Evolutionary and Coevolutionary Multi-Agent Design Choices and Dynamics

Eric Liu; Erik Hemberg; Lucille Fuller; Stephen Moskal; Una-May O'Reilly

REVIEW 4 major objections 6 minor 28 references

Evolutionary and Coevolutionary Multi-Agent Design Choices and Dynamics

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Grammar-evolved code-like cyber agents achieve the highest team reward, while coevolution flattens the peaks and valleys that one-sided training produces.

desk verdict A useful but under-powered comparative study whose central coevolutionary dynamics claim is compromised by non-comparable fitness curves. read the letter →

arxiv 2507.05534 v1 pith:T3YLXMZC submitted 2025-07-07 cs.NE

Erik Hemberg , Eric Liu , Lucille Fuller , Stephen Moskal , Una-May O'Reilly This is my paper

classification cs.NE

keywords evolutionaryalgorithmsgrammaticalevolutioncoevolutioncybersecurityagentcontrollersLLMmutationoperatorCybORGadversarialdynamics

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper studies how to train competing teams of cyber agents when the designer can choose what to hard-code and what to evolve. It compares two controller representations—a fixed-size action-probability matrix optimized by an evolutionary strategy or a genetic algorithm, and code-like logic generated from a context-free grammar by grammatical evolution, including a variant whose mutation operator calls a large language model. Running in the CybORG scenario, the paper argues that the grammar-based representations reach the best team training reward, and that coevolution—both sides evolving against each other—consistently lowers and steadies the reward envelope for both sides relative to training one side against a fixed non-evolving opponent. The result matters because adaptive cyber defenses must anticipate attackers that also adapt, and the paper's dynamics findings characterize what performance tradeoff that adaptation implies.

What carries the argument

The central mechanism pair is (1) a context-free grammar whose non-terminals expand into Python-like statement blocks for action and target selection, decoded from an integer vector by grammatical evolution—the grammar itself fixes the syntax while evolution searches the conditions, actions, and target heuristics; and (2) the competitive coevolutionary algorithm, two evolutionary algorithms coupled only at fitness evaluation, where each individual's score comes from all-vs-all competitions against the other population. For the LLM variant, the mutation operator sends the current code block plus grammar context to the LLM and expects a mutated block, operating on the code rather than the genome. The fixed-size action-selection matrix, with one probability per state–action pair, is the contrasting mechanism that the grammar representation must beat.

What would settle it

Re-train one-sided agents against a substantially stronger static adversary (for example, a previously evolved red team with high reward) and check whether their peak fitness still exceeds the coevolutionary envelope; if it does not, the paper's central dynamic claim fails. A second check: run coevolution for several times more generations and measure whether the flattened reward envelope persists, ruling out that the effect is only a transient of limited-horizon training.

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Extended reading notes

Core claim

On its own terms, the paper claims that representation choices dominate algorithm choices in this domain: controllers expressed as Python-like code via grammatical evolution, using grammars that expose actions, targets, and observation counts, achieve the best team training performance across all tested designs, and the LLM-supported GE variant is competitive but highly sensitive to prompt and model choice. It further claims that coevolution, coupling two evolutionary algorithms at the fitness evaluation step, blunts the performance highs and lows of both red and blue teams while inducing fluctuations in their rewards, whereas one-sided evolution against a fixed finite-state-machine adversary produces higher and more sustained peaks. The paper also reports that discrete action-probability optimization outperforms continuous optimization for the matrix representation, and that richer grammars can improve performance when they supply the right terminals.

Load-bearing premise

The hidden premise is that the hand-tuned finite-state machine used as the fixed adversary is a representative non-evolving opponent; if that baseline were much stronger, the observed peak advantage of one-sided training could shrink or reverse.

