During reinforcement learning, experience can be both internalized in LLM parameters and retained externally as reusable textual skills. Parameter updates alter the model's behavior and the interaction experience from which new skills are extracted. These skills, in turn, guide the model's subsequent interactions and parameter updates. As the model's capabilities evolve, previously beneficial skills may become redundant or detrimental. We present SkillDuet, a framework that coordinates parameter updates and skill evolution through model response feedback. Skills extracted from on-policy trajectories guide parameter updates through OPD at every step. A response-based score, Strength, ranks candidate skills by the magnitude of the shift they induce in the current model's responses, and the highest-scoring skills are periodically consolidated into a persistent global skill set (Global). The updated model and Global jointly guide subsequent interactions, generating experience for further parameter and skill updates. With Qwen3-4B, SkillDuet achieves success rates of 98.57% on ALFWorld and 92.97% on WebShop, exceeding the matched SEED-API baseline by 2.86 and 5.47 percentage points, respectively. Ablations show that response-based skill selection and Global consolidation improve task performance. Further experiments show that the benefits of retained skills depend on both their content and their compatibility with the model. SkillDuet provides a concrete mechanism for model-skill co-evolution and skill-level recursive self-improvement.

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