Concentration inequality using unconfirmed knowledge

Understand

We give a concentration inequality based on the premise that random variables take values within a particular region.

• The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the sum of conditional expectations and that of the observed values takes a small value with high probability when the expected values are evaluated under the condition that the past values are known.
• Our inequality outperforms other well-known inequalities, e.g.
• the Azuma-Hoeffding inequality, especially in terms of the convergence speed when the random variables are highly biased.