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Golden ratio primal-dual algorithm (GRPDA) is a new variant of the classical Arrow-Hurwicz method for solving structured convex optimization problem, in which the objective function consists of the sum of two closed proper convex functions,…

Reinforcement learning with verifiable rewards (RLVR) has become a standard recipe for improving large language models (LLMs) on reasoning tasks, with Group Relative Policy Optimization (GRPO) widely used in practice. Yet GRPO wastes…

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…

Instruction following (IF) is a critical capability for large language models (LLMs). However, handling complex instructions with multiple constraints remains challenging. Previous methods typically select preference pairs based on the…

Recent reasoning-focused language models such as DeepSeek R1 and OpenAI o1 have demonstrated strong performance on structured reasoning benchmarks including GSM8K, MATH, and multi-hop question answering tasks. However, their performance…

The paradigm of using Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs) as evaluative judges has emerged as an effective approach in RLHF and inference-time scaling. In this work, we propose Multimodal Reasoner as a…

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…

Recourse provides individuals who received undesirable labels (e.g., denied a loan) from algorithmic decision-making systems with a minimum-cost improvement suggestion to achieve the desired outcome. However, in practice, models often get…

Reinforcement Learning with Verifiable Rewards (RLVR) has become a standard recipe for post-training LLMs on reasoning tasks, with Group Relative Policy Optimization (GRPO) emerging as a leading approach. However, GRPO and its variants are…

Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via…

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…

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward…

Group-relative RL training (GRPO) samples a small group of parallel rollouts for every training prompt and uses their within-group reward spread to compute per-trajectory advantages. In agentic environments each rollout is a long multi-turn…

Many reinforcement learning (RL) problems admit multiple terminal solutions of comparable quality, where the goal is not to identify a single optimum but to represent a diverse set of high-quality outcomes. Nevertheless, policies trained by…

Reinforcement Learning with Verifiable Rewards (RLVR) has recently strengthened LLM reasoning, but its focus on final answer correctness leaves a critical gap: it does not ensure the robustness of the reasoning process itself. We adopt a…

Reinforcement learning (RL) has become a central post-training tool for improving the reasoning abilities of large language models (LLMs). In these systems, the rollout, the trajectory sampled from a prompt to termination, including…

Recent advances demonstrate that reinforcement learning with verifiable rewards (RLVR) significantly enhances the reasoning capabilities of large language models (LLMs). However, standard RLVR faces challenges with reward sparsity, where…

Reinforcement learning from human feedback (RLHF) or verifiable rewards (RLVR), the standard paradigm for aligning LLMs or building recent SOTA reasoning models, is highly sensitive to noise from inconsistent or erroneous rewards. Yet, the…

Large language models (LLMs) are increasingly adapted to downstream tasks via reinforcement learning (RL) methods like Group Relative Policy Optimization (GRPO), which often require thousands of rollouts to learn new tasks. We argue that…

Reinforcement Learning with Verifiable Rewards (RLVR) improves multimodal reasoning by rewarding verifiable final answers. Yet answer-correct trajectories may still rely on incomplete derivations, weak evidence, or statements that…