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Concentration bounds for CVaR estimation: The cases of light-tailed and heavy-tailed distributions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the empirical-distribution CVaR estimator for light-tailed samples | CVaR estimation · Light-tailed distributions | CVaR estimation error probability: 6\exp\left[-\frac{cn\epsilon^2(1-\alpha)^2}{2(\sigma^2+v_\alpha^2)}\right] for small \epsilon; 2\exp\left[-\frac{n\epsil | Helped |
| Use a truncation-based CVaR estimator under a bounded-moment assumption | CVaR estimation · Bounded-moment distributions, 1<p<2 | CVaR estimation error probability: 8\exp\left(- cn (1-\alpha)^{\frac{p}{(p-1)}} \epsilon^{\frac{p}{(p-1)}}\right) | Helped |
| Use a truncation-based CVaR estimator under a bounded second moment | CVaR estimation · Bounded second moment (p=2) | CVaR estimation error probability: 8\exp\left(- c'n (1-\alpha)^2 \epsilon^2\right) | Helped |
| Replace sample-mean arm estimates in successive rejects with empirical CVaR estimates | Successive rejects · K-armed stochastic bandit, light-tailed arms | Probability of incorrect identification: 4K(K-1) \exp \left( -\frac{(n-K)(1-\alpha) G_{\max}}{{H\overline{\log}K} \right) | Helped |
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