QLPO: Quadrant-weighted Sampling for Length-aware Policy Optimization
Authors: Siwei Chen, Siqi Chen, Xupeng Miao, Bin Cui
Organizations: School of Computer Science, Peking University · Beijing Key Laboratory of Software and Hardware Cooperative Artificial Intelligence Systems · Department of Electronic Engineering, Tsinghua University · Institute of Computational Social Science, Peking University (Qingdao)
Abstract
Recent large reasoning models often develop long chain-of-thought responses during reinforcement learning (RL), resulting in high inference latency and deployment cost. Existing methods for response length control typically rely on explicit length penalties or additional control modules, which require careful tuning and may compromise reasoning quality. We propose Quadrant-weighted Sampling for Length-aware Policy Optimization (QLPO), a simple resampling-based variant of GRPO that introduces implicit length control without modifying the reward function. QLPO first over-generates candidate responses and then resamples the training group by preserving the empirical correct/incorrect ratio while favoring short correct responses and long incorrect responses. This reshapes the training distribution and implicitly encourages shorter model outputs. Across models ranging from 1.5B to 32B parameters, including both base models and strong reasoning models, QLPO consistently improves the accuracy-length trade-off. It reduces response length by 30% to 70% while preserving reasoning performance. These results suggest that structured resampling provides an effective and robust approach to efficient reasoning.
Large reasoning models, such as OpenAI o1 and DeepSeek-R1, tend to become increasingly verbose as their reasoning capabilities improve. These inflated Chain-of-Thought (CoT) trajectories often exceed what the underlying problems require, wasting compute, latency, and context budgets. While introducing length-based efficiency rewards during reinforcement learning offers a natural remedy, existing methods struggle with two fundamental challenges: the optimal balance between correctness and efficiency is non-stationary throughout training, and intrinsic reasoning budgets vary drastically across problems. Relying on static reward weights and global length constraints inevitably forces a compromise between degraded accuracy and unrealized compression. To overcome these limitations, we propose LEAD (Length-Efficient Adaptive and Dynamic reasoning), a method that replaces static heuristics with online, self-adaptive mechanisms. LEAD dynamically calibrates the correctness-efficiency trade-off at each step using a Potential-Scaled Instability, directing optimization capacity to the most informative learning signal. Furthermore, it estimates an adaptive per-problem target length online based on the model's own correct rollouts, applying a symmetric efficiency reward that penalizes both overthinking and over-compression. Evaluated on five mathematical reasoning benchmarks, LEAD achieves the highest accuracy and Accuracy-Efficiency Score among RL-trained efficient-reasoning methods while producing substantially shorter outputs than the base model.
Existing reinforcement learning methods for LLM reasoning implicitly assume that the policy generating training trajectories should coincide with the one producing inference responses. We argue that this is a misleading inductive bias: the optimization-optimal trajectory distribution favors informative gradients, whereas the inference-optimal response distribution emphasizes accuracy and consistency. Forcing both into a single policy entangles their gradients and suppresses exploration. We propose R2PO (Residual Rollout Policy Optimization), which attaches a lightweight Residual Rollout-Head atop the policy to decouple training trajectories from inference responses, diversifying rollouts during training while keeping inference generation intact. Experiments show that R2PO consistently outperforms baselines, with average accuracy gains of 3.4% on MATH-500 and 1.3% on APPS, alongside more diverse rollouts and reduced length bias. Our code is available at https://github.com/RRPO-ARR/Code.
Reinforcement Learning with Verifiable Rewards (RLVR) has become a standard paradigm for enhancing the capability of large reasoning models. RLVR typically samples responses independently and optimizes the policy using from final answers. This paradigm has two limitations. First, independently responses often contain similar intermediate reasoning steps, causing redundant exploration and wasted computation. Second, sparse final-answer rewards make it hard to identify useful steps. Tree-based methods partly address this problem by sharing prefixes and comparing branches from the same prefix to provide fine-grained signals. However, tree branches are still expanded independently. When different branches reach similar reasoning states, they cannot share information and repeat similar exploration. Moreover, tree-based methods ignore such dispersion and only perform local comparisons within separate branches, which can lead to higher variance in advantage estimation. To address this challenge, we propose GraphPO (Graph-based Policy Optimization), a novel RL framework that represents rollouts as a directed acyclic graph, with reasoning steps as edges and semantic states summarized from the reasoning paths as nodes. GraphPO merges semantically equivalent reasoning paths into equivalence classes, allowing them to share suffixes and reallocating budget away from redundant expansions to diverse exploration. Furthermore, we assign efficiency advantages to incoming edges and correctness advantages to outgoing edges, thereby improving inference efficiency while deriving process supervision from outcome. Theory shows that GraphPO reduces advantage-estimation variance and enhances reasoning efficiency. Experiments on three LLMs across reasoning and agentic search benchmarks show that GraphPO consistently outperforms chain- and tree-based baselines with the same token budgets or response budgets.