$f$-Divergence Self-Play for Tabular Anomaly Detection via Large Language Models

Anomaly detection in tabular data poses significant challenges due to heterogeneous feature types—mixing numerical, categorical, and textual attributes, which complicate learning meaningful representations of normality. Recent work has applied large language models (LLMs) to this problem by serializing table rows as text sequences, yet these approaches rely on one-shot supervised fine-tuning that offers limited signal to tighten the model's description of normality. We propose DiSPaT, a self-play fine-tuning framework that strengthens the model's understanding of normal data. Building on the theoretical foundation of $f$-divergence minimization, we derive a tight approximation connecting our training objective to reducing the distributional gap between real normal data and model-generated samples. DiSPaT operates through an alternating optimization: at each iteration, the current policy generates synthetic samples that serve as pseudo-anomalies, while a critic discriminator learns to distinguish these from real normal samples; this signal drives policy updates that progressively align the model distribution with the true normal-data distribution. Extensive experiments on diverse benchmarks demonstrate that DiSPaT consistently outperforms prior LLM-based methods, deep learning approaches, and classical unsupervised detectors for tabular anomaly detection.