In-Context Operator Learning for Linear Propagator Models

2025-01-25

AI Summary

This paper addresses the challenge of optimal order execution under unknown and decaying instantaneous price impact dynamics. We propose In-Context Operator Networks (ICON), a context-aware operator learning framework that pioneers the integration of in-context learning into the operator learning paradigm, unifying offline pretraining with online few-shot prompting inference. ICON employs a Transformer architecture to implicitly model the unknown impact propagation kernel; given only a small number of observed impact trajectories, it generalizes to unseen kernel structures and accurately recovers the analytical optimal control policy of Abi Jaber & Neuman (2022). By leveraging contextual parameterization, ICON substantially improves data efficiency for stochastic control under unknown dynamics, enabling high-fidelity, interpretable, and low-sample-dependent execution strategies in high-frequency financial markets.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Operator Learning
• Optimal Order Execution
• Instantaneous Price Variation

Innovation

• ICON model
• Pre-trained and few-shot learning
• Optimal order execution