🧬 rqgm — Red Queen Gödel Machine

Co-Evolving Evaluators for Self-Improving AI Systems

First open implementation of arXiv 2606.26294 (Cambridge, June 2026)

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🚨 The Problem: Every Self-Improving Agent Eventually Cheats

Every self-improvement loop has a hidden failure mode. The agent learns to satisfy the evaluator rather than genuinely improving. The moment the judge stops getting harder, the loop stalls and reward hacking creeps in.

You've seen this before:

• RLHF reward hacking — models learn to produce plausible-sounding but vacuous text that scores well
• Benchmark overfitting — agents memorize benchmark patterns instead of learning general capabilities
• LLM-as-a-judge collapse — evaluator LLMs learn to prefer certain writing styles over correctness
• Your own agent loops — Dreamer padding source lists, Pragma satisfying checklists without real quality

The structural answer: Co-evolve the agent AND its evaluator together, so the bar keeps rising as the agent climbs.

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🧬 The Solution: RQGM

The Red Queen Gödel Machine (arXiv 2606.26294, Cambridge) introduces controlled utility evolution — the evaluator itself evolves at epoch boundaries, preventing reward hacking and keeping improvement loops honest.

Epoch 0 (tolerances: [0.0, 0.001, 0.01, 0.025, 0.05, 0.1])
  ├── Iteration 1: score 0.42
  ├── Iteration 2: score 0.51
  ├── Iteration 3: score 0.49
  ├── Iteration 4: score 0.53
  └── Iteration 5: score 0.55
       │
       └── Boundary check:
            ├── Hack ratio = 0.48 (strict/loose) → exploitation detected
            └── Drop loosest tolerance (0.1) → tighten evaluator

Epoch 1 (tolerances: [0.0, 0.001, 0.01, 0.025, 0.05])
  └── ... evaluator gets harder as agent improves

How It Works

Concept	What It Means	Why It Matters
Epoch	A fixed window of iterations with a frozen evaluator	Within-epoch guarantees hold; the agent can't game mid-epoch
Hack ratio	strict_score / loose_score — measures exploitation	Low ratio = agent gaming the evaluator
Utility evolution	Tolerances tighten when exploitation detected	The bar rises as the agent climbs
Adversarial scoring	Penalises answers that game loose criteria	Prevents pattern-matching the evaluator
Selective erasure	Invalidates scores from old evaluators	Stale hacked scores don't survive the boundary

Key Results from the Paper

Domain	Improvement
Coding benchmarks	1.35x–1.72x fewer tokens than prior SOTA
Scientific writing	1.78x–1.86x higher acceptance rates
Proof grading	9% higher ground-truth accuracy
Paper reviewing	Corrects 1.91x over-acceptance of AI-generated papers

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⚡ Quick Start

Zero dependencies. Python stdlib only. Install in 3 seconds.

pip install rqgm

from rqgm import EpochManager, EpochConfig, TransitionReason

# Configure: 5 iterations per epoch, tighten if hack_ratio < 0.6
config = EpochConfig(epoch_size=5, exploitation_hack_ratio_threshold=0.6)
mgr = EpochManager(config)

for i in range(20):
    # Your agent produces a result, you score it
    best_score = evaluate_agent()
    strict_score = evaluate_strict(agent_result)
    loose_score = evaluate_loose(agent_result)

    mgr.record_iteration_result(i, best_score, strict_score, loose_score)

    if mgr.is_epoch_boundary(i):
        transition = mgr.evaluate_epoch_boundary(i)
        if transition.reason != TransitionReason.NO_TRANSITION:
            print(f"⚠️  Epoch {mgr.epoch_index}: {transition.reason.name}")
            print(f"   Tolerances: {mgr.current_tolerances} → {transition.new_tolerances}")
            # Apply the new evaluator criteria
            update_evaluator(transition.new_tolerances)
        mgr.advance_epoch(transition)

