APE

BayesPO: Bayesian posterior sampling framework for discrete prompt optimization

BayesPO reframes prompt optimization as Bayesian posterior sampling over discrete prompt tokens, combining a task likelihood term with a language-model prior to form an energy-based objective. The framework uses a Metropolis-Hastings corrected Gibbs-with-Langevin proposal with parallel tempering to explore rugged LLM energy landscapes without updating model weights. Experiments on Qwen2.5 models show modest accuracy gains on instruction-induction tasks (60.04% to 63.23%), with identified limitations around overfitting and computational cost. The work positions principled probabilistic methods as an alternative to heuristic prompt search procedures.