Closed-Loop Generative Selection: Convergence, Memory, and Noisy Oracles

2026-07-27 · Source: cs.NE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

Kostantin Fackeldey and Christof Schütte's June 2026 paper introduces a rigorous convergence theory for closed-loop generative selection, a method widely used in computational drug discovery. This approach involves a generative model proposing molecules, a fitness oracle scoring them, and the model retraining on elite sets. The work addresses the previous lack of a formal convergence theory by recovering a Markov structure on an enlarged state space. It proves almost-sure convergence and provides runtime bounds, decomposing search time by fitness level. The analysis quantifies the role of the model's memory, showing that deeper memory generally helps, but excess memory can slow convergence if learning isn't consistently improved. The theory extends to multi-objective search and noisy oracles, detailing evaluation-minimal strategies. A reproducible study on a OneMax problem (n=40, N=20, M=40) confirms these predictions, including the surprising cost of excess memory.

Key takeaway

For AI Scientists and Research Scientists developing generative selection workflows in drug discovery, prioritize sequential evaluation (M=1) to minimize costly oracle calls, as this strategy is evaluation-optimal. Implement level-adaptive memory, matching depth to the current fitness level's learning profile, to optimize convergence speed. When dealing with noisy oracles, especially those with heavy-tailed distributions, employ robust estimators like median-of-means or distribution-free sign tests to ensure reliable progress certification and avoid false positives.

Key insights

This paper provides a rigorous theoretical framework for closed-loop generative selection, including convergence, runtime, and memory analysis.

Principles

• Elitism ensures non-decreasing fitness, making the search absorbing.
• Uniform positivity guarantees the algorithm never gets permanently stuck.
• More memory generally improves escape probabilities under monotone learning.

Method

The analysis recovers a Markov structure on an enlarged state space (augmented chain or history process) and uses layered hitting-time bounds to decompose search time by fitness level.

In practice

• Sequential evaluation (M=1) minimizes oracle calls in drug design.
• Adaptive memory depth (m_k^*) optimizes performance, especially with noisy oracles.
• Robust estimators (e.g., sign tests) restore guarantees under heavy-tailed noise.

Topics

• Generative Selection
• Evolutionary Algorithms
• Markov Chains
• Drug Discovery
• Runtime Analysis
• Noisy Oracles

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.