Skill$^{\infty}$: Recursive Self-Improvement for Agent Skill Optimization

Wangcheng Tao; Zhanglu Yan; Han Wu; Weng-Fai Wong

cs.AIOct 26, 2026

Skill $^{\infty}$ : Recursive Self-Improvement for Agent Skill Optimization

Authors: Wangcheng Tao, Zhanglu Yan, Han Wu, Weng-Fai Wong

Organizations: National University of Singapore · City University of Hong Kong

Abstract

Recursive self-improvement (RSI), in which a system also improves the way it improves, is a long-standing aspiration on the path to AGI. Language agents increasingly store procedural knowledge in reusable skills. Optimizing skills offers a direct way to achieve RSI, because the optimization procedure itself can be encoded as a skill. Existing skill optimizers, however, follow a hand-designed procedure. Even methods that evolve a meta-skill confine it to a fixed pipeline and relearn it for each task. We present Skill $^{\infty}$ , which makes skill optimization recursively self-improving: a meta agent follows a meta-skill to optimize task skills and optimizes the meta-skill itself using the same procedure. The optimization is agent-led. The meta agent diagnoses execution traces, proposes candidates, requests independent reviews, and allocates the search budget. The meta-skill defines these steps, allowing self-improvement to rewrite them. This meta-skill is also decoupled from task skills, refined on multiple skill optimization tasks and then reused to optimize task skills across diverse domains. As in deployment, skills at both levels are standard packages loaded through native skill discovery. On 83 SkillsBench tasks, Skill $^{\infty}$ reaches a pass rate of 60.7%, compared with 56.4% for human-curated skills and 54.5% for SkillEvolver.

Figures & tables

Panel of Figure 1 — Figure 1: Recursively self-improving skill optimization. Left: most skill optimizers follow a hand-designed procedure. Methods that evolve a meta-skill keep it inside a fixed pipeline and bound to the task skill it evolves with. Center: the $\infty$ shape shows the two loops of Skill $\infty$ , which meet at the meta-skill. In the left loop, the meta-skill optimizes itself on a set of skill optimization tasks, improving from $m_{0}$ to $m^{\star}$ . In each stacked loop on the right, the refined meta-skill is reused to optimize one task skill from $s_{0}$ to $s^{\star}$ . Right: the meta-skill at the crossing is a standard skill package loaded through native skill discovery, like any other skill. Each of its parts, from instructions to scripts, falls within the scope of self-improvement.

Panel of Figure 2 — Figure 2: Overview of Skill $\infty$ . Center: in each iteration, the meta agent follows six steps defined in the meta-skill, which is editable by self-improvement. The target is a task skill or the meta-skill itself. In the latter case, the meta agent revises the meta-skill while following it. Left: the archive records the optimization history. Drawing on this history, the meta agent steers the search and decides when to stop. An independent reviewer accepts or rejects each candidate. Right: the panels show one iteration on a task that exports the parts of a 3D scene. The meta agent attributes a failed check to one action of the task agent and proposes an exporter script as the fix.

Method	Overall $\uparrow$	SWE	Cyber	Science	Finance	Office	Media	Industrial	Math
	(83)	(14)	(7)	(14)	(9)	(14)	(9)	(11)	(5)
No skill	45.5	40.0	51.4	50.0	28.9	68.6	55.6	23.6	36.0
Human-curated	56.4	47.1	68.6	67.1	37.8	70.0	68.9	41.8	40.0
Self-generated	42.9	41.4	45.7	42.9	17.8	67.1	51.1	29.1	36.0
SkillCreator	48.0	55.7	51.4	48.6	24.4	61.4	53.3	27.3	60.0
SkillEvolver	54.5	60.0	42.9	52.9	28.9	74.3	66.7	34.5	72.0

Table 1: Main results on SkillsBench. Test pass rate (avg@5, %) overall and per domain, with the number of tasks in parentheses. Domains follow the SkillsBench taxonomy: software engineering (SWE), cybersecurity, natural science, finance and economics, office and white-collar work, media and content production, industrial and physical systems, and mathematics and formal reasoning. All methods use the Codex CLI with GPT-6 Luna.

