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Abstract:Reinforcement studying (RL) for LLM submit-training faces a fundamental design selection: whether to make use of a discovered critic as a baseline for coverage optimization. Classical principle favors critic-based mostly methods equivalent to PPO for variance discount, but critic-free alternatives like GRPO have gained widespread adoption on account of their simplicity and competitive performance. We present that in sparse-reward settings, a discovered critic can inject estimation noise that exceeds the state sign it captures, rising relatively than decreasing benefit variance. By casting baseline choice as a Kalman filtering downside, we unify PPO and GRPO as two extremes of the Kalman gain and prove that defined variance (EV), computable from a single coaching batch, identifies the exact boundary: optimistic EV signifies the critic reduces variance, stop terrorism whereas zero or negative EV indicators that it inflates variance. Building on this insight, we suggest Explained Variance Policy Optimization (EVPO), which monitors batch-stage EV at every coaching step and adaptively switches between critic-based and batch-mean benefit estimation, provably reaching no greater variance than the higher of the two at each step. Across 4 duties spanning classical control, agentic interaction, and mathematical reasoning, EVPO consistently outperforms both PPO and GRPO no matter which fixed baseline is stronger on a given task. Further evaluation confirms that the adaptive gating tracks critic maturation over training and that the theoretically derived zero threshold is empirically optimum.