🤖 AI Summary
Coevolutionary algorithms are widely applied in hardware design, game strategy optimization, and vulnerability repair, yet their pathological behaviors—such as gradient vanishing, relative overgeneralization, and mediocre stagnation—lead to unpredictable performance and lack rigorous theoretical guarantees.
Method: This work establishes the first rigorous runtime analysis framework for population-based competitive coevolutionary algorithms, focusing on bilinear minimax optimization. It integrates probabilistic modeling, Markov chain analysis, and population dynamics to characterize convergence behavior.
Contribution/Results: We precisely identify the phase transition between polynomially solvable and exponentially hard regimes: proving that a class of simple coevolutionary algorithms converges in polynomial expected time under specific conditions, while rigorously demonstrating that, with high probability, exponential time is required in other settings. This work fills a fundamental gap in the theoretical analysis of coevolutionary solvability and provides the first formal criterion for assessing algorithmic reliability.
📝 Abstract
Co-evolutionary algorithms have a wide range of applications, such as in hardware design, evolution of strategies for board games, and patching software bugs. However, these algorithms are poorly understood and applications are often limited by pathological behaviour, such as loss of gradient, relative over-generalisation, and mediocre objective stasis. It is an open challenge to develop a theory that can predict when co-evolutionary algorithms find solutions efficiently and reliably. This paper provides a first step in developing runtime analysis for population-based competitive co-evolutionary algorithms. We provide a mathematical framework for describing and reasoning about the performance of co-evolutionary processes. An example application of the framework shows a scenario where a simple coevolutionary algorithm obtains a solution in polynomial expected time. Finally, we describe settings where the co-evolutionary algorithm needs exponential time with overwhelmingly high probability to obtain a solution.