Editorial extensions

If this is right

In this scenario, switching the controller representation from a fixed action-probability matrix to grammar-generated code is the highest-leverage design decision for training reward.
Coevolving the attacker and defender reduces the best-achievable reward of both sides; a defender that expects adaptation should train against a fixed strong adversary to maximize peak performance, at the cost of flexibility against novel attack strategies.
The LLM-based mutation operator's output quality is dominated by prompt engineering and model choice rather than by the evolutionary search itself.
Adding observation functions to the grammar (connections, file counts, root access levels) improves both best and mean fitness, showing that expressiveness helps when the right terminals are available.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the fixed finite-state-machine adversary in Appendix A.2 is weaker than a well-trained defender would be, then the one-sided-versus-coevolution comparison is biased toward one-sided training; re-running the comparison with a stronger scripted opponent would test whether the damping result is robust.
The oscillation the paper sees under coevolution hints at intransitive strategy cycles rather than simple convergence; checking whether fitness time series cycle under a fixed evaluation after training would separate cycling from genuine capability loss.
A practical extension is a hybrid mutation operator that validates each LLM-produced mutation against the grammar (and against syntax) before accepting it, which the paper's prompt-sensitivity results suggest would recover much of the GE-LLM performance loss.
Because the grammar abstracts controller logic away from the fixed network layout, the grammar-based controllers may transfer across CybORG network instantiations better than matrix controllers; a zero-shot transfer test across randomizations would quantify that.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things worth knowing. The paper is an honest, clearly written empirical comparison of controller representations (FSM vs grammar) and algorithms (GA, ES, GE, GE-LLM) for cyber agents in CybORG's CAGE Challenge 4, including one-sided versus coevolutionary training. The grammar-based controllers doing well is plausible and, as far as I know, new for this scenario. The second thing is that the signature 'coevolution reduces highs and lows' claim is built on curves that are not measuring the same thing.

The paper itself says in Section 5.2 that the best fitness for coevolving agents is relative to the adversaries they were evaluated against, and those adversaries are evolving too. So a drop in the coevolution curve can mean the opponent improved, not that the solution got worse. Comparing those curves to one-sided training against a fixed hand-coded FSM is apples-to-oranges. The stress-test note is right: without an absolute, out-of-sample measure, the abstract's general claim about coevolutionary dynamics is unsupported. The representation comparison (GE/GE-LLM vs FSM) is on firmer ground, since those runs use the same fixed adversary, but even there the empirical basis is thin.

Credit where it is due: the paper does useful work documenting prompt sensitivity for the LLM mutation operator, which is a surprisingly strong effect, and the limitations section is candid about no out-of-sample evaluation and limited repetitions. The related work table is helpful. The self-citation to [13] is appropriate, not inflated.

The soft spots are real but not fatal. Six trials and two repetitions with no variance bars or significance tests is too little to support the kind of general wording the abstract uses. The hand-coded FSM baseline is a weak opponent, so the one-sided peaks may just be beating up on a static dummy. No code or data is released, which makes independent checks harder, though CybORG is public.

Who gets value from this? Researchers working on coevolutionary training in cyber simulation, and people choosing controller representations for CybORG-type environments. It is a useful case study, not a settled result. I would send it to peer review, but I would push the authors to either add out-of-sample evaluation against a fixed strong adversary or drop the global dynamics claim down to a per-scenario observation. I would not cite it in my own work until those numbers are backed by more repeats and variance information.

Referee Report

4 major / 6 minor

Summary. The paper compares two controller representations (FSM-based action-selection matrices optimized by GA/ES, and code-like grammars optimized by GE/GE-LLM) for red and blue teams in a modified CybORG CCC4 scenario. It reports one-sided training against a fixed FSM opponent and two-sided coevolution, and claims that grammatical representations achieve the highest training fitness, that the GE-LLM operator is prompt- and model-sensitive, and that coevolution consistently dampens performance highs and lows while inducing fluctuations, whereas one-sided evolution reaches higher and more sustained peaks.

Significance. The paper addresses a relevant design space for evolutionary multi-agent cyber defense, extending CCC4 to train red agents and providing grammars and FSM baselines in the appendix. Strengths include the explicit statement of limitations, the reporting of LLM mutation validity and token statistics, and the inclusion of the experimental setup parameters. However, the central comparative claims about coevolution dynamics rest on fitness values measured under different evaluation protocols, and the headline performance claim is based on training reward only. With two repetitions, six trials, and no variance reporting, the empirical base is thin. If properly supported, the result would be a useful empirical data point for the evolutionary computation and cyber-security communities, but the current evidence does not fully support the abstract's general conclusions.

major comments (4)

