The performance of Large Language Models (LLMs) depends heavily on the chosen prompting strategy, yet static approaches such as Zero-Shot, Few-Shot, or Chain-of-Thought (CoT) impose a rigid efficiency-accuracy trade-off. Highly accurate strategies like Self-Consistency (SC) incur substantial computational waste on simple tasks, while lightweight methods often fail on complex inputs. This paper introduces the Prompt Policy Network (PPN), a lightweight reinforcement learning framework that formalizes adaptive strategy selection as a single-step Markov Decision Process (MDP). The PPN, trained with Proximal Policy Optimization (PPO) and guided by a resource-explicit reward function, learns to allocate costly reasoning strategies only when necessary. Experiments on arithmetic reasoning benchmarks demonstrate that PPN achieves superior performance on the efficiency-accuracy Pareto front, delivering up to 61.5% token cost reduction compared to Self-Consistency while maintaining competitive accuracy. This work contributes a systematic, adaptive framework for cost-efficient LLM deployment, advancing the design of lightweight optimization techniques for scalable and sustainable language model applications.