A Decision-Theoretic Framework for Adaptive Integer Factorization

This repository contains the manuscript: Serhii Kanivets,"A Decision-Theoretic Framework for Adaptive Integer Factorization"(June 2026). The work proposes a unified decision-theoretic framework for adaptive integer factorization, combining Bayesian inference, optimal stopping theory, multi-armed bandits, and Markov decision processes. The central idea is to reinterpret key heuristic decisions in modern factorization pipelines as formal sequential decision-making problems under uncertainty. Specifically: • Early termination of candidate processing during sieving is formulated as an optimal stopping problem. • Elliptic Curve Method (ECM) parameter selection is modeled as a Bayesian multi-armed bandit. • The transition between ECM and General Number Field Sieve (GNFS) phases is derived as a Bayesian stopping criterion. • The complete factorization workflow is represented as a Markov Decision Process (MDP) with approximately separable subproblems. The manuscript derives theoretical regret bounds for adaptive early-abort policies and establishes a decomposition bound for the global optimization framework. The proposed methodology aims to replace empirically tuned thresholds with adaptive policies derived from probabilistic inference and decision theory. The projected computational improvements reported in the manuscript are analytical estimates. Full empirical validation on standard factorization benchmarks remains future work.