Design an information-gathering gambling strategy

Q: Design an information-gathering gambling strategy

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Question

Two-Arm Bernoulli Bandit: Strategy, Stopping, and Design Variants

Context

You repeatedly choose between two casino games (arms) G1 and G2 over rounds t = 1, …, N. Each play of arm i yields a Bernoulli reward with an unknown success probability p_i. Your goals are:

maximize expected cumulative wins, or
identify the better arm (the one with larger p_i) with at least 95% confidence by or before round N.

Assume rewards are i.i.d. per arm and independent across arms.

Tasks

(a) Propose and justify an exploration–exploitation strategy (e.g., UCB1 or Thompson sampling) and give the update rules.

(b) Specify a stopping/commitment rule and derive the sample complexity needed to identify the better arm when |p1 − p2| ≥ δ with error ≤ 5%.

(c) Discuss how prior information, unequal play costs, or nonstationarity would change your design.

Design an information-gathering gambling strategy

Two-Arm Bernoulli Bandit: Strategy, Stopping, and Design Variants

Context

Tasks

Solution (Locked)

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