Adaptive Collaboration with Humans: Metacognitive Policy Optimization for Multi-Agent LLMs with Continual Learning

While scaling individual Large Language Models (LLMs) has delivered remarkable progress, the next frontier lies in scaling collaboration through multi-agent systems (MAS). However, purely autonomous MAS remain ``closed-world'' systems, constrained by the static knowledge horizon of pre-trained models. This limitation makes them brittle on tasks requiring knowledge beyond training data, often leading to collective failure under novel challenges. To address this, we propose the Learning to Intervene via Metacognitive Adaptation (LIMA) framework, a principled paradigm for human--agent collaboration. LIMA trains agents to learn a metacognitive policy that governs when to solve problems autonomously and when to defer to a human expert. To operationalize this policy, we introduce Dual-Loop Policy Optimization (DLPO), which disentangles immediate decision-making from long-term capability growth. The inner loop applies Group Relative Policy Optimization (GRPO) with a cost-aware reward to optimize deferral decisions, while the outer loop implements continual learning, transforming expert feedback into high-quality supervised signals that strengthen the agent's reasoning ability. Experiments on challenging mathematical and problem-solving benchmarks show that LIMA, equipped with Dual-Loop Optimization, consistently outperforms state-of-the-art MAS, establishing a principled foundation for collaborative and continually improving agentic systems.