PBSD: Privileged Bayesian Self-Distillation for Long-Horizon Credit Assignment

Yang Tian; Rui Wang; Xumeng Wen; Junjie Li; Shizhao Sun; Lei Song; Jiang Bian; Bo Zhao

title	PBSD: Privileged Bayesian Self-Distillation for Long-Horizon Credit Assignment
authors	Yang Tian, Rui Wang, Xumeng Wen, Junjie Li, Shizhao Sun, Lei Song, Jiang Bian, Bo Zhao
date	2026-06-08
venue	arXiv (preprint, not peer reviewed)
id	arXiv:2606.09348
affiliation	Shanghai Jiao Tong University
links	abs pdf hf
abstract	Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.

cite

@misc{tian2026pbsd,
  title={PBSD: Privileged Bayesian Self-Distillation for Long-Horizon Credit Assignment},
  author={Yang Tian and Rui Wang and Xumeng Wen and Junjie Li and Shizhao Sun and Lei Song and Jiang Bian and Bo Zhao},
  year={2026},
  eprint={2606.09348},
  archivePrefix={arXiv},
  url={https://arxiv.org/abs/2606.09348}
}