# On Group Relative Policy Optimization Collapse in Agent Search: The Lazy Likelihood-Displacement

arXiv: https://arxiv.org/abs/2512.04220 · HTML: https://mlsanity.com/paper/2512.04220/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 32 of its 35 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## 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/)

## Builds on (most cited first, 30 of 32)

- [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)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Dense Passage Retrieval for Open-Domain Question Answering](https://mlsanity.com/paper/2004.04906/) (2020)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Search-R1: Training LLMs to Reason and Leverage Search Engines with Reinforcement Learning](https://mlsanity.com/paper/2503.09516/) (2025)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Text Embeddings by Weakly-Supervised Contrastive Pre-training](https://mlsanity.com/paper/2212.03533/) (2022)
- [HuggingGPT: Solving AI Tasks with ChatGPT and its Friends in Hugging Face](https://mlsanity.com/paper/2303.17580/) (2023)
- [When Not to Trust Language Models: Investigating Effectiveness of Parametric and Non-Parametric Memories](https://mlsanity.com/paper/2212.10511/) (2022)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Search-o1: Agentic Search-Enhanced Large Reasoning Models](https://mlsanity.com/paper/2501.05366/) (2025)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [Chameleon: Plug-and-Play Compositional Reasoning with Large Language Models](https://mlsanity.com/paper/2304.09842/) (2023)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [ZeroSearch: Incentivize the Search Capability of LLMs without Searching](https://mlsanity.com/paper/2505.04588/) (2025)
- [SimpleTIR: End-to-End Reinforcement Learning for Multi-Turn Tool-Integrated Reasoning](https://mlsanity.com/paper/2509.02479/) (2025)
- [VerlTool: Towards Holistic Agentic Reinforcement Learning with Tool Use](https://mlsanity.com/paper/2509.01055/) (2025)
- [Learning Dynamics of LLM Finetuning](https://mlsanity.com/paper/2407.10490/) (2024)
- [StepSearch: Igniting LLMs Search Ability via Step-Wise Proximal Policy Optimization](https://mlsanity.com/paper/2505.15107/) (2025)
- [Tree Search for LLM Agent Reinforcement Learning](https://mlsanity.com/paper/2509.21240/) (2025)
- [Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization](https://mlsanity.com/paper/2410.08847/) (2024)
- [Multi-modal Agent Tuning: Building a VLM-Driven Agent for Efficient Tool Usage](https://mlsanity.com/paper/2412.15606/) (2024)
- [On the Effect of Negative Gradient in Group Relative Deep Reinforcement Optimization](https://mlsanity.com/paper/2505.18830/) (2025)

## Built on by (most cited first, 15 of 15)

- [OpenSearch-VL: An Open Recipe for Frontier Multimodal Search Agents](https://mlsanity.com/paper/2605.05185/) (2026)
- [Beyond Monolithic Architectures: A Multi-Agent Search and Knowledge Optimization Framework for Agentic Search](https://mlsanity.com/paper/2601.04703/) (2026)
- [MindWatcher: Toward Smarter Multimodal Tool-Integrated Reasoning](https://mlsanity.com/paper/2512.23412/) (2025)
- [JADE: Bridging the Strategic-Operational Gap in Dynamic Agentic RAG](https://mlsanity.com/paper/2601.21916/) (2026)
- [ResRL: Boosting LLM Reasoning via Negative Sample Projection Residual Reinforcement Learning](https://mlsanity.com/paper/2605.00380/) (2026)
- [When Top-K Misses the Decision: Tool-Call Drift in Multi-Teacher On-Policy Distillation](https://mlsanity.com/paper/2607.07050/) (2026)
- [Self-Evolving Deep Research via Joint Generation and Evaluation](https://mlsanity.com/paper/2606.04507/) (2026)
- [Eliciting Self-Verification in Multimodal Reasoning Agents with Reinforcement Learning](https://mlsanity.com/paper/2609.08025/) (2026)
- [CoScale-RL: Efficient Post-Training by Co-Scaling Data and Computation](https://mlsanity.com/paper/2601.14695/) (2026)
- [Metacognitive Behavioral Tuning of Large Language Models for Multi-Hop Question Answering](https://mlsanity.com/paper/2602.22508/) (2026)
- [LC-ERD: Mining Latent Logic for Self-Evolving Reasoning via Consistency-Regulated Reward Decomposition](https://mlsanity.com/paper/2605.24005/) (2026)
- [Peak-Then-Collapse and the Four Interface Channels of Knowledge-Graph Tool Use](https://mlsanity.com/paper/2605.26037/) (2026)
- [Beyond Success and Failure: Length-Aware Contrastive Learning for GUI Agents](https://mlsanity.com/paper/2608.21830/) (2026)
- [Learning Dynamics of Continual Learning: A Unified View of Data Attribution, Forgetting, and Plasticity Loss](https://mlsanity.com/paper/2609.33620/) (2026)
- [Self-Evolving Agents via Likelihood-Guided Tool-Space Optimization](https://mlsanity.com/paper/2609.34151/) (2026)

## Abstract (arXiv)

Tool-integrated (TI) reinforcement learning (RL) enables large language models (LLMs) to perform multi-step reasoning by interacting with external tools such as search engines and retrievers. Group Relative Policy Optimization (GRPO), exemplified by the recent Search-R1, offers fast convergence and a value-free formulation that makes it appealing for this setting, yet consistently suffers from training collapse. We identify Lazy Likelihood Displacement (LLD), a systematic reduction or stagnation in the likelihood of both correct and incorrect responses, as the core mechanism driving this failure. LLD emerges early and triggers a self-reinforcing LLD Death Spiral, where declining likelihood leads to low-confidence responses, inflating gradients, and ultimately causing collapse. We empirically characterize this process across models on a Search-R1-style, search-integrated question answering task, revealing a consistent three-phase trajectory: early stagnation, steady decay, and accelerated collapse. To address this, we propose a likelihood-preserving regularization LLDS that activates only when a response action's likelihood decreases, and regularizes only the tokens responsible. This fine-grained structure mitigates LLD with minimal interference. Our method stabilizes training, prevents gradient explosion, and yields substantial performance improvements across seven benchmarks, including relative improvements of +45.2% on Qwen2.5-3B and +37.1% on Qwen2.5-7B over vanilla GRPO training. Our results establish LLD as a previously overlooked bottleneck in GRPO-based TIRL and provide a practical path toward stable, scalable training of tool-integrated RL.