The MAB problem
The MAB problem is one of the classic problems in reinforcement learning. A MAB is a slot machine where we pull the arm (lever) and get a payout (reward) based on some probability distribution. A single slot machine is called a one-armed bandit and when there are multiple slot machines it is called a MAB or k-armed bandit, where k denotes the number of slot machines.
Figure 6.1 shows a 3-armed bandit:
Figure 6.1: 3-armed bandit slot machines
Slot machines are one of the most popular games in the casino, where we pull the arm and get a reward. If we get 0 reward then we lose the game, and if we get +1 reward then we win the game. There can be several slot machines, and each slot machine is referred to as an arm. For instance, slot machine 1 is referred to as arm 1, slot machine 2 is referred to as arm 2, and so on. Thus, whenever we say arm n, it actually means that we are referring to slot machine n.
Each arm has its own probability distribution...