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Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional…

We propose FSPO (Fair Sequence Policy Optimization), a sequence-level reinforcement learning method for LLMs that enforces length-fair clipping on the importance-sampling (IS) weight. We study RL methods with sequence-level IS and identify…

Existing post-training techniques are broadly categorized into supervised fine-tuning (SFT) and reinforcement learning (RL) methods; the former is stable during training but suffers from limited generalization, while the latter, despite its…

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning ability of large language models (LLMs), but it often suffers from \textit{restricted exploration}, where the policy rapidly concentrates on a…

Reinforcement learning (RL) for large language models (LLMs) is dominated by the cost of rollout generation, which has motivated the use of low-precision rollouts (e.g., FP8) paired with a BF16 trainer to improve throughput and reduce…

Recently, GRPO-based reinforcement learning has shown remarkable progress in optimizing flow-matching models, effectively improving their alignment with task-specific rewards. Within these frameworks, the policy update relies on…

Reinforcement learning (RL) plays an increasingly important role in enhancing the reasoning capabilities of large language models (LLMs), yet stable and performant policy optimization remains challenging. Token-level importance ratios often…

Off-policy updates are inevitable in reinforcement learning (RL) for large language models (LLMs) due to rollout staleness from asynchronous training and mismatches between training and inference engines. Naive importance sampling gives an…

This paper introduces Group Sequence Policy Optimization (GSPO), our stable, efficient, and performant reinforcement learning algorithm for training large language models. Unlike previous algorithms that adopt token-level importance ratios,…

Group Relative Policy Optimization (GRPO) was introduced and used recently for promoting reasoning in LLMs under verifiable (binary) rewards. We show that the mean + variance calibration of these rewards induces a weighted contrastive loss…

Large language models (LLMs) have achieved impressive reasoning performance, with reinforcement learning with verifiable rewards (RLVR) emerging as a standard paradigm for post-training. A representative algorithm, group relative policy…

Reinforcement learning with verifiable rewards has driven recent advances in LLM post-training, in particular for reasoning. Policy optimization algorithms generate a number of responses for a given prompt and then effectively weight the…

Reinforcement Learning with Verifiable Rewards (RLVR) offers a promising framework for optimizing large language models in reasoning tasks. However, existing RLVR algorithms focus on different granularities, and each has complementary…

The widespread adoption of large language models (LLMs) across industries has increased the demand for high-quality and customizable outputs. However, traditional alignment methods often require retraining large pretrained models, making it…

Existing Reinforcement Learning with Verifiable Rewards (RLVR) algorithms, such as GRPO, rely on rigid, uniform, and symmetric trust region mechanisms that are fundamentally misaligned with the complex optimization dynamics of Large…

Diffusion large language models (dLLMs) offer a promising route to parallel and efficient text generation, but improving their reasoning ability requires effective post-training. Reinforcement learning with verifiable rewards (RLVR) is a…

While Reinforcement Learning (RL) shows promise in training tool-use Large Language Models (LLMs) using verifiable outcome rewards, existing methods largely overlook the potential of reasoning rewards based on chain-of-thought quality for…

Reinforcement learning (RL) has become a cornerstone for fine-tuning Large Language Models (LLMs), with Proximal Policy Optimization (PPO) serving as the de facto standard algorithm. Despite its ubiquity, we argue that the core ratio…

Reinforcement learning with verifiable rewards has emerged as a promising paradigm for enhancing the reasoning capabilities of large language models particularly in mathematics. Current approaches in this domain present a clear trade-off:…

Reinforcement learning (RL) has become a powerful paradigm for optimizing large language models (LLMs) to handle complex reasoning tasks. A core challenge in this process lies in managing policy entropy, which reflects the balance between…