论文标题
数据驱动的最小值优化和期望约束
Data-Driven Minimax Optimization with Expectation Constraints
论文作者
论文摘要
在最近几十年中，人们对数据驱动的优化方法（包括众所周知的随机梯度下降方法）的关注显着增长，但是由于投影的计算挑战在这些硬限制所定义的可行集合上，因此很少研究数据驱动的约束。在本文中，我们专注于非平滑凸孔concave随机minimax制度，并将数据驱动的约束作为期望约束。 Minimax期望限制了问题，包括一系列广泛的现实应用程序，包括两人游戏零和游戏和数据驱动的强大优化。我们提出了一类有效的原始二重式算法来解决最小值期望约束的问题，并表明我们的算法以$ \ Mathcal {o}的最佳速率收敛（\ frac {1} {1} {\ sqrt {n}}）$。我们通过在大型现实世界应用上进行数值实验来证明我们的算法的实际效率。
Attention to data-driven optimization approaches, including the well-known stochastic gradient descent method, has grown significantly over recent decades, but data-driven constraints have rarely been studied, because of the computational challenges of projections onto the feasible set defined by these hard constraints. In this paper, we focus on the non-smooth convex-concave stochastic minimax regime and formulate the data-driven constraints as expectation constraints. The minimax expectation constrained problem subsumes a broad class of real-world applications, including two-player zero-sum game and data-driven robust optimization. We propose a class of efficient primal-dual algorithms to tackle the minimax expectation-constrained problem, and show that our algorithms converge at the optimal rate of $\mathcal{O}(\frac{1}{\sqrt{N}})$. We demonstrate the practical efficiency of our algorithms by conducting numerical experiments on large-scale real-world applications.
