Constructing efficient and reliable policies to assist humans is indispensable for human-AI collaboration. Existing methods mainly follow two lines of work. The majority of prior work relies on multi-agent reinforcement learning (MARL) to learn black-box policies, which limits interpretability and raises safety concerns. Recent methods query large language models (LLMs) at each decision step, causing slow responses and high inference costs. We propose Co-𝜋-tree, a closed-loop method that learns an executable policy tree consisting of a partner-behavior prediction tree and an agent-action selection tree. Co-𝜋-tree constructs a policy through distilling LLM reasoning into policy tree code. It then evaluates the policy through partner interaction, obtains feedback, and uses natural language summaries of interaction feedback to improve problematic branches. Experiments in Overcooked-AI show that Co-π-tree improves average reward by 6.4% over the strongest LLM baseline, while reducing the number of LLM queries by 77.7% and test-time latency by 97.1%. Project page: https://beiwenzhang.github.io/Co-pi-tree/.