When Does External Guidance Help LLM Reasoning? A Bias-Variance Theory of Guidance-Augmented GRPO

arXiv:2610.06861 · cs.LG, cs.CL · Submitted 2026-07-08 · Read on arXiv

cs.LG, cs.CL

Submitted: 2026-07-08

Updated: 2026-07-08

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• GRPO — 1× in this paper · explained in 6 episodes

Sources

• DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning
• Proximal Policy Optimization Algorithms
• Perception-Aware Policy Optimization for Multimodal Reasoning
• TemplateRL: Structured Template-Guided Reinforcement Learning for LLM Reasoning
• Global Convergence of Policy Gradient Methods to (Almost) Locally Optimal Policies
• Trust Region Policy Optimization
• Policy Gradient with Active Importance Sampling
• Reusing Historical Trajectories in Natural Policy Gradient via Importance Sampling: Convergence and Convergence Rate
• Loaded DiCE: Trading off Bias and Variance in Any-Order Score Function Estimators for Reinforcement Learning
• Off Policy Lyapunov Stability in Reinforcement Learning
• Trajectory-Aware Eligibility Traces for Off-Policy Reinforcement Learning
• Reward Shaping via Diffusion Process in Reinforcement Learning
• From Reward Shaping to Q-Shaping: Achieving Unbiased Learning with LLM-Guided Knowledge
• Vanishing Bias Heuristic-guided Reinforcement Learning Algorithm
• Internally Rewarded Reinforcement Learning
• Causal-Paced Deep Reinforcement Learning
• Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction
• Reconciling modern machine learning practice and the bias-variance trade-off
• On lower bounds for the bias-variance trade-off
• Training language models to follow instructions with human feedback

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