Multi-Armed Bandit Problem

The Multi-Armed Bandit Problem is a classic problem in probability theory and decision-making that involves balancing exploration and exploitation. It models a scenario where a gambler must choose between multiple slot machines (or 'arms'), each with an unknown probability distribution of payouts. The challenge lies in determining which machines to play in order to maximize total rewards over time. Common applications include online advertising, clinical trials, and adaptive experimentation, where decisions must be made sequentially based on observed outcomes. The problem is fundamental in machine learning and reinforcement learning, as it helps in developing algorithms that optimize decision-making under uncertainty.