Demo: agent improves → starts gaming → evaluator tightens → adversarial scoring penalises gaming

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🎯 Where to Use It

RQGM is a general-purpose primitive for any self-improvement loop. Here are real applications:

AI Agent Loops

# Detect when your agent is gaming the evaluator
mgr = EpochManager(EpochConfig(epoch_size=10))
for walk in agent_walks:
    mgr.record_iteration_result(i, quality_score, strict_score, loose_score)
    if mgr.is_epoch_boundary(i):
        transition = mgr.evaluate_epoch_boundary(i)
        if transition.reason == TransitionReason.EXPLOITATION_DETECTED:
            tighten_evaluation_criteria()  # Agent is gaming you

RLHF / Preference Learning

# Prevent reward model overfitting
dist = ScoreDistribution(scores_at_strict=human_preferences, scores_at_loose=model_scores)
new_tols, log = evolve_tolerances(current_tolerances, dist, params, 0.6, 0.02, 0.02)
# new_tols drops the loosest criterion → reward model gets harder

Benchmark Evaluation

# Detect benchmark overfitting
score = adversarial_score(
    question="What is 2+2?",
    predicted="approximately 4",  # gaming answer
    ground_truth="4",
    current_tolerances=[0.0, 0.1],
    adversarial_pool=gaming_examples,
)
# Returns 0.7 instead of 1.0 — penalised for gaming

CI/CD Quality Gates

# Evolve test pass thresholds based on historical exploitation
if transition.reason == TransitionReason.STAGNATION:
    raise_quality_bar()  # Tests haven't caught a bug in N cycles

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📦 Components

Module	Class / Function	Purpose
epoch.py	EpochManager	Tracks iterations, detects boundaries, triggers transitions
epoch.py	EpochConfig	Configuration: epoch size, thresholds, mutation params
epoch.py	EpochTransition	What the runner should do after a boundary
epoch.py	AdversarialExample	A gaming example (high loose score, low strict score)
evolution.py	evolve_tolerances()	Pure function: given scores, returns new tolerance schedule
evolution.py	adversarial_score()	Scorer that penalises answers resembling gaming patterns
evolution.py	ScoreDistribution	Stats over a set of per-answer scores
evolution.py	UtilityEvolution	Applies mutations to evaluator config at boundaries

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📊 Tested

35 unit tests, all passing. Covers:

• Epoch boundary detection
• Tolerance tightening on exploitation
• Tolerance relaxation on genuine improvement
• Adversarial pool collection
• Checkpoint serialisation round-trip
• evolve_tolerances() pure function
• adversarial_score() penalty computation
• ScoreDistribution.get_gaming_indices()

python3 -m tests.test_rqgm

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🔧 Installation

pip install rqgm

Or from source:

git clone https://github.com/observeco/rqgm-core
cd rqgm-core
pip install -e .

Dependencies: Zero. Python stdlib only. No PyTorch, no transformers, no numpy.

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📚 Reference

• The Red Queen Gödel Machine: Co-Evolving Agents and Their Evaluators — Iacob et al., University of Cambridge, June 2026
• EvoSkill-RQGM — Full integration with EvoSkill's self-improvement loop (first open RQGM implementation)

📖 Citation

If you use rqgm in your research, please cite the original paper:

@article{iacob2026redqueen,
      title={The Red Queen G{\"o}del Machine: Co-Evolving Agents and Their Evaluators},
      author={Iacob, Alex and Jovanovi{\'c}, Andrej and Shen, William F. and
              Burkhardt, Daniel and Kurmanji, Meghdad and Tastan, Nurbek and
              Sani, Lorenzo and Venanzi, Niccol{\`o} Alberto Elia and
              Odonnat, Ambroise and Cao, Zeyu and Marino, Bill and
              Qiu, Xinchi and Lane, Nicholas D.},
      year={2026},
      eprint={2606.26294},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

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📄 License

Apache 2.0 — free for commercial and research use.

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