McDiarmid's Inequality

McDiarmid's Inequality provides a way to estimate how much a function of several independent random variables is likely to deviate from its expected value. If changing one variable slightly doesn't cause a big change in the function's outcome (bounded influence), then the probability that the actual value significantly differs from the expected value decreases exponentially with the size of the deviation. Essentially, it assures that with high probability, the function's outcome will stay close to its average, provided no single input has an overly large impact. This is useful for understanding stability and concentration in randomized processes.