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

arXiv: https://arxiv.org/abs/2606.09348 · HTML: https://mlsanity.com/paper/2606.09348/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 34 of its 40 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)
- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)
- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 30 of 34)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [GAIA: a benchmark for General AI Assistants](https://mlsanity.com/paper/2311.12983/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [BrowseComp: A Simple Yet Challenging Benchmark for Browsing Agents](https://mlsanity.com/paper/2504.12516/) (2025)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [Policy Distillation](https://mlsanity.com/paper/1511.06295/) (2015)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [BrowseComp-ZH: Benchmarking Web Browsing Ability of Large Language Models in Chinese](https://mlsanity.com/paper/2504.19314/) (2025)
- [Revisiting On-Policy Distillation: Empirical Failure Modes and Simple Fixes](https://mlsanity.com/paper/2603.25562/) (2026)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [xbench: Tracking Agents Productivity Scaling with Profession-Aligned Real-World Evaluations](https://mlsanity.com/paper/2506.13651/) (2025)
- [Privileged Information Distillation for Language Models](https://mlsanity.com/paper/2602.04942/) (2026)
- [StepSearch: Igniting LLMs Search Ability via Step-Wise Proximal Policy Optimization](https://mlsanity.com/paper/2505.15107/) (2025)
- [MiroThinker: Pushing the Performance Boundaries of Open-Source Research Agents via Model, Context, and Interactive Scaling](https://mlsanity.com/paper/2511.11793/) (2025)
- [Reinforcing Multi-Turn Reasoning in LLM Agents via Fine-Grained Reward Structure and Credit Assignment](https://mlsanity.com/paper/2505.11821/) (2025)
- [Tree Search for LLM Agent Reinforcement Learning](https://mlsanity.com/paper/2509.21240/) (2025)
- [Stabilizing MoE Reinforcement Learning by Aligning Training and Inference Routers](https://mlsanity.com/paper/2510.11370/) (2025)
- [TreeRPO: Tree Relative Policy Optimization](https://mlsanity.com/paper/2506.05183/) (2025)
- [OpenSeeker: Democratizing Frontier Search Agents by Fully Open-Sourcing Training Data](https://mlsanity.com/paper/2603.15594/) (2026)
- [MiroThinker-1.7 & H1: Towards Heavy-Duty Research Agents via Verification](https://mlsanity.com/paper/2603.15726/) (2026)
- [CriticSearch: Fine-Grained Credit Assignment for Search Agents via a Retrospective Critic](https://mlsanity.com/paper/2511.12159/) (2025)

## Built on by (most cited first, 6 of 6)

- [Agentic Reinforcement Learning with Observation-Calibrated Self-Distillation](https://mlsanity.com/paper/2608.04788/) (2026)
- [How Much, Then Where: Credit-Conserving Action-to-Token Allocation for Multi-Turn Agent Reinforcement Learning](https://mlsanity.com/paper/2608.07118/) (2026)
- [Trust Is Not Enough: Influence Calibration for On-Policy Self-Distillation in Agentic RL](https://mlsanity.com/paper/2608.14945/) (2026)
- [Train Ahead, Distill Back: Bootstrapping On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2609.37132/) (2026)
- [AdviSD: Learning to Advise Frontier LLMs via Targeted Multi-Turn Self-Distillation](https://mlsanity.com/paper/2609.38142/) (2026)
- [From Given to Gathered Evidence: Agentic Learning for Longitudinal Medical Reasoning](https://mlsanity.com/paper/2609.39566/) (2026)

## Abstract (arXiv)

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.