Searching with known error probability
Theoretical Computer Science
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Noisy binary search and its applications
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Nonlinear Optimization
The Bayesian Learner is Optimal for Noisy Binary Search (and Pretty Good for Quantum as Well)
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
The stochastic root-finding problem: Overview, solutions, and open questions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Sequential transmission using noiseless feedback
IEEE Transactions on Information Theory
A Framework for Selecting a Selection Procedure
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Sequential screening: a Bayesian dynamic programming analysis of optimal group-splitting
Proceedings of the Winter Simulation Conference
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A stylized model of one-dimensional stochastic root-finding involves repeatedly querying an oracle as to whether the root lies to the left or right of a given point x. The oracle answers this question, but the received answer is incorrect with probability 1 − p(x). A Bayesian-style algorithm for this problem that assumes knowledge of p(·) repeatedly updates a density giving, in some sense, one's belief about the location of the root. We demonstrate how the algorithm works, and provide some results that shed light on its performance, both when p(·) is constant and when p(·) varies with x.