Phylogeny-Informed Interaction Estimation Accelerates Co-Evolutionary Learning

TL;DR

Co-evolutionary fitness evaluation is computationally intensive due to all-versus-all interactions. The authors propose phylogeny-informed interaction estimation and matchmaking, using runtime phylogenies to estimate interaction outcomes from relatives via a k-nearest-neighbor approach and to select informative interactions for evaluation. They demonstrate the approach on three domains (Numbers Game, Sorting Networks, Collision Game), showing substantial early-stage reductions in evaluations and accelerated complexity growth in open-ended settings, with domain-dependent effects and occasional biases. Overall, the method offers a scalable path to maintain open-ended co-evolution while cutting computational costs, though it requires careful matchmaking choices and further refinements for different problem classes.

Abstract

Co-evolution is a powerful problem-solving approach. However, fitness evaluation in co-evolutionary algorithms can be computationally expensive, as the quality of an individual in one population is defined by its interactions with many (or all) members of one or more other populations. To accelerate co-evolutionary systems, we introduce phylogeny-informed interaction estimation, which uses runtime phylogenetic analysis to estimate interaction outcomes between individuals based on how their relatives performed against each other. We test our interaction estimation method with three distinct co-evolutionary systems: two systems focused on measuring problem-solving success and one focused on measuring evolutionary open-endedness. We find that phylogeny-informed estimation can substantially reduce the computation required to solve problems, particularly at the beginning of long-term evolutionary runs. Additionally, we find that our estimation method initially jump-starts the evolution of neural complexity in our open-ended domain, but estimation-free systems eventually "catch-up" if given enough time. More broadly, continued refinements to these phylogeny-informed interaction estimation methods offers a promising path to reducing the computational cost of running co-evolutionary systems while maintaining their open-endedness.

Figures (4)

• Figure 1: Results for the CompareOnOne setting of the Numbers Game across thirty trials, 95% confidence intervals are shown, but very small. Left: Mean genotype sum across both populations for all three matchmaking methods. Right: Average estimation error between our two match making methods. The possible error of interaction estimation is bounded between 0 and 1, where 0 is perfect accuracy. Parents-versus-all results in consistently less error on this domain compared to random cohorts ($p\ll0.001$, Wilcoxon test; Glass's $\Delta=-1.15$).
• Figure 2: Results for the CompareOnAll setting of the Numbers Game across thirty trials, 95% confidence intervals shown. Left: The average sum of all dimensions over all genotypes for each population. While all methods appear to perform well initially, the progress of parents-versus-all plateaus, unlike random cohorts. Right: Estimation error in the CompareOnAll setting. Parents-versus-all matchmaking results in lower average error than random cohorts ($p < 0.05$ at 2e6 evaluations, Wilcoxon test; Glass's $\Delta=-0.36$), even when performing worse.
• Figure 3: Results for Sorting Networks across thirty trials, 95% confidence intervals are shown. Top: Average percentage of perfect sorting networks. Middle: Average number of swaps of the best sorting network. Bottom: Error of our estimators on 16-Input Sorting Network. The minimum possible error is 0, and the maximum possible error is 16. The parents-versus-all method has significantly lower error than random cohorts during initial stages of evolution ($p\ll0.0001$ at 1e7 evaluations, Wilcoxon test; Glass's $\Delta=-2.42$).
• Figure 4: Collision Game results across thirty trials, 95% confidence intervals shown. Left: Average number of connections across all minimized neural networks. Despite appearances, only parents-versus-all significantly accelerates growth during the first 50-100 million evaluations ($p<0.001$ at 5e7 evaluations, Wilcoxon test; Glass's $\Delta=1.3$), whereas random cohorts does not ($p<0.35$ at 5e7 evaluations, Wilcoxon test; Glass's $\Delta=0.48$) due to high variance between trials. All-versus-all eventually "catches up" in terms of the development by 3e8 evaluations (overlapping confidence intervals). Neither estimation methods performs worse than the baseline. Right: Estimator error. Minimum possible error is 0, maximum is 1. Despite appearances, parents-versus-all produces significantly lower error towards the beginning of the runs ($p<0.001$, Wilcoxon test; Glass's $\Delta=-1.02$) while errors near the end are not significantly different ($p<0.11$, Wilcoxon test; Glass's $\Delta=-0.57$).