Hoeffding's inequality

Hoeffding's inequality is a statistical tool that provides a way to understand how the average of random samples relates to the true average of a population. Specifically, it states that if you take multiple independent samples, the likelihood that their average differs significantly from the true average decreases as you increase the number of samples. Essentially, it assures us that with enough data, our estimate of the average will be close to the actual average, limiting the chances of large errors in predictions or estimates based on those samples.