# Concentration bounds for CVaR estimation: The cases of light-tailed and heavy-tailed distributions

arXiv: https://arxiv.org/abs/1901.00997 · HTML: https://mlsanity.com/paper/1901.00997/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jan 2019.

## Built on by (most cited first, 2 of 2)

- [Risk averse non-stationary multi-armed bandits](https://mlsanity.com/paper/2109.13977/) (2021)
- [A Risk-Averse Framework for Non-Stationary Stochastic Multi-Armed Bandits](https://mlsanity.com/paper/2310.19821/) (2023)

## Abstract (arXiv)

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 light-tailed and heavy-tailed distributions. In the light-tailed case, 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. Notably, our concentration bounds enjoy an exponential decay in the sample size, for heavy-tailed as well as light-tailed distributions. To demonstrate the applicability of our concentration results, we consider a CVaR optimization problem in a multi-armed bandit setting. Specifically, we address the best CVaR-arm identification problem under a fixed budget. We modify the well-known successive rejects algorithm to incorporate a CVaR-based criterion. Using the CVaR concentration result, we derive an upper-bound on the probability of incorrect identification by the proposed algorithm.