compositional) stochastic optimization to the minimization of compositions of functions. Each composition may introduce an additional expectation. The series of expectations may be nested. Stochastic compositional optimization is gaining popularity in applications such as reinforcement learning and meta learning. This paper presents a new Stochastically Corrected Stochastic Compositional gradient method (SCSC). SCSC runs in a single-time scale with a single loop, uses a fixed batch size, and guarantees to converge at the same rate as the stochastic gradient descent (SGD) method for non-compositional stochastic optimization. This is achieved by making a careful improvement to a popular stochastic compositional gradient method. It is easy to apply SGD-improvement techniques to accelerate SCSC. This helps SCSC achieve state-of-the-art performance for stochastic compositional optimization. In particular, we apply Adam to SCSC, and the exhibited rate of convergence matches that of the original Adam on non-compositional stochastic optimization. We test SCSC using the portfolio management and model-agnostic meta-learning tasks.
