论文标题
用牛顿型方法解决随机优化的尺寸自适应稀疏网格正交
Solving Stochastic Optimization by Newton-type methods with Dimension-Adaptive Sparse Grid Quadrature
论文作者
论文摘要
随机优化问题最大程度地减少了对随机成本功能的期望。我们使用“优化然后离散”方法来解决随机优化。在我们的方法中，需要准确的正交方法来计算实际上是积分的客观，梯度或Hessian。当问题是高维时，我们将尺寸自适应的稀疏网格正交正交正交正交到近似这些积分时。尺寸自适应稀疏的网格正交正交在计算平滑积分的积分时表现出很高的精度和效率。这是对经典稀疏网格方法的一种概括，它根据其重要性来完善不同的维度。我们表明，维度自适应稀疏的网格正交正交在优化的优化方面具有更好的性能，而不是“离散然后优化”方法。
Stochastic optimisation problems minimise expectations of random cost functions. We use 'optimise then discretise' method to solve stochastic optimisation. In our approach, accurate quadrature methods are required to calculate the objective, gradient or Hessian which are in fact integrals. We apply the dimension-adaptive sparse grid quadrature to approximate these integrals when the problem is high dimensional. Dimension-adaptive sparse grid quadrature shows high accuracy and efficiency in computing an integral with a smooth integrand. It is a kind of generalisation of the classical sparse grid method, which refines different dimensions according to their importance. We show that the dimension-adaptive sparse grid quadrature has better performance in the optimise then discretise' method than the 'discretise then optimise' method.
