Agentic Skill Optimization over Lie Algebroids

Skill documents, structured natural-language instructions that guide Large Language Model (LLM) agents, are critical to modern agent frameworks, yet LLMs struggle to write skills that actually work. On SkillsBench, human-authored skills improve pass rates by 16.2 percentage points, while LLM-authored skills provide no measurable gain. We introduce SkillAxe, a fully unsupervised framework that enables LLMs to iteratively diagnose and refine their own skills. SkillAxe decomposes skill quality into four interpretable dimensions (quality impact, trigger precision, instruction compliance with fault attribution, and solution-path coverage), producing structured improvement briefs that require no ground-truth labels, test suites, or environment rewards. On SkillsBench, SkillAxe improves pass rates by 28% relative over unimproved LLM skills and closes 47--67% of the gap to human-authored skills. We validate the approach as a continuous improvement engine in the wild on SpreadsheetBench, where a SkillAxe-built skill library learns from past agent trajectories and raises pass rate from 16.0% to 52.0% using only 22 skills.

Agent skills provide a lightweight way to adapt LLM agents to specialized domains by storing reusable procedural knowledge in structured files. However, whether downloaded from third parties or self-generated, these skills are often unreliable, incomplete, or outdated. Existing skill-evolution methods often address these deficiencies through heuristic reflections without an explicit optimization formulation. In this paper, we propose SkillGrad, a gradient-descent-inspired framework for optimizing agent skills. SkillGrad treats the skill package as a structured parameter to optimize in a gradient descent fashion: task executions provide trajectory-level loss evidence, automatic diagnoses then provide text-based gradients that indicate the correction directions. To stabilize optimization across iterations, a momentum agent accumulates recurring diagnostic patterns into a persistent memory overlay. Finally, an LLM-based patcher executes the parameter update by applying layer-aware edits to the skill package. Evaluated on SpreadsheetBench Verified and WikiTableQuestions, SkillGrad consistently outperforms training-based skill evolution baselines across two backbone LLMs, improving over the strongest training-based baseline by $6.7$ percentage points on average. Ablations further show that momentum and contrastive diagnosis both contribute to the final skill quality.

Agentic large language models often rely on skills, reusable natural language procedures that guide planning, action, and tool use. In practice, skills are typically improved through prompt engineering or by aligning the task LLM itself, which is costly, model-specific, and often infeasible for closed-source models. Skill optimization is not a one-step problem but a recurrent process with two coupled levels of credit assignment: a useful skill must improve rollout quality under current conditioning, while a useful revision must turn observed outcomes into a better skill for the next round. We propose Skill-R1, a reinforcement learning framework for instance-level recurrent skill optimization from verifiable rewards. Rather than updating the task LLM, Skill-R1 trains a lightweight skill generator that conditions on the task context, prior rollouts, and their verified outcomes to produce skills that steer a frozen task LLM. This preserves black-box compatibility with both open- and closed-source models while making adaptation substantially cheaper than model-level updates. Skill-R1 proceeds over multiple generations: at each step, the current skill induces rollouts whose verified outcomes are fed back to produce the next revision. To optimize this recurrent process, we introduce a bi-level group-relative policy optimization objective combining intra-generation and inter-generation advantages. The intra-generation term compares rollouts under shared skill conditioning, while the inter-generation term rewards revisions that improve behavior across successive generations. Together, these provide a principled objective for directional skill evolution rather than one-shot self-refinement. Empirically, Skill-R1 achieves consistent gains over no-skill baselines and standard GRPO across benchmarks with verifiable rewards, with particularly strong improvements on complex, multi-step tasks.