The Red Queen Gödel Machine: Co-Evolving Agents and Their Evaluators
Authors: Alex Iacob, Andrej Jovanović, William F. Shen, Daniel Burkhardt, Meghdad Kurmanji, Nurbek Tastan, Lorenzo Sani, Niccolò Alberto Elia Venanzi, +5 more
Organizations: University of Cambridge · 3Flower Labs · 2NVIDIA · 4MBZUAI · 5Inria
Self-improving agents are state-of-the-art (SOTA) on agentic coding benchmarks and have recently been extended to general domains. However, their search methods generally assume a stationary evaluation criterion: a fixed verifier, benchmark, or labeled dataset that remains valid as the agent improves. This ignores a central feature of evolution: species adapt as their environments change with them. We aim to bring the same principle to recursive self-improvement, making evaluation part of the improvement loop and opening search to evolving evaluators, adversarial objectives, and dynamic utilities that may surpass static benchmarks. We introduce the Red Queen Godel Machine (RQGM), an evolutionary framework for recursive self-improvement under non-stationary utilities. The RQGM makes this possible through controlled utility evolution: search is organized into epochs with a fixed within-epoch evaluation criterion, while the utility can be updated at epoch boundaries, so self-improvement guarantees hold per epoch as the objective evolves across them. We begin by showing that even on verifiable coding tasks, the RQGM improves test pass rate over the prior SOTA by adding a complementary agent-as-a-judge code-review signal. This signal is cheaper and the RQGM uses 1.35x-1.72x fewer tokens. We then turn to scientific paper writing and reviewing, and Olympiad-level proof writing and grading, where the RQGM improves performance over prior self-improving agents: co-evolved writers reach 1.78x-1.86x higher acceptance rates under a diverse agent-as-a-judge panel, while co-evolved graders reach 9% higher ground-truth accuracy. In paper reviewing, the strongest baseline reviewer over-accepts AI-generated papers at up to 1.91x the human rate. The RQGM corrects this by introducing an adversarial objective that discovers reviewers equally stringent on AI and human work.
Self-evolving agent systems improve by creating, revising, and retiring their own skills, but every such loop rests on a hidden assumption: a reliable evaluation metric already exists. In many real applications it does not. We make three claims. First, metrics can be \emph{evolved}: our metric loop searches compositions of small drawback detectors under a full evolutionary lifecycle, trained to agree with a ten-item anchored reference set, regularized by consensus over unlabeled outputs, and audited against a held-out anchor it never reads, yielding a transparent, inspectable metric rather than an opaque judge. Second, since no metric exists to beat, the yardstick is recovering what an accurate metric would have enabled, and \emph{Double Ratchet}, our co-evolution of the metric with a lifecycle-managed skill loop, does so: across code generation (MBPP+), enterprise text-to-SQL (Spider~2.0-Snow), and reference-free report generation, it retains 88--110% of the held-out lift achieved by the same skill loop driven by ground truth or the best available rubric. Third, safety comes from anchor discipline plus outer audits: removing anchor guards collapses the metric into a vacuous detector while removing the lifecycle does not; and when evolved skills gamed the report rubric, an independent judge caught it, one detector repaired it, and a task-aware judge then preferred the evolved outputs over the pre-evolution baseline in 77% of decided pairs. We argue this failure-expecting architecture is the right default wherever no reliable automatic verifier exists.
Self-evolving agents improve by repeatedly proposing changes to their own prompts, skills, or workflows and keeping those that score higher on a small held-out set. Almost all effort has gone into the proposer that generates candidates; we argue the weak point is the acceptor, the rule that decides whether to commit a change. Applied hundreds of times against the same noisy dev estimate, the ubiquitous "keep it if the score went up" rule is uncontrolled adaptive multiple testing: the agent effectively p-hacks itself, accumulating false commits that make it churn and drift rather than improve. We recast committing as a sequential hypothesis test and propose PACE (Paired Anytime-valid Commit Evaluation), a training-free, anytime-valid commit gate. Each candidate is compared to the incumbent on identical instances and committed only when a testing-by-betting e-process accumulates decisive evidence, stopping early to save evaluations and controlling each candidate's false-commit probability at a user-set level even under optional stopping (a per-decision guarantee). On Qwen2.5 agents (0.5B-3B) self-evolving at the prompt level on GSM8K, SVAMP, and ARC-Challenge, greedy acceptance commits 30-42% false and 10-33% harmful edits when a genuine improvement is hidden among noisy proposals, while PACE commits the real one and essentially nothing else, matching greedy's held-out accuracy at sharply lower variance and about 18% lower evaluation cost. With no real gain available, greedy commits 13-21 spurious self-modifications per run (72-100% false) and degrades the most fragile agent by 4.9 points, while PACE holds at baseline. Reliability of self-evolution depends on the acceptor, not only on the proposer.
Self-improving coding agents that iteratively rewrite their own source code have demonstrated impressive performance on coding tasks. However, existing solutions generally derive self-modification from a single failure trajectory at a time, overlooking rich comparative signals available in the agent's expanding archive of past attempts. According to Mendelian principles of controlled inheritance, we introduce Mendel Gödel Machine (MGM). In addition to the general single-trajectory clonal mutation, MGM includes two new types of self-modification that better utilizes evidences accumulated: the reaction-norm mutation edits an agent based on its trajectories on multiple tasks simultaneously, and the cross-lineage hybridization edits an agent using the trajectory of a reference agent from another lineage on the same task. Under an additive fitness landscape model, we prove theoretically and demonstrate via controlled surrogate simulation that the new strategies facilitate a faster and better convergence over single-trajectory baselines. Experiments on SWE-bench and Polyglot confirm MGM's consistent improvement in performance, efficiency, and generalizability.