ResearchResearch paperTraining & Scaling · Large Language Models · Reinforcement Learning1 source · Oct 19, 2026

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

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.

Key points

  • 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-$L1$), while selection-matched random-perturbation and compute-matched continued-pre-training controls yield no improvement.

Sources (1)

  • [1]Adversarial Post-Training of Foundation Models for High-Frequency Trading
    arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 19, 12:15 AM
    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.

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