Statistical Learning with Conditional Value at Risk

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 $O(1/\sqrt{n})$-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.

References in corpus (2)

• Scikit-learn: Machine Learning in Python
• Risk-Averse Stochastic Convex Bandit

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• Adaptive Sampling for Stochastic Risk-Averse Learning
• Off-Policy Risk Assessment in Contextual Bandits
• Spectral risk-based learning using unbounded losses
• Risk-Constrained Thompson Sampling for CVaR Bandits
• On Empirical Risk Minimization with Dependent and Heavy-Tailed Data
• Noisy Linear Convergence of Stochastic Gradient Descent for CV@R Statistical Learning under Polyak-Łojasiewicz Conditions
• Non-convex Distributionally Robust Optimization: Non-asymptotic Analysis
• A Stochastic Subgradient Method for Distributionally Robust Non-Convex Learning
• A Survey of Learning Criteria Going Beyond the Usual Risk
• Learning with CVaR-based feedback under potentially heavy tails
• Multiplicative Reweighting for Robust Neural Network Optimization
• Non-asymptotic estimation of risk measures using stochastic gradient Langevin dynamics