arXiv Machine Learning By Eric Balkanski, Paul D\"utting, Federico Fusco, Silvio Lattanzi, Ashkan Norouzi-Fard, Ola Svensson, Morteza Zadimoghaddam

Consistent Submodular Maximization with Full Foresight

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The paper studies online algorithms for monotone submodular maximization with full knowledge of the future and unlimited computation. It establishes optimal approximation thresholds of 3/4 for deterministic algorithms and approximately 0.7942 for randomized algorithms, while allowing a constant number of changes per step. The authors provide matching impossibility results and achieve these bounds by balancing preparation for future arrivals with protection of the current solution, using techniques such as interval-selection analysis for randomized algorithms and certificate-based rounding for deterministic ones.

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arXiv Machine Learning
Sep 21

Schedule optimization for tau-leaping in masked discrete diffusion

The paper studies how to choose sampling schedules for tau‑leaping in masked discrete diffusion models. By deriving an exact integral representation of the factorization error ε_fact in terms of a dependence density ρ, the authors develop estimators and recursive equations that identify the unique optimal schedule under a monotonicity condition. In the large‑scale limit, they provide explicit characterizations of the optimal smooth schedule and show that while optimizing smooth schedules can improve constants, it does not change the N/K scaling unless the dependence density degenerates, in which case asymptotic improvements are possible.

By Cecilia Secchi, Giacomo Zanella