Group Relative Policy Optimization (GRPO) is the dominant reinforcement learning algorithm for training reasoning capabilities in large language models, notably adopted by DeepSeek-R1. The recent improvement Dr. GRPO (COLM 2025) identifies the response-level length bias caused by per-trajectory length normalization in GRPO and proposes removing this normalization, claiming the resulting optimizer is "unbiased." We show that this claim is incomplete. Specifically, we establish an impossibility theorem: under the standard outcome reward + GRPO setting, no length-based weighting scheme can simultaneously achieve the following two properties. (P1) Gradient unbiasedness: the gradient estimator is an unbiased estimate of the true policy gradient. (P2) Length invariance: each trajectory's effective contribution to the gradient is independent of its token length. GRPO approximately satisfies P2 but violates P1; Dr. GRPO satisfies P1 but violates P2. We characterize the complete tradeoff spectrum via the parametric family f_alpha(L) = L^{alpha - 1}, where alpha = 0 recovers GRPO, alpha = 1 recovers Dr. GRPO, and provide quantitative analysis showing that Dr. GRPO's length bias can cause longer trajectories to dominate gradient updates by a factor proportional to the length ratio. Our results reveal that neither algorithm is universally "done right"; they occupy opposite ends of a fundamental and unavoidable tradeoff.
Multiple-choice benchmarks that rank candidate completions by conditional log-probability suffer from a length bias: because log-probabilities sum over tokens, longer answers tend to be penalized relative to shorter ones in practice. A common mitigation is to normalize scores by completion length, but we show empirically that this heuristic frequently over-corrects, introducing a bias toward longer answers instead. We first analyze these scoring rules, characterizing when standard and length-normalized accuracy are appropriate and how their length biases depend on the distribution of completion lengths. Motivated by this analysis, we introduce \emph{Bayesian accuracy}, a scoring rule that computes the posterior probability of each candidate under an explicit prior over answer length, thereby removing linear length effects. Bayesian accuracy is a drop-in replacement for likelihood-based multiple-choice evaluation, requires no additional forward passes, and consistently exhibits lower empirical length bias than both standard and length-normalized accuracy across benchmarks and few-shot settings.
Large language models (LLMs) have recently emerged as powerful backbones for recommender systems by reformulating recommendation as a token-level generation task. Despite their promise, we identify a pervasive yet underexplored issue: $\textit{Length Bias}$. Because items are represented by textual descriptions of varying lengths, LLM-based recommenders can be systematically biased in two ways. On the input side, longer item descriptions occupy more tokens in the context and thus receive disproportionately large aggregate attention mass during user preference modeling. On the output side, decoding based on summed autoregressive log-likelihood score inherently disfavors long items. Worse still, conventional length normalization can introduce an additional bias and even degrade recommendation performance. To address this problem, we propose $\textbf{LBR}$ ($\textbf{L}$ength $\textbf{B}$ias $\textbf{R}$eduction), a lightweight and model-agnostic framework for mitigating length bias in LLM-based recommendation. LBR mitigates input-side bias via Length-Aware Attention Calibration, which incorporates a length-dependent offset into attention logits to neutralize attention skew. For the output side, LBR introduces Effective Information Length Normalization, replacing naive token count with an information-theoretic length surrogate derived from the branching structure of the prefix tree. Extensive experiments on three real-world Amazon datasets and two representative LLM-based recommenders demonstrate that LBR substantially alleviates length bias while consistently improving recommendation accuracy and fairness, with negligible additional training and inference overhead (with an average NDCG@5 gain of 16.82%). The code is available at https://github.com/Void-JackLee/LBR.