Group Relative Policy Optimization (GRPO) is a promising policy-based approach for Large Language Model alignment, yet its performance is often limited by training instability and suboptimal convergence. In this paper, we identify and analyze two main GRPO issues: (i) the token-level penalization, where valuable tokens shared across different responses receive contradictory feedback signals, leading to conflicting gradient updates that can reduce their likelihood; and (ii) the policy collapse, where negatively rewarded completions may penalize confident responses and shift model decisions toward unlikely tokens, destabilizing training process. To address these issues we introduce GTPO (Group-relative Trajectory-based Policy Optimization), which prevents conflicting gradients on valuable tokens by skipping negative updates while amplifying positive ones and filters out completions whose entropy exceeds a provable threshold, to prevent policy collapse. By omitting KL-divergence regularization, GTPO eliminates the reference model while achieving superior stability and performance over GRPO and DAPO. Extensive evaluations across GSM8K, MATH, R1, AIME 2024–2025, AMC 2023, and MMLU validate these gains. The code is available here.1.

Group-based reinforcement learning methods, like Group Relative Policy Optimization (GRPO), are widely used nowadays to post-train large language models. Despite their empirical success, they exhibit structural mismatches between reward optimization and the underlying training objective. In this paper, we present a theoretical analysis of GRPO style methods by studying them within a unified surrogate formulation. This perspective reveals recurring properties that affect all the methods under analysis: (i) non-uniform group weighting induces systematic gradient biases on shared prefix tokens; (ii) interactions with the AdamW optimizer make training dynamics largely insensitive to reward scaling; and (iii) optimizer momentum can push policy updates beyond the intended clipping region under repeated optimization steps. We believe that these findings highlight fundamental limitations of current approaches and provide principled guidance for the design of future formulations.