Given a line-art sketch and user-specified color intent, controllable colorization must assign intended colors to fine-grained regions while preserving the underlying line structure. Existing methods have improved visual quality, but precise local adjustment remains difficult. In this work, we argue that the key limitation is the absence of a persistent correction state. Such a state records user intent, localized mismatches, grounded edit regions, and preservation constraints to guide targeted repairs. To address this, we introduce PaletteAgent, an agentic, self-evolving correction framework for controllable line-art colorization. PaletteAgent translates user intent into structured color prompts, employs judgment agents to diagnose mismatches, grounds problematic regions, preserves correct fields, and adaptively decides whether to refine globally, repair locally, or stop. This iterative process naturally defines the GRPO training objective for optimizing the agent’s correction policy. Empirical results show that PaletteAgent outperforms line-art colorization and general image-editing baselines. Further ablations confirm the role of maintaining a persistent correction state for controllable colorization.