Statistical Learning with Conditional Value at Risk

2020/02/14 by Tasuku Soma, Yuichi Yoshida, Soma, Tasuku +1 · 3 citations
Computer Science · Mathematics · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Statistical Methods and Inference #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2002.05826

openalex publication_date 2020/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic gradient descent for this framework. While existing studies of CVaR optimization require direct access to the underlying distribution, our algorithms make a weaker assumption that only i.i.d. samples are given. For convex and Lipschitz loss functions, we show that our algorithm has O(1/√(n))-convergence to the optimal CVaR, where n is the number of samples. For nonconvex and smooth loss functions, we show a generalization bound on CVaR. By conducting numerical experiments on various machine learning tasks, we demonstrate that our algorithms effectively minimize CVaR compared with other baseline algorithms.

Citations

• Gradient-based learning applied to document recognition

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