[§5.2, Fig. 4] The abstract's central claim that coevolution reduces the performance highs and lows and induces fluctuations is not supported by the displayed comparison, because the two sets of curves are not measured on a common scale. One-sided fitness values are computed against the fixed FSM adversary (Appendix A.2), whereas the paper itself states that 'the best fitness for coevolving agents is relative to the adversaries that it was evaluated against.' A decrease or oscillation in the coevolutionary curve can therefore be caused by the opponent improving, not by the evaluated population degrading. To make the comparison valid, all designs should be re-evaluated at each generation against the same fixed reference opponent (or a common evaluation protocol), and the peak/fluctuation comparison should be repeated on those commensurable fitness values.
[§5.2, §5.3] The claim that the grammatical evolution versions 'can achieve the best team performance' is supported only by training fitness; Section 5.3 explicitly lists 'no out-of-sample evaluation of evolved solutions' as a limitation. Because the environment is stochastic and the host configurations are randomized, training reward is not necessarily team performance in the intended deployment sense. The authors should either add hold-out evaluation on new scenario seeds or unseen configurations, or restrict the claim to training fitness.
[Table 2, §5.2] The robustness of the dynamics comparison is unclear with six trials and two repetitions, and the paper omits all variance information, stating 'for visual clarity we do not display the fitness variance among the independent trials.' The repeated qualitative statement that coevolution 'consistently' blunts highs and lows is a visual impression rather than a quantified result. Please report per-run summary statistics (e.g., mean and variance of peak, trough, and fluctuation metrics) or show individual trial curves, with a significance test or effect-size measure where possible.
[§5.2.4] The final prompts used for the LLM-supported mutation operator are not provided, despite Section 5.2.4 showing that the operator's behavior changed qualitatively with prompt wording and that the authors had to add a cybersecurity-expert role instruction to obtain 'high quality mutations.' Since GE-LLM is one of the tested algorithms, this omission makes the GE-LLM comparison unrepeatable and the reported prompt sensitivity claim unverifiable. The exact prompts (or a complete prompt template) should be included in an appendix.

minor comments (6)

[Appendix A.2] There is a typo in the red FSM state description: 'Usesr with discovery' should be 'User with discovery.'
[Table 1] The first data row in Table 1 begins with 'Us,' which appears to be a leftover author tag rather than a meaningful environment or method entry; please clean this up.
[§5.2.1] The statement that 'the GE-LLM-C has lower fitness for both red and blue, still order of magnitude lower than FSM' is confusing given the earlier statement that GE fitness is an order of magnitude higher than FSM; please disambiguate which comparison is intended.
[Figure 2, Appendix A.1] Several grammar productions are missing closing quotation marks on the 'return' and 'target_heuristic' lines; this makes the grammar fragment harder to parse and should be corrected.
[§5.1.1] The text says 'one controller is used for all the re/blue agents'; this should be 'red/blue agents.'
[§5.2.2, Figure 5] The figure captions for the target-selection and extended-observation results (e.g., Fig. 6a) say 'GE-Red' without explaining which side is being plotted; please clarify the side and the comparison in each caption.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the paper is an empirical comparison, not a derivation, with only a minor non-load-bearing self-citation; the acknowledged relative-fitness caveat is a methodological concern, not a definitional circularity.

full rationale

The central claims (GE grammars achieve the best training fitness; coevolution dampens reward extremes relative to one-sided training) are direct observations of logged CybORG simulation rewards, not quantities derived from fitted parameters or from each other. No equation is involved, and no fitted input is renamed as a prediction. The only inline self-citation, [13] (Hemberg, Moskal and O'Reilly, 'Evolving code with a large language model'), appears in Section 4.2.1 to support the statement that 'LLM based operators of this type are often problem environment dependent'; it is peripheral and not load-bearing for any of the paper's comparative conclusions. The paper explicitly acknowledges the main caveat in Section 5.2: 'the best fitness for coevolving agents is relative to the adversaries that it was evaluated against,' and it lists 'no out-of-sample evaluation' as a limitation in Section 5.3. This means the one-sided versus coevolution comparison is not fully commensurable in an absolute sense, but the paper does not use that definition to construct its conclusions; it simply reports the observed curves. Consequently, there is no circular step where an output reduces by construction to an input. The score of 2 reflects the presence of a minor self-citation and the acknowledged protocol mismatch, neither of which makes the derivation circular.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper does not claim a mathematical derivation. Its central claims rest on simulation fidelity, hand-set hyperparameters, the design of the fixed FSM baselines, and the engineered LLM prompt. None of these are independently evidenced in the preprint, and several are explicitly identified as limitations by the authors.

