标题： 上下文算子学习用于线性传播模型 显示英文标题

标题： In-Context Operator Learning for Linear Propagator Models

摘要： 我们研究了算子学习在最优订单执行问题的线性传播模型中的应用，该问题具有瞬时价格影响（类似于Bouchaud等人，2004年；Gatheral，2010年）。瞬时价格影响会随着时间根据某种传播核持续存在并衰减。具体来说，我们建议使用由杨等人（2023年）引入的上下文算子网络（ICON），这是一种基于变压器的新神经网络架构，它通过合并离线预训练和在线少量提示推理来促进数据驱动的算子学习。首先，我们训练ICON从各种传播模型中学习算子，这些模型将交易率映射到诱导的瞬时价格影响。然后，推理步骤基于上下文预测，其中ICON仅呈现少数示例。我们展示了ICON能够准确地从数据提示中推断出底层价格影响模型，即使是在训练数据中未见过的传播核。在第二步中，我们利用提供上下文的预训练ICON模型作为代理算子，通过神经网络控制策略解决最优订单执行问题，并证明了Abi Jaber和Neuman（2022年）针对生成上下文的模型得到的精确最优执行策略被正确检索到。我们介绍的方法非常通用，提供了一种解决具有未知状态动态的最优随机控制问题的新方法，通过利用变压器网络的少量学习和迁移学习能力，从有限数量的示例中高效推断数据。 显示英文摘要

摘要： We study operator learning in the context of linear propagator models for optimal order execution problems with transient price impact \`a la Bouchaud et al. (2004) and Gatheral (2010). Transient price impact persists and decays over time according to some propagator kernel. Specifically, we propose to use In-Context Operator Networks (ICON), a novel transformer-based neural network architecture introduced by Yang et al. (2023), which facilitates data-driven learning of operators by merging offline pre-training with an online few-shot prompting inference. First, we train ICON to learn the operator from various propagator models that maps the trading rate to the induced transient price impact. The inference step is then based on in-context prediction, where ICON is presented only with a few examples. We illustrate that ICON is capable of accurately inferring the underlying price impact model from the data prompts, even with propagator kernels not seen in the training data. In a second step, we employ the pre-trained ICON model provided with context as a surrogate operator in solving an optimal order execution problem via a neural network control policy, and demonstrate that the exact optimal execution strategies from Abi Jaber and Neuman (2022) for the models generating the context are correctly retrieved. Our introduced methodology is very general, offering a new approach to solving optimal stochastic control problems with unknown state dynamics, inferred data-efficiently from a limited number of examples by leveraging the few-shot and transfer learning capabilities of transformer networks.