Kullback-Leibler (KL) divergence regularization is essential for stabilizing reinforcement learning from human feedback (RLHF) in large language models (LLMs), yet its exact computation requires summing over vocabularies of all tokens, incurring prohibitive memory costs during training. Existing stochastic estimators circumvent this bottleneck by estimating KL divergence using only the sampled token from the trajectory, but suffer from high variance (k₁) or systematic bias (k₂). We propose TIKE (Top-k Importance-weighted KL Estimator), which exploits the Zipfian structure of language model distributions: by deterministically integrating over only the top-k tokens, TIKE captures most of the probability mass while effectively reducing memory cost. To ensure correctness in off-policy settings characteristic of Group Relative Policy Optimization (GRPO), we incorporate importance sampling weights that correct for distribution shift between rollout and optimization policies. Experiments on models across diverse benchmarks demonstrate that TIKE consistently outperforms stochastic baselines, while exhibiting substantially lower gradient variance. Our analysis reveals that TIKE closely tracks the exact Rao-Blackwellized estimator with near-zero variance, offering a practical path toward stable, memory-efficient KL regularization for reasoning-intensive LLMs training.

The evolution of Large Language Models (LLMs) into autonomous agents has expanded the scope of AI coding from localized code generation to complex, repository-level, and execution-driven problem solving. However, current benchmarks predominantly evaluate code logic in static contexts, neglecting the dynamic, full-process requirements of real-world engineering, particularly in backend development which demands rigorous environment configuration and service deployment. To address this gap, we introduce ABC-Bench, a benchmark explicitly designed to evaluate agentic backend coding within a realistic, executable workflow. Using a scalable automated pipeline, we curated 224 practical tasks spanning 8 languages and 19 frameworks from open-source repositories. Distinct from previous evaluations, ABC-Bench require the agents to manage the entire development lifecycle from repository exploration to instantiating containerized services and pass the external end-to-end API tests. Our extensive evaluation reveals that even state-of-the-art models struggle to deliver reliable performance on these holistic tasks, highlighting a substantial disparity between current model capabilities and the demands of practical backend engineering.