Binary Matrix Guessing Problem

TL;DR

This paper introduces the Binary Matrix Guessing Problem and presents two algorithms: a fast elementwise probing method and a slower, more general reinforcement learning approach, with performance comparisons and plans for further validation.

Contribution

The paper proposes two novel algorithms for the Binary Matrix Guessing Problem, including a fast Frobenius Distance-based method and a reinforcement learning approach with broader applicability.

Findings

EPA is very fast under Frobenius Distance scoring

Reinforcement learning algorithm is more general but slower

Performance comparison shows trade-offs between speed and flexibility

Abstract

We introduce the Binary Matrix Guessing Problem and provide two algorithms to solve this problem. The first algorithm we introduce is Elementwise Probing Algorithm (EPA) which is very fast under a score which utilizes Frobenius Distance. The second algorithm is Additive Reinforcement Learning Algorithm which combines ideas from perceptron algorithm and reinforcement learning algorithm. This algorithm is significantly slower compared to first one, but less restrictive and generalizes better. We compare computational performance of both algorithms and provide numerical results. reason for withdrawal: Paper will be rewritten with experiments replicated on verified and validated hardware and software.