Target-driven recommendation dialogues present unique challenges in dialogue management due to the necessity of anticipating user interactions for successful conversations. Current methods face significant limitations: (I) inadequate capabilities for conversation anticipation, (II) computational inefficiencies due to costly simulations, and (III) neglect of valuable past dialogue experiences. To address these limitations, we propose a new framework, Experiential Policy Learning (EPL), for enhancing such dialogues. EPL embodies the principle of Learning From Experience, facilitating anticipation with an experiential scoring function that estimates dialogue state potential using similar past interactions stored in long-term memory. To demonstrate its flexibility, we introduce Tree-structured EPL (T-EPL) as one possible training-free realization with Large Language Models (LLMs) and Monte-Carlo Tree Search (MCTS). T-EPL assesses past dialogue states with LLMs while utilizing MCTS to achieve hierarchical and multi-level reasoning. Extensive experiments on two published datasets demonstrate the superiority and efficacy of T-EPL.