Finding a most biased coin with fewest flips

TL;DR

This paper presents an optimal adaptive algorithm for identifying the most biased coin among many with minimal flips, using Bayesian methods and Markov game theory, advancing the efficiency of adaptive coin bias detection.

Contribution

It introduces the first Bayesian optimal adaptive strategy for finding the most biased coin with minimal flips, employing Markov game tools.

Findings

Algorithm minimizes expected flips to identify the most biased coin.

Proves optimality of the strategy under Bayesian setting.

Applicable to adaptive multi-armed bandit problems.

Abstract

We study the problem of learning a most biased coin among a set of coins by tossing the coins adaptively. The goal is to minimize the number of tosses until we identify a coin i* whose posterior probability of being most biased is at least 1-delta for a given delta. Under a particular probabilistic model, we give an optimal algorithm, i.e., an algorithm that minimizes the expected number of future tosses. The problem is closely related to finding the best arm in the multi-armed bandit problem using adaptive strategies. Our algorithm employs an optimal adaptive strategy -- a strategy that performs the best possible action at each step after observing the outcomes of all previous coin tosses. Consequently, our algorithm is also optimal for any starting history of outcomes. To our knowledge, this is the first algorithm that employs an optimal adaptive strategy under a Bayesian setting for this problem. Our proof of optimality employs tools from the field of Markov games.