ABC: Advantage-Based Control Variates for Reinforcement Learning with Verifiable Rewards

arXiv:2609.36058 · cs.LG · Submitted 2026-09-28 · Read on arXiv

cs.LG

Submitted: 2026-09-28

Updated: 2026-09-28

Code: https://github.com/huggingface/math-verify

Terminology

• Reinforcement Learning — 1× in this paper · explained in 4 episodes
• Verifiable Rewards — 1× in this paper · explained in 2 episodes

Sources

• Q-Prop: Sample-Efficient Policy Gradient with An Off-Policy Critic
• LoRA: Low-Rank Adaptation of Large Language Models
• Tulu 3: Pushing Frontiers in Open Language Model Post-Training
• RePO: Replay-Enhanced Policy Optimization
• Let's Verify Step by Step
• Action-depedent Control Variates for Policy Optimization via Stein's Identity
• Understanding R1-Zero-Like Training: A Critical Perspective
• Counterfactual Credit Assignment in Model-Free Reinforcement Learning
• Direct Advantage Estimation for Scalable and Sample-efficient Deep Reinforcement Learning
• On the Variance of Temporal Difference Learning and its Reduction Using Control Variates
• PipelineRL: Faster On-policy Reinforcement Learning for Long Sequence Generation
• High-Dimensional Continuous Control Using Generalized Advantage Estimation
• Proximal Policy Optimization Algorithms
• DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models
• VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks

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