# PCSD: Persistent Consistency for Self-Distillation in Agentic Reinforcement Learning

arXiv: https://arxiv.org/abs/2608.01837 · HTML: https://mlsanity.com/paper/2608.01837/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Placed in

- 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/)

## Builds on (most cited first, 29 of 29)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [AndroidWorld: A Dynamic Benchmarking Environment for Autonomous Agents](https://mlsanity.com/paper/2405.14573/) (2024)
- [ToolRL: Reward is All Tool Learning Needs](https://mlsanity.com/paper/2504.13958/) (2025)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [WebRL: Training LLM Web Agents via Self-Evolving Online Curriculum Reinforcement Learning](https://mlsanity.com/paper/2411.02337/) (2024)
- [Mobile-Agent-v3: Fundamental Agents for GUI Automation](https://mlsanity.com/paper/2508.15144/) (2025)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [RLEF: Grounding Code LLMs in Execution Feedback with Reinforcement Learning](https://mlsanity.com/paper/2410.02089/) (2024)
- [SKILL0: In-Context Agentic Reinforcement Learning for Skill Internalization](https://mlsanity.com/paper/2604.02268/) (2026)
- [TCOD: Exploring Temporal Curriculum in On-Policy Distillation for Multi-turn Autonomous Agents](https://mlsanity.com/paper/2604.24005/) (2026)
- [GVPO: Group Variance Policy Optimization for Large Language Model Post-Training](https://mlsanity.com/paper/2504.19599/) (2025)
- [OPID: On-Policy Skill Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2606.26790/) (2026)
- [SEED: Self-Evolving On-Policy Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.14777/) (2026)
- [MAD-OPD: Breaking the Ceiling in On-Policy Distillation via Multi-Agent Debate](https://mlsanity.com/paper/2605.01347/) (2026)
- [PhysAgent: Automating Physics-Based 4D Synthesis via Trajectory-Grounded Multi-Agent Feedback](https://mlsanity.com/paper/2606.08688/) (2026)

## Built on by (most cited first, 7 of 7)

- [AgenticRag-R1: Agentic Reinforcement Learning with Stack Memory for Multi-Step Reasoning, Retrieval and Memorizing](https://mlsanity.com/paper/2608.29622/) (2026)
- [PR-OPD: Privileged Representation On-policy Self-Distillation for Agentic Reinforcement Learning](https://mlsanity.com/paper/2609.36642/) (2026)
- [DRG-MAPPO: Hierarchical Dynamic Role-Graph Multi-Agent Reinforcement Learning for Cooperative Air Combat](https://mlsanity.com/paper/2609.11155/) (2026)
- [OpenFC: Learning Verification Policies towards Open-Search Fact Checking](https://mlsanity.com/paper/2609.33579/) (2026)
- [Know Thyself, Teach Thyself: Internal Information Flow for Selective Self-Distillation](https://mlsanity.com/paper/2609.36695/) (2026)
- [EVOKE: Eliciting World Knowledge in Agents for Transferable Decision-Making](https://mlsanity.com/paper/2609.38334/) (2026)
- [More Methods, Better Agents? A Reality Check on Self-Distillation in Agentic Reinforcement Learning](https://mlsanity.com/paper/2610.19789/) (2026)

## Abstract (arXiv)

Large language model agents have shown strong potential in complex interactive tasks, yet their reinforcement learning (RL) is often hindered by sparse rewards, as a long multi-turn trajectory may receive only a single outcome-level signal. On-policy self-distillation (OPSD) provides dense token-level supervision from a privileged teacher, but the teacher may not be reliable at every position. Existing methods commonly rely on isolated token-level discrepancies, which can be sensitive to noise, or assign a shared step-level weight that may overlook positional variation. We propose Persistent Consistency Self-Distillation (PCSD), which derives token-level distillation weights from the local persistence of teacher-favoring signals. PCSD combines adaptive windows with exponentially decayed aggregation to capture persistent relative teacher support, applies trend-aware modulation to attenuate locally declining support, and produces continuous weights through sigmoid gating. The resulting objective is jointly optimized with GRPO, combining dense teacher guidance with sparse environmental feedback. Without inference-time skills, PCSD achieves the best ALFWorld Overall results among all baselines on both backbones, exceeding GRPO by 15.6 and 13.3 points and SDAR by 6.2 and 5.5 points, while remaining competitive on WebShop and gaining 15.8 points over GRPO on unseen ALFWorld split.