Adversarial Post-Training of Foundation Models for High-Frequency Trading

Alexandre Bismuth, Kang Li, Aramis Marti-Shahandeh, Valentin Mohl, Jakob Foerster +1

While autoregressive foundation models trained on limit order book (LOB) data show state-of-the-art performance for market simulation, pre-training with cross-entropy neither penalizes the compounding of sampling errors over free-running rollouts nor targets desired market properties. We introduce a post-training method for LOB foundation models using a Wasserstein generative adversarial network (GAN) objective. A critic, trained online on rollouts through the true, non-differentiable matching engine, guides updates from evolution strategies over rank-4 LoRA perturbations of the pre-trained generator, under a KL trust region. For efficiency, we use EGGROLL (Evolution Guided GeneRal Optimisation via Low-rank Learning), a memory-efficient variant of evolution strategies. On a held-out panel, adversarial post-training improves LOB-Bench realism by 17.6% (WS-21) and 17.0% (Mean-$L_1$), while selection-matched random-perturbation and compute-matched continued-pre-training controls yield no improvement. Post-training is thus a necessary stage that more pre-training does not replace. Per-position divergence measurements show that it slows error accumulation over 500-message rollouts…