SkillAdam: Stable and Efficient Skill Evolution for Agents

Agent skills provide a lightweight mechanism for equipping frozen language-model agents with domain knowledge and procedural guidance. However, building high-quality skills remains costly and difficult to scale. As expert-written skills require substantial human effort, recent skill self-evolution methods automate skill optimization using execution feedback. Yet these methods still rely on heuristic update strategies that often lead to unstable optimization and low iteration efficiency. To address these limitations, we identify two key principles for stable and efficient skill optimization. (1) Direction Stability requires effective corrections to accumulate across iterations rather than be overwritten by iteration-local feedback. (2) Update Adaptivity requires the scope of each revision to reflect the consistency of recent case-level improvements. We introduce SkillAdam, an Adam-inspired framework that applies these principles to the optimization of discrete and non-differentiable skill documents. Inspired by Adam's first moment, SkillAdam maintains an optimization memory that accumulates identified problems and prior solution attempts to stabilize the update direction. Inspired by Adam's second moment, it maintains a volatility-driven edit budget that tracks the history-weighted variation of recent case-level improvements to adaptively control the update magnitude. Extensive experiments on seven benchmarks spanning both short- and long-horizon tasks show that SkillAdam achieves state-of-the-art performance with substantially more stable optimization, while requiring substantially fewer optimization iterations and lower optimization cost than prior methods. Code is available in the supplementary materials.