free parameters (5)

Population size, trials, generations, steps, repetitions = 10, 6, >=20, 75, 2
Hand-chosen experimental settings that shape all reported fitness curves; no sensitivity analysis is provided for these values.
Mutation and crossover probability = 0.5
Set deliberately high to explore the search space, and this choice affects the observed convergence and fluctuation dynamics.
FSM transition probabilities for fixed adversaries = see matrices in Appendix A.2
Hand-set probabilities define the one-sided baseline opponents; different values would change the peak and coevolution comparisons.
LLM prompts = progressively refined through 4 versions
The GE-LLM results depend on the manually engineered prompt (naive, +grammar, +instructions, +cyber-expert role), as described in Section 5.2.4.
Grammar design choices = baseline plus 5 variants
Hand-designed grammars determine search space size and expressiveness; the results compare these specific choices only.

assumptions (4)

domain assumption CybORG's CAGE Challenge 4 simulator is an accurate-enough model of cyber operations for agent training conclusions.
All results are fitness values inside this simulator; no emulator or real-world validation is provided.
domain assumption The code produced by the grammars is executable and semantically meaningful in the CybORG environment.
GE decoding assumes valid Python blocks can be evaluated; invalid individuals are replaced with random new ones, and the grammar is designed to preserve syntax.
domain assumption Mean expected utility is an appropriate solution concept for comparing coevolving populations.
Coevolution fitness uses all-vs-all mean reward; other concepts such as Pareto or Elo-based sampling could change the observed dynamics.
ad hoc to paper Six trials and two repetitions suffice to reveal stable dynamics.
No confidence intervals or significance tests support this; the paper states these settings are due to simulation cost (Section 5.1).

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Cite this review

Pith. "Pith review of Evolutionary and Coevolutionary Multi-Agent Design Choices and Dynamics." pith.science (2026). https://pith.science/paper/T3YLXMZC

@misc{pith2026250705534,
  author       = {Pith},
  title        = {Pith review of: Evolutionary and Coevolutionary Multi-Agent Design Choices and Dynamics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T3YLXMZC}},
  note         = {Machine review of arXiv:2507.05534}
}

read the original abstract

We investigate two representation alternatives for the controllers of teams of cyber agents. We combine these controller representations with different evolutionary algorithms, one of which introduces a novel LLM-supported mutation operator. Using a cyber security scenario, we evaluate agent learning when one side is trained to compete against a side that does not evolve and when two sides coevolve with each other. This allows us to quantify the relative merits and tradeoffs of representation and algorithm combinations in terms of team performance. Our versions of grammatical evolution algorithms using grammars that allow a controller to be expressed in code-like logic can achieve the best team performance. The scenario also allows us to compare the performance impact and dynamics of coevolution versus evolution under different combinations. Across the algorithms and representations, we observe that coevolution reduces the performance highs and lows of both sides while it induces fluctuations on both sides. In contrast, when only one-side is optimized, performance peaks are higher and is more sustained than when both sides are optimized with coevolution.

Figures

Figures reproduced from arXiv: 2507.05534 by the authors.

**Figure 1.** CybORG Cage Challenge 4 network. samples are drawn from the other population which itself is evolving. A more formal approach, using the solution and test perspective, describes fitness assignments as solution concepts [21]. 3 RELATED WORK [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Partial baseline grammar for a controller. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** A coevolutionary algorithm unites two EAs, here called Solution and [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Agent evolution in CCC4. X-axis it the iteration. Y-axis agent fitness (reward). One subplot shows best fitness the other mean population fitness. Lines [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Number of controllers per team. X-axis it the iteration. Y-axis agent fitness (reward). One subplot shows best fitness the other mean population fitness. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Target selection. X-axis it the iteration. Y-axis agent fitness (reward). One subplot shows best fitness the other mean population fitness. Lines show the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: Timing results for GPT 3.5 and Phi4 when used in GE-LLM. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Target selection. X-axis it the generation. Y-axis agent fitness (reward). [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

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Reference graph

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