Consensus Distributionally Robust Optimization With Phi-Divergence
Consensus Distributionally Robust Optimization With Phi-Divergence
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DOI：
10.1109/access.2021.3091432
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发表时间：
2021
期刊：
影响因子：
3.9
通讯作者：
S. Ohmori
中科院分区：
文献类型：
--
作者：
S. Ohmori
我们研究了一种有效的算法来解决分布式鲁棒优化（DRO）问题，这是最近引起人们注意的一个新的范例决策在不确定的情况下。在传统的随机规划中，寻求在未知参数的概率分布上最小化期望成本的决策。相反，在DRO中，可以从数据中导出鲁棒的决策，而无需假设概率分布;因此，它有望为数据驱动的决策提供强大的方法。然而，解决DRO问题在计算上是困难的，即使是最先进的求解器，可以解决的最优问题的大小仍然是有限的。因此，我们提出了一个有效的算法来解决DRO基于共识优化（CO）。CO是一个分布式算法，其中一个大规模的问题被分解成更小的子问题。由于不同的局部解是通过求解子问题获得的，因此施加共识约束以确保这些解是相等的，从而保证全局收敛。将该方法应用于线性规划、二次规划和二阶锥规划的数值实验，验证了其有效性。
We study an efficient algorithm to solve the distributionally robust optimization (DRO) problem, which has recently attracted attention as a new paradigm for decision making in uncertain situations. In traditional stochastic programming, a decision is sought that minimizes the expected cost over the probability distribution of the unknown parameters. In contrast, in DRO, robust decision making can be derived from data without assuming a probability distribution; thus, it is expected to provide a powerful method for data-driven decision making. However, it is computationally difficult to solve the DRO problem and even by state-of-art solvers the problem size that can be solved to optimality is still limited. Therefore, we propose an efficient algorithm for solving DRO based on consensus optimization (CO). CO is a distributed algorithm in which a large-scale problem is decomposed into smaller subproblems. Because different local solutions are obtained by solving subproblems, a consensus constraint is imposed to ensure that these solutions are equal, thereby guaranteeing global convergence. We applied the proposed method to linear programming, quadratic programming, and second-order cone programming in numerical experiments and verified its effectiveness.