Learning with Simulators: No Regret in a Computationally Bounded World

2026-06-11 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A new framework, "simulatable processes," addresses the challenge of generalization in learning theory when data-generating processes are strongly dependent, moving beyond traditional reliance on data independence. Introduced on 2026-06-11, this framework demonstrates that by providing a learner access to a simulator approximating the data distribution, it is possible to achieve learning guarantees comparable to those in classical settings with independent data. Specifically, the framework recovers error bounds dependent on the VC dimension. Furthermore, the research explores conditional sampling within this context, revealing distinct statistical and computational benefits. A key achievement is an algorithm capable of learning any given VC class under all processes samplable in bounded polynomial time, with its regret controlled by the time-bounded Kolmogorov complexity of the process, significantly expanding the classical PAC model.

Key takeaway

For AI Scientists and Research Scientists designing learning algorithms for environments with strongly dependent data, this work suggests a fundamental shift. You should consider integrating high-fidelity simulators into your learning pipelines, as this approach can recover classical VC dimension-based learning guarantees. This framework provides a robust theoretical foundation for achieving generalization in computationally bounded settings, potentially enabling more reliable model performance where traditional independence assumptions fail.

Key insights

Given a simulator for dependent data, classical VC dimension learning guarantees can be recovered, broadening the PAC model.

Principles

• Simulators enable classical learning guarantees for dependent data.
• Conditional sampling offers statistical and computational advantages.
• Regret can be controlled by time-bounded Kolmogorov complexity.

Topics

• Simulatable Processes
• Learning Theory
• VC Dimension
• Dependent Data
• PAC Model
• Kolmogorov Complexity

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.