论文标题
在风险受限的非凸功能编程中二元性强
Strong Duality in Risk-Constrained Nonconvex Functional Programming
论文作者
论文摘要
我们表明，与一般可构成的非凸线瞬时奖励/约束功能有关的风险受限的功能优化问题表现出很强的二元性，而不论非凸度。我们考虑具有凸面和均质风险措施的风险限制，以有界风险信封的双重表示，概括了期望。我们设置中支持的流行风险措施包括有条件的危险价值（CVAR），平均吸毒偏差（MAD，包括非单酮案例），某些分布强大的表示形式以及更常见的所有实用值的相干风险度量$ L_1 $。我们通过进一步讨论基本模型的各种概括，$ l_ {p> 1} $支持的风险措施的扩展，对均值风险交易模型的含义以及无线系统资源分配中更具体的应用程序的含义以及受监管的约束学习来强调结果的有用性。我们的核心证明技术似乎是新的，并且依赖于J. J. Uhl对A. A. Lyapunov的凸凸定理的弱扩展，以进行矢量测量，以使用一般的无限二维Banach空间，以进行矢量测量。
We show that risk-constrained functional optimization problems with general integrable nonconvex instantaneous reward/constraint functions exhibit strong duality, regardless of nonconvexity. We consider risk constraints featuring convex and positively homogeneous risk measures admitting dual representations with bounded risk envelopes, generalizing expectations. Popular risk measures supported within our setting include the conditional value-at-risk (CVaR), the mean-absolute deviation (MAD, including the non-monotone case), certain distributionally robust representations and more generally all real-valued coherent risk measures on the space $L_1$. We highlight the usefulness of our results by further discussing various generalizations of our base model, extensions for risk measures supported on $L_{p>1}$, implications in the context of mean-risk tradeoff models, as well as more specific applications in wireless systems resource allocation, and supervised constrained learning. Our core proof technique appears to be new and relies on risk conjugate duality in tandem with J. J. Uhl's weak extension of A. A. Lyapunov's convexity theorem for vector measures taking values in general infinite-dimensional Banach spaces.
