Learning Multiple Secrets in Mastermind
Milind Prabhu, David Woodruff

TL;DR
This paper introduces efficient algorithms and bounds for learning hidden subsets in high-dimensional spaces through adaptive queries, advancing understanding of query complexity in generalized Mastermind problems.
Contribution
It provides a two-round adaptive algorithm with near-optimal query complexity for the generalized Mastermind problem and establishes lower bounds on the number of rounds needed for learning.
Findings
Two-round adaptive algorithm with $ ilde{O}( ext{exp}( oot{2}\sqrt{d ext{log} n}))$ queries.
Lower bounds showing exponential query requirements for multi-round algorithms.
An $O(n^{d/2})$ query deterministic algorithm for the continuous variant.
Abstract
In the Generalized Mastermind problem, there is an unknown subset of the hypercube containing points. The goal is to learn by making a few queries to an oracle, which, given a point in , returns the point in nearest to . We give a two-round adaptive algorithm for this problem that learns while making at most queries. Furthermore, we show that any -round adaptive randomized algorithm that learns with constant probability must make queries even when the input has points; thus, any query algorithm must necessarily use rounds of adaptivity. We give optimal query complexity bounds for the variant of the problem where queries are allowed to be from . We also study a continuous variant of the problem in…
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Taxonomy
TopicsDigital and Traditional Archives Management · User Authentication and Security Systems · Digital and Cyber Forensics
