Time series models predict numbers; decision-makers need advisory -- directional signals with reasoning, actionable suggestions, and risk management. Training language models for such predictive advisory faces a fundamental challenge: quality depends on outcomes unknown at prediction time. We bridge two ideas from reinforcement learning -- using information unavailable during execution to retrospectively generate training signal, and preference alignment -- and propose Hindsight Preference Optimization: observed outcomes let an LLM judge rank candidate advisories on dimensions that scalar metrics cannot capture, producing preference pairs for DPO without human annotation. We apply this to Vision-Language-Model-based predictive advisories on S&P 500 equity time series, demonstrated by a 4B model outperforming its 235B teacher on both accuracy and advisory quality.
@article{arxiv.2604.23988,
title = {Hindsight Preference Optimization for Financial Time Series Advisory},
author = {Yanwei Cui and Guanghui Wang and Xing Zhang and Peiyang He and Ziyuan Li and Bing Zhu and Wei Qiu and Xusheng Wang and Zheng Yu and Anqi Xin},
journal= {arXiv preprint arXiv:2604.23988},
year = {2026}
}