Most stochastic optimization methods use gradients once before discarding them. While variance reduction methods have shown that reusing past gradients can be beneficial when there is a finite number of datapoints, they do not easily extend to the online setting. One issue is the staleness due to using past gradients. We propose to correct this staleness using the idea of implicit gradient transport (IGT) which transforms gradients computed at previous iterates into gradients evaluated at the current iterate without using the Hessian explicitly. In addition to reducing the variance and bias of our updates over time, IGT can be used as a drop-in replacement for the gradient estimate in a number of well-understood methods such as heavy ball or Adam. We show experimentally that it achieves state-of-the-art results on a wide range of architectures and benchmarks. Additionally, the IGT gradient estimator yields the optimal asymptotic convergence rate for online stochastic optimization in the restricted setting where the Hessians of all component functions are equal.

本文提出了一种基于隐式梯度传输的在线随机优化方法，通过修正过去梯度的陈旧性，提高了更新稳定性和收敛速度，在多种结构和基准问题下均取得了最先进的结果，并且在约束条件下获得了最优的渐进收敛率。

通过传输过去的梯度来减少在线优化中的方差