In this paper, we study the conditional stochastic optimization (CSO) problem which covers a variety of applications including portfolio selection, reinforcement learning, robust learning, causal inference, etc. The sample-averaged gradient of the CSO objective is biased due to its nested structure and therefore requires a high sample complexity to reach convergence. We introduce a general stochastic extrapolation technique that effectively reduces the bias. We show that for nonconvex smooth objectives, combining this extrapolation with variance reduction techniques can achieve a significantly better sample complexity than existing bounds. We also develop new algorithms for the finite-sum variant of CSO that also significantly improve upon existing results. Finally, we believe that our debiasing technique could be an interesting tool applicable to other stochastic optimization problems too.

本文提出了一种新的随机外推技术来有效减少样本平均渐变在条件随机优化问题中的偏差，并且结合方差降低技术在非凸光滑目标中能够显著地提高样本复杂度。本文还为CSO的有限和变体开发了新的算法，最后提出我们的去偏差技术可能是适用于其他随机优化问题的有意思的工具。

去偏置条件随机优化