What is the multi-armed bandit problem?

The multi-armed bandit problem describes a scenario in which an agent encounters multiple options—analogous to multiple slot machines (or "bandits")—and needs to make decisions about which one to play in order to maximize their total reward. The challenge lies in balancing exploration, where the agent tries out different machines to gather information about their payout rates, and exploitation, where the agent chooses the machine that has provided the best reward based on current knowledge. This trade-off is fundamental to the problem and is central to many algorithms designed in reinforcement learning and decision-making processes.

Exploration allows the agent to discover potentially better options, while exploitation utilizes known information to gain immediate rewards. The key to solving the multi-armed bandit problem is through various strategies that manage this balance effectively, leading to optimal decision-making over time. This is why the provided answer accurately captures the essence of the problem.