Panel of Figure 3 — Figure 3: Results on KernelBench. Correctness-weighted speedup over the PyTorch reference, averaged over five trials, on three level-3 problems. The dashed line marks the speed of the reference. Runtimes are measured as in KernelBench on an NVIDIA A100 GPU. All methods use the Codex CLI with GPT-6 Luna.

Panel of Figure 4 — Figure 4: Results with another backbone model or harness. Test pass rate (avg@5, %) on SkillsBench. Appendix D gives the per-domain results.

Method	A	B1	B2	B3	C1	C2	D
	(33)	(8)	(6)	(2)	(13)	(2)	(19)
No skill	95.2	37.5	36.7	60.0	0.0	0.0	0.0
Human-curated	92.1	70.0	36.7	30.0	58.5	20.0	0.0
Self-generated	85.5	50.0	30.0	40.0	1.5	20.0	1.1
SkillCreator	89.1	52.5	43.3	10.0	6.2	30.0	10.5
SkillEvolver	91.5	65.0	33.3	20.0	15.4	60.0	22.1

Table 2: Pass rate by skill-utility category. Test pass rate (avg@5, %) on SkillsBench, with the number of tasks in parentheses. Appendix A defines the categories.

Panel of Figure 5 — Figure 5: Pass rate under different search budgets. Test pass rate (avg@5, %) on a subset of SkillsBench tasks. The solid line shows the optimized task skills, and the dashed line the agent without a skill.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Codex CLI with GPT-5.6 Luna
Method	Overall $\uparrow$	SWE	Cyber	Science	Finance	Office	Media	Industrial	Math
	(83)	(14)	(7)	(14)	(9)	(14)	(9)	(11)	(5)
Human-curated	61.2	40.0	74.3	71.4	37.8	64.3	77.8	61.8	76.0
Skill $\infty$	66.5	54.3	62.9	68.6	40.0	87.1	75.6	60.0	88.0
OpenCode with GPT-6 Luna
Human-curated	53.3	52.9	65.7	58.6	28.9	62.9	64.4	38.2	52.0

Appendix

Table 3: Per-domain results with another backbone model or harness. Test pass rate (avg@5, %) on SkillsBench, with the number of tasks in parentheses. Domains follow Table 1 .

Self-improvement
Method	Input (M)	Cached (M)	Output (k)
Skill $\infty$	8.74	8.23	66.3
SkillEvolver	8.06	7.64	75.8
SkillCreator	2.86	2.69	30.6
Total	97.65	92.00	778.6
Per task skill	1.18	1.11	9.4

Appendix

Table 4: Tokens consumed during optimization. Means per task skill over the 83 SkillsBench tasks with the Codex CLI and GPT-6 Luna. Token counts cover all agents involved in optimization and exclude the test trials. Input tokens include cached ones. Self-improvement is given in total and spread over the 83 task skills.

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Recent LLM agents tackle increasingly long-horizon, open-ended tasks, and external skills, reusable procedural knowledge supplied to the agent, further extend this capability. However, a fixed, hand-authored skill is rarely optimal, and cannot adapt to the diversity of tasks an agent encounters. Self-improving agents address this by rewriting their own skill files from execution traces, yielding meaningful gains on challenging benchmarks. Yet such self-evolution remains non-recursive: it improves only the task skill (what the agent does) while the improvement procedure (how it improves) is authored once and held fixed. We introduce MetaSkill-Evolve, a two-timescale framework that makes agentic skill improvement recursive: every branch carries both a task skill

s

and a branch-local meta-skill

m=(ψ,σ,α,π,\varepsilon)

whose five components parameterise the Analyzer, Retriever, Allocator, Proposer, and Evolver agents of the improvement pipeline. Task skills evolve on a fast loop while the meta-skill evolves on a slower one under the same pipeline applied to itself, with no additional model or objective. With all five pipeline agents sharing a single frozen backbone, MetaSkill-Evolve outperforms no-skill, static-skill, and single-level evolution baselines on three agentic benchmarks (OfficeQA, SealQA, ALFWorld), improving held-out test accuracy over the raw backbone by +23.54, +16.09, and +1.92 points respectively.

Abstract

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