We propose a general framework for machine learning based optimization under uncertainty. Our approach replaces the complex forward model by a surrogate, which is learned simultaneously in a one-shot sense when solving the optimal control problem. Our approach relies on a reformulation of the problem as a penalized empirical risk minimization problem for which we provide a consistency analysis in terms of large data and increasing penalty parameter. To solve the resulting problem, we suggest a stochastic gradient method with adaptive control of the penalty parameter and prove convergence under suitable assumptions on the surrogate model. Numerical experiments illustrate the results for linear and nonlinear surrogate models.

翻译：我们提出了一种基于机器学习的通用不确定性优化框架。该方法在求解最优控制问题时，采用一次性同步学习方式，用代理模型替代复杂正向模型。该框架将问题重构为带惩罚项的经验风险最小化问题，并针对大数据量和递增惩罚参数两种情况提供了一致性分析。为求解该问题，我们提出了一种带惩罚参数自适应控制的随机梯度方法，并在代理模型的合理假设下证明了收敛性。数值实验分别展示了线性和非线性代理模型的应用效果。