# Runtime Analysis of Competitive co-Evolutionary Algorithms for Maximin Optimisation of a Bilinear Function

arXiv: https://arxiv.org/abs/2206.15238 · HTML: https://mlsanity.com/paper/2206.15238/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2022.

## Built on by (most cited first, 2 of 2)

- [Concentration Tail-Bound Analysis of Coevolutionary and Bandit Learning Algorithms](https://mlsanity.com/paper/2405.04480/) (2024)
- [Randomised Optimism via Competitive Co-Evolution for Matrix Games with Bandit Feedback](https://mlsanity.com/paper/2505.13562/) (2025)

## Abstract (arXiv)

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 reliable. 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. To illustrate the framework, we introduce a population-based co-evolutionary algorithm called pdcoea, and prove that it obtains a solution to a bilinear maximin optimisation problem in expected polynomial time. Finally, we describe settings where pdcoea needs exponential time with overwhelmingly high probability to obtain a solution.