Objective Shaping with Hard Negatives: Windowed Partial AUC Optimization for RL-based LLM Recommenders

Reinforcement learning (RL) effectively optimizes Large Language Model (LLM)-based recommenders by contrasting positive and negative items. Empirically, training with beam-search negatives consistently outperforms random negatives, yet the mechanism is not well understood. We address this gap by analyzing the induced optimization objective and show that: (i) Under binary reward feedback, optimizing LLM recommenders with Group Relative Policy Optimization (GRPO) is theoretically equivalent to maximizing the Area Under the ROC Curve (AUC), which is often misaligned with Top-$K$ recommendation; and (ii) Replacing random negatives with beam-search negatives reshapes the objective toward partial AUC, improving alignment with Top-$K$ metrics. Motivated by this perspective, we introduce **W**indowed **P**artial **AUC** (**WPAUC**), which constrains the false positive rate (FPR) to a window [$\alpha,\alpha+d$] to more directly align with Top-$K$ metrics. We further propose an efficient **T**hreshold-**A**djusted **Win**dowed reweighting (**TAWin**) RL method for its optimization, enabling explicit control over the targeted Top-$K$ performance. Experiments on four real-world datasets validate the theory and deliver consistent state-of-the-art performance.