# Who Grades the Grader? Co-Evolving Evaluation Metrics and Skills for Self-Improving LLM Agents

> A self-evolving evaluation metric gains +0.21 agreement with hidden ground truth, but anchor discipline—not detector lifecycle—prevents collapse, and downstream task scores cannot validate a self-evolved evaluator.

- **Source:** [arXiv](https://arxiv.org/abs/2607.12790)
- **Published:** 2026-08-17
- **Permalink:** https://picx.dev/p/77192p
- **Whiteboard:** https://picx.dev/p/77192p/image

## Summary

## Summary (Overview)

- **Core contribution**: This paper introduces the first system to treat the evaluation metric itself as a first-class evolving object under a full evolutionary lifecycle, in a "sparse-anchor regime" where only ten anchored items with golden references are available—no pre-existing evaluator exists to score the search.
- **Key mechanism**: The metric is an expression tree composed of small typed drawback detectors (static, execution, and judge ops), evolved via synthesis, birth gating, marginal-contribution scoring, and retirement. Selection optimizes recall-weighted agreement with a ten-item anchor plus reliability-weighted consensus over unlabeled outputs.
- **Main finding on validity**: The evolved metric gains **+0.21 agreement** with hidden ground truth on MBPP+ (paired p = 0.014), beating the bare LLM judge it contains. Anchor discipline—not the detector lifecycle—is load-bearing for evaluator safety, inverting the lesson from skill evolution.
- **Critical warning**: Downstream task score *cannot* validate a self-evolved evaluator—a collapsed "always-pass" metric trains skills just as well as a valid one (Figure 3 demonstrates this dissociation).
- **Sufficiency result**: "Double Ratchet" (co-evolving metric + skill loop) retains **88–110%** of the lift that ground truth or a hand-written rubric would buy across MBPP+, Spider 2.0-Snow, and report generation.

## Introduction and Theoretical Foundation

### Background and Motivation

Self-evolving agent systems create, revise, and retire their own skills, but every such loop assumes a reliable evaluation metric already exists. In many real applications none does. Industry products fill the gap by hand: Claude's managed agents require developers to write outcome rubrics for a separate grader, and Codex's Record & Replay requires a human to demonstrate each workflow once. This paper automates that step.

### Problem Setup

Three disjoint splits play distinct roles:

- **train** (large, unlabeled): exposes where candidate metrics disagree or abstain; in co-evolution, the evolved metric grades these tasks for the skill loop.
- **dev** (tiny, anchored, ten items): each carries a golden reference against which a teacher emits soft pass/fail labels—the only supervised signal any loop reads.
- **test** (locked against the metric): holds the strongest available reference (unit tests, official execution comparison, rubric); no part of metric evolution reads it.

### Design Stance

> "We rarely know what good is, but given an output we can usually find drawbacks, so a clean verdict means no known drawback was found, not certified correctness."

Mostly deterministic detectors fail differently from the LLM being graded, resisting the shared-blind-spot collusion a bare LLM judge invites. Because a metric grading the loop that produced it is a Goodhart hazard, anchor discipline is strict: the tiny dev set is the only supervised signal.

## Methodology

### Metrics as Compositions of Drawback Detectors

An op is an atomic drawback detector $o(t, y, c) \to \{\text{drawback}, \text{clean}, \text{abstain}\}$ checking exactly one failure class. Ops come in three cost tiers:

- **Static ops**: parse the artifact
- **Execution ops**: run it (sandbox for code, live warehouse for SQL)
- **Judge ops**: ask an LLM one narrow question

A metric expression composes op verdicts with logical operators. Writing $v(e) \in \{1, 0, \bot\}$ for the verdict of expression $e$ on $(t, y)$, the grammar is:

$$
\begin{array}{r l} e: := o & \big | \bigvee_ {i \leq k} e _ {i} \big | \bigwedge_ {i \leq k} e _ {i} \big | \neg e \\ & \big | \big [ \sum_ {i \leq k} v (e _ {i}) \geq K \big ] \big | \big [ \sum_ {i \leq k} w _ {i} v (e _ {i}) \geq \theta \big ], \end{array}\tag{1}
$$

The output **passes** when the root finds no drawback. Verdicts are cached (ops are pure functions), so evaluation is a set of table lookups.

### The Metric Loop (Algorithm 1)

Two signals feed synthesis:
- **Misses**: dev items the current metric passes although their soft label is fail
- **Gaps**: train outputs on which the op pool abstains entirely or splits

A new op must pass a **birth gate**: fire on at least half its cluster and stay clean on known-good outputs. Ops born from anchored misses enter active; ops born only from unlabeled gaps enter as shadows (record verdicts but cannot be selected until they raise dev agreement).

