Yansong Feng

Chengjun Pan, Shichun Liu, Jiahang Lin et al.

Reinforcement learning (RL) for LLM post-training faces a fundamental design choice: whether to use a learned critic as a baseline for policy optimization. Classical theory favors critic-based methods such as PPO for variance reduction, yet critic-free alternatives like GRPO have gained widespread adoption due to their simplicity and competitive performance. We show that in sparse-reward settings, a learned critic can inject estimation noise that exceeds the state signal it captures, increasing rather than reducing advantage variance. By casting baseline selection as a Kalman filtering problem, we unify PPO and GRPO as two extremes of the Kalman gain and prove that explained variance (EV), computable from a single training batch, identifies the exact boundary: positive EV indicates the critic reduces variance, while zero or negative EV signals that it inflates variance. Building on this insight, we propose Explained Variance Policy Optimization (EVPO), which monitors batch-level EV at each training step and adaptively switches between critic-based and batch-mean advantage estimation, provably achieving no greater variance than the better of the two at every step. Across four tasks spanning classical control, agentic interaction, and mathematical reasoning, EVPO consistently outperforms both PPO and GRPO regardless of which fixed baseline is stronger on a given task. Further analysis confirms that the adaptive gating tracks critic maturation over training and that the theoretically derived zero threshold is empirically optimal.

Kangcheng Luo, Tinglang Wu, Yansong Feng

Recent search-augmented LLMs trained with reinforcement learning (RL) can interleave searching and reasoning for multi-hop reasoning tasks. However, they face two critical failure modes as the accumulating context becomes flooded with both crucial evidence and irrelevant information: (1) ineffective search chain construction that produces incorrect queries or omits retrieval of critical information, and (2) reasoning hijacking by peripheral evidence that causes models to misidentify distractors as valid evidence. To address these challenges, we propose **D$^2$Plan**, a **D**ual-agent **D**ynamic global **Plan**ning paradigm for complex retrieval-augmented reasoning. **D$^2$Plan** operates through the collaboration of a *Reasoner* and a *Purifier*: the *Reasoner* constructs explicit global plans during reasoning and dynamically adapts them based on retrieval feedback; the *Purifier* assesses retrieval relevance and condenses key information for the *Reasoner*. We further introduce a two-stage training framework consisting of supervised fine-tuning (SFT) cold-start on synthesized trajectories and RL with plan-oriented rewards to teach LLMs to master the **D$^2$Plan** paradigm. Extensive experiments demonstrate that **D$^2$Plan** enables more coherent multi-step reasoning and stronger resilience to irrelevant information, thereby achieving superior performance on challenging QA benchmarks.