PAC-Bayesian Bound for the Conditional Value at Risk
arXiv:2006.14763
Abstract
Conditional Value at Risk (CVaR) is a family of "coherent risk measures" which generalize the traditional mathematical expectation. Widely used in mathematical finance, it is garnering increasing interest in machine learning, e.g., as an alternate approach to regularization, and as a means for ensuring fairness. This paper presents a generalization bound for learning algorithms that minimize the CVaR of the empirical loss. The bound is of PAC-Bayesian type and is guaranteed to be small when the empirical CVaR is small. We achieve this by reducing the problem of estimating CVaR to that of merely estimating an expectation. This then enables us, as a by-product, to obtain concentration inequalities for CVaR even when the random variable in question is unbounded.
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- Algorithms for CVaR Optimization in MDPs
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Cited by in corpus (6)
- Adaptive Sampling for Stochastic Risk-Averse Learning
- Noisy Linear Convergence of Stochastic Gradient Descent for CV@R Statistical Learning under Polyak-Łojasiewicz Conditions
- On Empirical Risk Minimization with Dependent and Heavy-Tailed Data
- Learning via Wasserstein-Based High Probability Generalisation Bounds
- A PAC-Bayesian Perspective on Structured Prediction with Implicit Loss Embeddings
- Comparing Comparators in Generalization Bounds