论文标题
光谱投影的亚级别级别方法用于非平滑凸优化问题
Spectral Projected Subgradient Method for Nonsmooth Convex Optimization Problems
论文作者
论文摘要
我们考虑以数学期望的形式使用非平滑目标函数的限制优化问题。样本平均近似（SAA）用于估计目标函数，并采用可变样本策略。所提出的算法将SAA亚级别与光谱系数结合在一起，以提供合适的方向，从而改善一阶方法的性能，如数值结果所示。步骤大小是从预定义的间隔中选择的，并且该方法几乎确定的收敛性在随机环境中的标准假设下证明。为了提高所提出的算法的性能，我们通过引入适合此框架的类似Armijo的过程来进一步指定步长的选择。考虑到机器学习问题的计算成本，我们得出的结论是，线路搜索可显着提高性能。在有限总和问题上进行的数值实验还表明，可变样品策略的表现优于完整的样本方法。
We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy is employed. The proposed algorithm combines an SAA subgradient with the spectral coefficient in order to provide a suitable direction which improves the performance of the first order method as shown by numerical results. The step sizes are chosen from the predefined interval and the almost sure convergence of the method is proved under the standard assumptions in stochastic environment. To enhance the performance of the proposed algorithm, we further specify the choice of the step size by introducing an Armijo-like procedure adapted to this framework. Considering the computational cost on machine learning problems, we conclude that the line search improves the performance significantly. Numerical experiments conducted on finite sums problems also reveal that the variable sample strategy outperforms the full sample approach.
