🤖 AI Summary
Closed-loop generative selection algorithms are widely used in computational drug discovery, yet they lack convergence guarantees due to the violation of the Markov property caused by model retraining at each iteration. This work restores the Markov structure by expanding the state space and provides, for the first time, an almost sure convergence proof along with a decomposition of runtime complexity for such algorithms. We further reveal a dual role of memory depth in search efficiency: excessive memory depth can paradoxically slow convergence. By integrating absorbing-state analysis, exit-time estimation, and robust multi-objective optimization, we propose a practical strategy that minimizes the number of evaluation calls. Theoretical predictions are corroborated through reproducible experiments, demonstrating consistent performance under both light- and heavy-tailed noise conditions.
📝 Abstract
Closed-loop generative selection has become a workhorse of computational drug discovery: a learned generative model proposes candidate molecules, a fitness oracle scores them, the best are kept, and the model is retrained on this elite set before the next round. Despite its wide use, the method has lacked a rigorous convergence theory, largely because retraining the model each round breaks the Markov property on which classical evolutionary-algorithm analysis relies. We develop a self-contained theory of convergence and expected running time for this class of algorithms. By recovering a Markov structure on an enlarged state space, we show that elitism makes the search absorbing, and we prove almost-sure convergence together with a runtime bound that decomposes the search into the time spent escaping each fitness level. We then analyse the role of the model's memory---how much of the past it is trained on. When learning improves steadily with more data, deeper memory never hurts; when it does not, an exit-time analysis pinpoints the optimal memory depth and shows that excess memory can actually slow convergence. The theory extends to multi-objective search and to noisy oracles: we quantify how many repeated evaluations certify progress under light-tailed noise, and how robust estimators restore guarantees under heavy tails. Recast in terms of oracle evaluations - the true bottleneck in drug design - the analysis yields a concrete, evaluation-minimal strategy. Areproducible study confirms the predictions, including the surprising cost of excess memory. We close with three open problems.