GANs training: A game and stochastic control approach
研究了生成对抗网络训练中的适定性和凸性问题，提出随机控制框架调优超参数，推导出最优学习率和批大小，实证表明该方法在收敛性和鲁棒性上优于标准ADAM方法。
Abstract Training generative adversarial networks (GANs) are known to be difficult, especially for financial time series. This paper first analyzes the well‐posedness problem in GANs minimax games and the widely recognized convexity issue in GANs objective functions. It then proposes a stochastic control framework for hyper‐parameters tuning in GANs training. The weak form of dynamic programming principle and the uniqueness and the existence of the value function in the viscosity sense for the corresponding minimax game are established. In particular, explicit forms for the optimal adaptive learning rate and batch size are derived and are shown to depend on the convexity of the objective function, revealing a relation between improper choices of learning rate and explosion in GANs training. Finally, empirical studies demonstrate that training algorithms incorporating this adaptive control approach outperform the standard ADAM method in terms of convergence and robustness. From GANs training perspective, the analysis in this paper provides analytical support for the popular practice of “clipping,” and suggests that the convexity and well‐posedness issues in GANs may be tackled through appropriate choices of hyper‐parameters.