一种用于箱式约束期望相关与风险规避随机优化问题的统一高效梯度启发式算法
A Unified Efficient Gradient-Based Heuristic For Box-Constrained Expectation-Related and Risk-Averse Stochastic Optimization Problems
- Univ. Grenoble Alpes, CNRS, Grenoble INP（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种统一高效的梯度启发式算法，基于热启动解与候选集采样，解决箱式约束下期望相关及风险规避（VaR/CVaR）随机优化问题。
AI中文摘要：
本文提出了一种新算法，用于解决成本函数依赖于具有已知统计特性的不确定参数向量的随机优化问题。该算法通过参数化设计，能够处理从期望导向到风险价值（VaR）以及条件风险价值（CVaR）导向的各种随机优化问题。该算法利用了最近提出的基于梯度的搜索与加速算法，该算法最初专门用于确定性优化问题。该方法基于对问题实例的一系列热启动解。这些解连同属于第一个解集凸包的其他解样本一起，构成了可行候选集。在这个离散候选集中，根据目标准则的基于样本的近似来选择最优解。通过一个定制的说明性示例，讨论并展示了该算法的相关性和效率。
英文摘要：
This paper presents a new algorithm addressing the problem of stochastic optimization where the cost function depends on a vector of uncertain parameters with known statistics. The algorithm is parameterized so as to address various stochastic formulations spanning from Expectation-focused to Value-at-Risk (VaR) as well as Conditional-Value-at-Risk (CVaR)-focused formulations. The algorithm leverages a recently proposed gradient-based Search & Accelerate algorithm which is originally dedicated to deterministic optimization problems. The approach is based on a sequence of warm-started solutions of instances of the problem. These solutions together with a samples of other solutions belonging to the convex hull of the first ones constitute the set of admissible candidates. Among this discrete set of candidates, the optimal solution is selected with regards to a sample-based approximation of the targeted criterion. The relevance of the algorithm and its efficiency are discussed and shown using a tailored illustrative example.
