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Poster
Concentration bounds for CVaR estimation: The cases of light-tailed and heavy-tailed distributions
Prashanth L.A. · Krishna Jagannathan · Ravi Kolla

Tue Jul 14 07:00 AM -- 07:45 AM & Tue Jul 14 06:00 PM -- 06:45 PM (PDT) @ Virtual #None

Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of sub-Gaussian, light-tailed and heavy-tailed distributions. For the sub-Gaussian and light-tailed cases, we use a classical CVaR estimator based on the empirical distribution constructed from the samples. For heavy-tailed random variables, we assume a mild `bounded moment' condition, and derive a concentration bound for a truncation-based estimator. Our concentration bounds exhibit exponential decay in the sample size, and are tighter than those available in the literature for the above distribution classes. To demonstrate the applicability of our concentration results, we consider the CVaR optimization problem in a multi-armed bandit setting. Specifically, we address the best CVaR-arm identification problem under a fixed budget. Using our CVaR concentration results, we derive an upper-bound on the probability of incorrect arm identification.

Author Information

Prashanth L.A. (IIT Madras)
Krishna Jagannathan (Indian Institute of Technology Madras)
Ravi Kolla (ABInBev)

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