An Approximate Algorithm for Sparse Distributionally Robust Optimization

In this paper, we propose a sparse distributionally robust optimization (DRO) model incorporating the Conditional Value-at-Risk (CVaR) measure to control tail risks in uncertain environments. The model utilizes sparsity to reduce transaction costs and enhance operational efficiency. We reformulate t...

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Veröffentlicht in:Information (Basel) Jg. 16; H. 8; S. 676
Hauptverfasser: Wang, Ruyu, Hu, Yaozhong, Liu, Cong, Gao, Quanwei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.08.2025
Schlagworte:
Algorithms
Analysis
approximate algorithm
Black swan event
Conditional Value-at-Risk (CVaR)
Decision making
distributionally robust optimization (DRO)
Investment analysis
Optimization
portfolio selection
Production planning
Random variables
Robustness
sparse optimization
ISSN:2078-2489, 2078-2489
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Zusammenfassung:In this paper, we propose a sparse distributionally robust optimization (DRO) model incorporating the Conditional Value-at-Risk (CVaR) measure to control tail risks in uncertain environments. The model utilizes sparsity to reduce transaction costs and enhance operational efficiency. We reformulate the problem as a Min-Max-Min optimization and convert it into an equivalent non-smooth minimization problem. To address this computational challenge, we develop an approximate discretization (AD) scheme for the underlying continuous random vector and prove its convergence to the original non-smooth formulation under mild conditions. The resulting problem can be efficiently solved using a subgradient method. While our analysis focuses on CVaR penalty, this approach is applicable to a broader class of non-smooth convex regularizers. The experimental results on the portfolio selection problem confirm the effectiveness and scalability of the proposed AD algorithm.
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ISSN:2078-2489
2078-2489
DOI:10.3390/info16080676