**Selection** keeps the best-so-far candidate by:

$$
S (e) = A _ {\mathrm{dev}} (e) \cdot A _ {\mathrm{train}} (e) ^ {w} - \lambda C (e),\tag{2}
$$

where $A_{\mathrm{dev}}(e)$ is agreement with dev soft labels, $A_{\mathrm{train}}(e)$ is agreement with the consensus verdict of opining pool ops on unlabeled train outputs, $C(e)$ is expression size.

Key weighting choices:
- **Dev agreement is recall-weighted**: $(w_F r_{FAIL} + w_P r_{PASS})/(w_F + w_P)$ with $w_F = 2$, $w_P = 1$—a missed drawback costs twice a false alarm.
- **Consensus is reliability-weighted**: each op's vote scaled by $1 + \kappa \max(0, m_o)$ for anchored leave-one-out marginal $m_o$.

Two guards apply: **selection fails closed** (candidate with no usable dev opinion is unselectable) and a **validity gate** drops candidates that pass/fail/abstain on everything.

### Co-Evolution with the Skill Loop: Double Ratchet

The skill loop (Ratchet, adopted unchanged) needs a grader for its training tasks. Co-evolution hands it the current best evolved metric. Loops alternate under a fixed front-loaded curriculum (metric phases of 15/8/5/2 rounds between four 25-round skill phases). The comparison is a reference skill loop with ground-truth grading.

**Two ablations**:
- **Naive arm**: disables anchor guards (fail-closed anchoring, validity gate, skill-loop rollback) with the detector lifecycle fully on—the collusion-prone configuration unanchored agent-judge co-evolution implicitly runs.
- **No-lifecycle arm**: keeps guards but disables birth gate and merit-based retirement.

### Independent Final Judge

A stronger LLM (Claude Opus 4.8, kept outside all loops) compares each final output pairwise against the pre-evolution baseline, judged twice with positions swapped; a win counts only when both orders agree.

## Empirical Validation / Results

### Metric Validity: The Evolved Metric Lifts and Transfers

**Table 1: Op lifecycle (anchored arm, 100 rounds)**

| Task | Seed | Born | Rejected | Pool | In metric |
|------|------|------|----------|------|-----------|
| MBPP+ | 10 | 2–4 | 997–1014 | 12–14 | 3 |
| Spider | 9 | 24–30 | 612–785 | 33–39 | 1–2 |
| Report | 11 | 11–15 | 172–188 | 22–26 | 2 |

The birth gate rejects **orders of magnitude more detectors than it admits**, and selection composes only one to three survivors. The objective rises from 0.16 to 0.52 on MBPP+ while the expression shrinks from six ops to three.

**Key results**:
- Evolved compositions beat the bare LLM judge op they contain: peak agreement $0.625 \pm 0.050$ vs. $0.55 \pm 0.04$ on MBPP+ and $0.500 \pm 0.026$ vs. $0.45 \pm 0.07$ on Spider.
- Round 0 (hand-authored seed composition) sits at $0.417 \pm 0.058$ on MBPP+, so the +0.21 is lift over static engineering.
- **Paired McNemar test**: across 120 matched verdicts, evolution corrects 61 items against 36 broken at peak (p = 0.014), every seed net positive.
- **Anchor robustness**: replaying report selection offline on 200 stratified subsamples of size 4, 6, and 8 anchored items gives held-out agreement $0.871 \pm 0.063$, $0.882 \pm 0.051$, and $0.874 \pm 0.041$ vs. 0.854 at the full ten—smaller anchors are noisier but means do not fall.

### Which Guard Carries the Load

**Table 2: Metric-validity ablations on report generation, final-rounds values**

| Arm | Objective | Held-out | Train | Outcome |
|-----|-----------|----------|-------|---------|
| anchored | $0.865 \pm 0.002$ | $0.830 \pm 0.012$ | .78–.82 | composes |
| naive | 1.000 (vacuous) | fail-open | .97–1.0 | collapses |
| no-lifecycle | $0.896 \pm 0.072$ | $0.868 \pm 0.061$ | n/a | no collapse |

Disabling anchor guards collapses the metric into a vacuous always-pass grader on 3/3 seeds. Disabling the lifecycle does **not**—this inverts the skill-evolution literature's emphasis: for evaluators under anchored selection, **anchor discipline carries the safety load**, not pool lifecycle.

