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Sampling multiple responses improves language model reasoning, but uniform compute allocation is inefficient: easy questions are over-sampled while hard questions remain under-explored. We propose Uncertainty-Aware Budget Allocation (UAB),…

Computation and Language · Computer Science 2026-05-27 Manh Nguyen , Sunil Gupta , Hung Le

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a key approach for enhancing LLM reasoning. However, standard frameworks like Group Relative Policy Optimization (GRPO) typically employ a uniform rollout budget, leading…

Machine Learning · Computer Science 2026-02-09 Zhiyuan Yao , Yi-Kai Zhang , Yuxin Chen , Yueqing Sun , Zishan Xu , Yu Yang , Tianhao Hu , Qi Gu , Hui Su , Xunliang Cai

We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…

Systems and Control · Electrical Eng. & Systems 2020-09-29 Yunchuan Li , Michael C. Fu , Jie Xu

Reinforcement learning from verifiable rewards has emerged as a powerful technique for enhancing the complex reasoning abilities of Large Language Models (LLMs). However, these methods are fundamentally constrained by the ''learning cliff''…

Computation and Language · Computer Science 2026-03-03 Xichen Zhang , Sitong Wu , Yinghao Zhu , Haoru Tan , Shaozuo Yu , Ziyi He , Jiaya Jia

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current…

Machine Learning · Computer Science 2025-10-01 Ziniu Li , Congliang Chen , Tianyun Yang , Tian Ding , Ruoyu Sun , Ge Zhang , Wenhao Huang , Zhi-Quan Luo

Reinforcement Learning with Verifiable Rewards (RLVR), particularly with algorithms like Group Relative Policy Optimization (GRPO), has proven highly effective in enhancing the reasoning capabilities of large language models. However, a…

Computation and Language · Computer Science 2026-03-03 Shangyu Xing , Siyuan Wang , Chenyuan Yang , Xinyu Dai , Xiang Ren

Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…

Machine Learning · Statistics 2011-09-22 Christos Dimitrakakis

Recent advancements in aligning large language models via reinforcement learning have achieved remarkable gains in solving complex reasoning problems, but at the cost of expensive on-policy rollouts and limited exploration of diverse…

Recent advances in large reasoning models have leveraged reinforcement learning with verifiable rewards (RLVR) to improve reasoning capabilities. However, scaling these methods typically requires extensive rollout computation and large…

Machine Learning · Computer Science 2025-09-03 Xinyu Tang , Zhenduo Zhang , Yurou Liu , Wayne Xin Zhao , Zujie Wen , Zhiqiang Zhang , Jun Zhou

Effective information seeking in multi-turn medical dialogues is critical for accurate diagnosis, especially when dealing with incomplete information. Aligning Large Language Models (LLMs) for these interactive scenarios is challenging due…

Machine Learning · Computer Science 2026-03-04 Ruike Cao , Shaojie Bai , Fugen Yao , Liang Dong , Jian Xu , Li Xiao

Sampling efficiency is a key bottleneck in reinforcement learning with verifiable rewards. Existing group-based policy optimization methods, such as GRPO, allocate a fixed number of rollouts for all training prompts. This uniform allocation…

Machine Learning · Computer Science 2026-03-06 Hieu Trung Nguyen , Bao Nguyen , Wenao Ma , Yuzhi Zhao , Ruifeng She , Viet Anh Nguyen

Reinforcement learning (RL) is a dominant paradigm for improving the reasoning abilities of large language models, yet its effectiveness varies across tasks and compute budgets. We propose a \emph{relative-budget} theory explaining this…

Machine Learning · Computer Science 2026-02-03 Akifumi Wachi , Hirota Kinoshita , Shokichi Takakura , Rei Higuchi , Taiji Suzuki

Recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) for Large Language Model (LLM) reasoning have been hindered by a persistent challenge: exploration collapse. The semantic homogeneity of random rollouts often traps…

Machine Learning · Computer Science 2026-01-12 Huilin Deng , Hongchen Luo , Yue Zhu , Long Li , Zhuoyue Chen , Xinghao Zhao , Ming Li , Jihai Zhang , Mengchang Wang , Yang Cao , Yu Kang

Reinforcement learning (RL) has recently become the core paradigm for aligning and strengthening large language models (LLMs). Yet, applying RL in off-policy settings--where stale data from past policies are used for training--improves…

Reinforcement learning (RL) for large language model reasoning is frequently hindered by signal loss, a phenomenon where standard uniform sampling with small group sizes fails to uncover informative learning signals for difficult prompts.…

Machine Learning · Computer Science 2025-12-08 Wei Xiong , Chenlu Ye , Baohao Liao , Hanze Dong , Xinxing Xu , Christof Monz , Jiang Bian , Nan Jiang , Tong Zhang

Real-time bidding (RTB) is an important mechanism in online display advertising, where a proper bid for each page view plays an essential role for good marketing results. Budget constrained bidding is a typical scenario in RTB where the…

Artificial Intelligence · Computer Science 2018-10-24 Di Wu , Xiujun Chen , Xun Yang , Hao Wang , Qing Tan , Xiaoxun Zhang , Jian Xu , Kun Gai

Reinforcement learning with verifiable rewards (RLVR) has improved the reasoning ability of large language models, yet training remains costly because many rollouts contribute little to optimization, considering the amount of computation…

Machine Learning · Computer Science 2026-02-20 Yan Sun , Jia Guo , Stanley Kok , Zihao Wang , Zujie Wen , Zhiqiang Zhang

Test-time reinforcement learning generates multiple candidate answers via repeated rollouts and performs online updates using pseudo-labels constructed by majority voting. To reduce overhead and improve exploration, prior work introduces…

Machine Learning · Computer Science 2026-05-28 Chu Zhao , Enneng Yang , Yuting Liu , Jianzhe Zhao , Guibing Guo

Reinforcement learning with verifiable rewards (RLVR) has recently enhanced the reasoning capabilities of large language models (LLMs), particularly for mathematical problem solving. However, a fundamental limitation remains: as the…

Machine Learning · Computer Science 2025-11-03 Wenhao Deng , Long Wei , Chenglei Yu , Tailin Wu

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an indispensable paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard policy optimization methods, such as Group Relative Policy…

Machine Learning · Computer Science 2026-02-09 Pengyi Li , Elizaveta Goncharova , Andrey Kuznetsov , Ivan Oseledets
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