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Reinforcement learning with verifiable rewards (RLVR) has become a powerful paradigm for improving language models on reasoning-intensive tasks, but its effectiveness is often limited by exploration. For example, models often fail on hard…

Policy optimization for large language models often suffers from sparse reward signals in multi-step reasoning tasks. Critic-free methods like GRPO assign a single normalized outcome reward to all tokens, providing limited guidance for…

Aligning large language models with pointwise absolute rewards has so far required online, on-policy algorithms such as PPO and GRPO. In contrast, simpler methods that can leverage offline or off-policy data, such as DPO and REBEL, are…

Many strong decoding methods for text generation follow a sample-and-rerank paradigm: they draw multiple candidates, score each under a utility (reward) function using consensus across samples, and return the best one. Although effective,…

Agentic Reinforcement Learning (Agentic RL) has shown remarkable potential in large language model-based (LLM) agents. These works can empower LLM agents to tackle complex tasks via multi-step, tool-integrated reasoning. However, an…

The success of Deepseek-R1 has drawn the LLM community's attention to reinforcement learning (RL) methods like GRPO. However, such rule-based 0/1 outcome reward methods lack the capability to regulate the intermediate reasoning processes…

This paper provides a self-contained, from-scratch, exposition of key algorithms for instruction tuning of models: SFT, Rejection Sampling, REINFORCE, Trust Region Policy Optimization (TRPO), Proximal Policy Optimization (PPO), Group…

Memory-augmented LLM agents tackle complex long-horizon tasks by recursively summarizing interaction trajectories into compact memory. However, existing approaches typically train these memory policies using outcome-based reinforcement…

While Large Language Models (LLMs) excel at generating human-like text, aligning their outputs with complex, qualitative goals like pedagogical soundness remains a significant challenge. Standard reinforcement learning techniques often rely…

Group Relative Policy Optimization (GRPO) has been a key driver of recent progress in reinforcement learning with verifiable rewards (RLVR) for large language models, but it is typically trained in a low-staleness, near-on-policy regime…

Large language models (LLMs) demonstrate strong reasoning abilities via Chain-of-Thought (CoT), but their token-level generation encourages local decisions and lacks global planning, often leading to redundant or inaccurate reasoning.…

Recent advances in large language models (LLMs) have shown that reasoning ability can be significantly enhanced through Reinforcement Learning with Verifiable Rewards (RLVR). Group Relative Policy Optimization (GRPO) has emerged as the de…

The rapid development of large language model (LLM) alignment algorithms has resulted in a complex and fragmented landscape, with limited clarity on the effectiveness of different methods and their inter-connections. This paper introduces…

Large language models (LLMs) trained with reinforcement objectives often achieve superficially correct answers via shortcut strategies, pairing correct outputs with spurious or unfaithful reasoning and degrading under small causal…

Recent Large Reasoning Models (LRMs) have achieved remarkable performance in solving complex problems via supervised fine-tuning (SFT) and reinforcement learning (RL). Although existing RL algorithms significantly enhance model accuracy,…

Standard reinforcement learning from human feedback (RLHF) trains a reward model on pairwise preference data and then uses it for policy optimization. However, while reward models are optimized to capture relative preferences, existing…

Group Relative Policy Optimization (GRPO) has emerged as a promising approach for improving the reasoning capabilities of large language models. However, it struggles to effectively balance the tradeoff between exploration and exploitation…

Group Relative Policy Optimization (GRPO) has proven effective in RLVR by using outcome-based rewards. While fine-grained dense rewards can theoretically improve performance, we reveal that under practical sampling budgets, Monte Carlo…

We propose Process-Aware Policy Optimization (PAPO), a method that integrates process-level evaluation into Group Relative Policy Optimization (GRPO) through decoupled advantage normalization, to address two limitations of existing reward…

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…