### Co-Evolution: Sufficiency

**Table 3: Double Ratchet retains 88–110% of supervised lift**

| | MBPP+ | Spider | Report |
|---|---|---|---|
| Peak: skill | 0.700±0.025 | 0.483±0.038 | 0.850±0.010 |
| Peak: co | 0.717±0.038 | 0.458±0.038 | 0.812±0.006 |
| Peak: co naive† | 0.742±0.014 | 0.458±0.029 | 0.841±0.003 |
| **Lift retention (co)** | **106%** | **110%** | **88%** |
| Δpeak (co - skill) | +.02 | -.03 | -.04 |
| 95% CI | [-.03, .06] | [-.08, .03] | [-.05, -.03] |
| Improved: skill | 16/23 | 4/12 | 99% |
| Improved: co | 19/23 | 6/12 | 99% |

The naive arm's vacuous metric scores as well as the anchored one—**downstream task performance cannot validate a self-evolved evaluator**. The arms stay ordered at the unselected End column exactly as at peak, so retention is not an artifact of the peak argmax.

### The Goodhart Episode

The rubric's metric-discipline dimension counts inline evidence tags; evolved skills gamed it by writing the tag without the number (~30% of tags at peak rounds had no value) and inventing confident forecasts.

**Table 5: Final-judge win rate of evolved report outputs over baselines**

| | Generic judge | Task-aware judge |
|---|---|---|
| pre-repair (gamed proxy) | 0.122 | 0.515 |
| post-repair (erasure fixed) | 0.126 | 0.770 |

The repair (a vocabulary-aware value-erasure check plus failure hints) cut erased tags to ~1% while rubric score rose to 0.850±0.010. The task-aware judge reveals the fix moves real content quality from 0.515 to 0.770; the generic judge (which penalized a required output format as a defect) shows almost no movement—**the audit needs the task contract**.

### The Detectability Spectrum

A within-task Spider 2.0-Snow contrast: grounding the solver prompt with typed schemas raised the baseline by half but pushed residual failures from compile errors (mechanically checkable) to semantically wrong values under clean execution (invisible to deterministic ops). The same metric loop's held-out agreement fell from **0.85 to 0.500** even as the objective lifted.

## Theoretical and Practical Implications

1. **Task score cannot certify a self-evolved evaluator**: The naive arm's vacuous metric trains skills as well as the anchored one (Figure 3). The experiment this literature reaches for first—co-evolve a judge with a policy and report the policy improved—would have certified a grader that passes everything.

2. **Anchor discipline vs. lifecycle for evaluators**: For skills, lifecycle management is the key finding; for evaluators under anchored selection, anchor discipline carries the safety load. The metric-side analog of library drift is **anchor drift**, not pool drift.

3. **Validity vs. sufficiency are different questions**: Sufficiency asks whether a loop trained on the evolved metric reaches where ground truth would take it (largely yes, since skill loops consume grades directionally). Validity asks whether the grader is right—the question every use outside a training loop turns on.

4. **Legibility enables repair**: An inspectable expression (vs. an opaque learned scalar) localized the rubric-gaming defect to a nameable check, enabling a one-line diagnosis and repair.

5. **The detectability boundary moves toward harder**: Every improvement to the solver retires the failures a static op could catch and leaves behind the ones only judgment can.

## Conclusion

The evaluation metric can itself be the evolving object, and it evolves into something valid: +0.21 held-out agreement on MBPP+ against a locked reference no part of selection reads, beyond seed noise under a paired test. Anchor discipline, not the pool lifecycle, makes that hold—and the arm without it warns that task score certifies nothing, a worthless metric training skills just as well.

Read for sufficiency rather than validity, Double Ratchet retains 88–110% of the supervised lift across code, enterprise SQL, and report writing. On the one task where no golden metric exists, an outer judge caught the loop gaming its own reference, one detector plus its hints repaired it without cost to the score, and auditing the judge caught the audit mistaking a required output format for a defect.

**Who grades the grader**: an anchor it predicts but never sees, and an outside judge that must itself be checked.

**Limitations**: A mechanism study, not a scaling result—three task families, one model family, rounds in the low hundreds, held-out sets of tens of items. Teacher quality is held fixed; the Goodhart repair is claimed as a coupled pair (detector + hints); the task-aware rubric is a diagnosis, not independent confirmation. Metamorphic detectors—the natural next op family for the semantic regime—are built but unexercised.

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