Question 16: In a faulty -armed bandit with -noise activation, suppos…

Consider an N-armed bandit problem in which each arm , for , produces a reward of 1 with probability and otherwise, where denotes the arm’s base success probability. Assume the bandit machine suffers from a hardware malfunction: when the agent attempts to pull arm , the intended action is not always executed. Instead, with probability a wiring fault causes the machine to randomly activate one arm chosen uniformly from the set , regardless of the agent’s selection, and the reward is generated according to that arm’s reward distribution. We refer to this malfunction as -noise activation Based on the above data, answer the given subquestions.

In a faulty -armed bandit with -noise activation, suppose you mistakenly model the environment as a standard bandit without activation noise. You estimate each arm’s success probability using sample averages of observed rewards. How does the -noise affect your estimates of the true base success probabilities ?