# Solving Optimal Execution Problems via In-Context Operator Networks

arXiv: https://arxiv.org/abs/2501.15106 · HTML: https://mlsanity.com/paper/2501.15106/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 25 references that are in the map.
- First posted on arXiv 25 Jan 2025.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Pricing options on flow forwards by neural networks in Hilbert space](https://mlsanity.com/paper/2202.11606/) (2022)
- [Statistical Learning with Sublinear Regret of Propagator Models](https://mlsanity.com/paper/2301.05157/) (2023)
- [An Offline Learning Approach to Propagator Models](https://mlsanity.com/paper/2309.02994/) (2023)

## Built on by (most cited first, 4 of 4)

- [Continuum Transformers Perform In-Context Learning by Operator Gradient Descent](https://mlsanity.com/paper/2505.17838/) (2025)
- [Graph In-Context Operator Networks for Generalizable Spatiotemporal Prediction](https://mlsanity.com/paper/2603.12725/) (2026)
- [Evolving Ensemble of Agents](https://mlsanity.com/paper/2605.09018/) (2026)
- [Chain of Operators: An Inference-Time Harness for In-Context Operator Learning](https://mlsanity.com/paper/2606.12318/) (2026)

## Abstract (arXiv)

We propose a novel transformer-based neural network architecture (ICON-OCnet) for solving optimal order execution problems in the presence of unknown price impact. Our architecture facilitates data-driven in-context operator learning for the incurred price impact by merging offline pre-training with online few-shot prompting inference. First, the operator learning component (ICON) learns the prevailing price impact environment from only a few executed trade and price impact trajectories (time series data) provided as context. Second, we employ ICON as a surrogate operator to train a neural network policy (OCnet) for the optimal order execution strategy for the price impact regime inferred from the in-context examples. We study the efficiency of our approach for linear propagator models with path-dependent transient price impact and explicitly known optimal execution strategies. In this model class, price impact persists and decays over time according to some propagator kernel. We illustrate that ICON is capable of accurately inferring the underlying price impact model from the data prompts, even for propagator kernels not seen in the training data. Moreover, we demonstrate that ICON-OCnet correctly retrieves the exact optimal order execution strategy for the model generating the in-context examples. Our introduced methodology is very general, offering a new approach to solving path-dependent optimal stochastic control problems sample-based with unknown state dynamics.