On GRPO Collapse in Search-R1: The Lazy Likelihood-Displacement Death Spiral

• URL: http://arxiv.org/abs/2512.04220v1
• Date: Wed, 03 Dec 2025 19:41:15 GMT
• Title: On GRPO Collapse in Search-R1: The Lazy Likelihood-Displacement Death Spiral
• Abstract summary: We identify Lazy Likelihood Displacement (LLD) as the core mechanism driving this failure.<n>LLD emerges early and triggers a self-reinforcing LLD Death Spiral, where declining likelihood leads to low-confidence responses.<n>We propose a lightweight likelihood-preserving regularization LLDS for GRPO that activates only when a trajectory's likelihood decreases.
• Score: 59.14787085809595
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 lightweight likelihood-preserving regularization LLDS for GRPO that activates only when a trajectory's likelihood decreases, and regularizes only the tokens responsible. This fine-grained structure mitigates LLD with minimal interference to optimization. Across seven open-domain and multi-hop QA benchmarks, our method stabilizes training, prevents gradient explosion, and yields substantial performance improvements, including +37.8% gains on Qwen2.5-3B and +32.0% gains on Qwen2.5-7B. Our results establish LLD as a fundamental bottleneck in GRPO-based TIRL and provide a practical path toward stable, scalable training of tool-integrated LLM.

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