Large language models (LLMs) are typically aligned with population-level preferences, despite substantial variation across individual users. We introduce POPI, a user-level personalization framework that separates the problem into two components connected by a natural-language interface: a shared inference model that distills heterogeneous user signals into a concise preference summary, and a shared generator that conditions on this summary to produce personalized responses. Both components are trained under a unified preference-optimization objective, with reinforcement learning handling the non-differentiable inference step. This objective decomposes into generator approximation error and summary informativeness, revealing how a single loss simultaneously drives accurate generation and informative summarization. Because the interface is natural language, learned summaries can be inferred once per user and reused across different generators -- including frozen, black-box commercial APIs. Across four personalization benchmarks, POPI generally improves personalization quality while reducing context overhead by up to an order of magnitude.