scope_rl.utils.estimate_confidence_interval_by_hoeffding#
- scope_rl.utils.estimate_confidence_interval_by_hoeffding(samples, alpha=0.05, **kwargs)[source]#
Estimate the confidence interval by the Hoeffding’s inequality.
Note
The Hoeffding’s inequality provides high-probability bounds of the expectation \(\mu := \mathbb{E}[X], X \sim p(X)\) as follows.
\[|\hat{\mu} - \mu| \leq X_{\max} \sqrt{\frac{\log(1 / \alpha)}{2 n}},\]which holds with probability \(1 - \alpha\) where \(n\) is the data size.