# Statistical Learning with Sublinear Regret of Propagator Models

arXiv: https://arxiv.org/abs/2301.05157 · HTML: https://mlsanity.com/paper/2301.05157/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 47 references that are in the map.
- First posted on arXiv 12 Jan 2023.

## Builds on (most cited first, 6 of 6)

- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Optimal Rates For Regularization Of Statistical Inverse Learning Problems](https://mlsanity.com/paper/1604.04054/) (2016)
- [Logarithmic regret for episodic continuous-time linear-quadratic reinforcement learning over a finite-time horizon](https://mlsanity.com/paper/2006.15316/) (2020)
- [Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls](https://mlsanity.com/paper/2104.09311/) (2021)
- [Logarithmic regret bounds for continuous-time average-reward Markov decision processes](https://mlsanity.com/paper/2205.11168/) (2022)
- [Optimal scheduling of entropy regulariser for continuous-time linear-quadratic reinforcement learning](https://mlsanity.com/paper/2208.04466/) (2022)

## Built on by (most cited first, 5 of 5)

- [Data-driven rules for multidimensional reflection problems](https://mlsanity.com/paper/2311.06639/) (2023)
- [Solving Optimal Execution Problems via In-Context Operator Networks](https://mlsanity.com/paper/2501.15106/) (2025)
- [An Offline Learning Approach to Propagator Models](https://mlsanity.com/paper/2309.02994/) (2023)
- [Learning to steer with Brownian noise](https://mlsanity.com/paper/2410.03221/) (2024)
- [Learning Optimal Search Strategies](https://mlsanity.com/paper/2603.02356/) (2026)

## Abstract (arXiv)

We consider a class of learning problems in which an agent liquidates a risky asset while creating both transient price impact driven by an unknown convolution propagator and linear temporary price impact with an unknown parameter. We characterize the trader's performance as maximization of a revenue-risk functional, where the trader also exploits available information on a price predicting signal. We present a trading algorithm that alternates between exploration and exploitation phases and achieves sublinear regrets with high probability. For the exploration phase we propose a novel approach for non-parametric estimation of the price impact kernel by observing only the visible price process and derive sharp bounds on the convergence rate, which are characterised by the singularity of the propagator. These kernel estimation methods extend existing methods from the area of Tikhonov regularisation for inverse problems and are of independent interest. The bound on the regret in the exploitation phase is obtained by deriving stability results for the optimizer and value function of the associated class of infinite-dimensional stochastic control problems. As a complementary result we propose a regression-based algorithm to estimate the conditional expectation of non-Markovian signals and derive its convergence rate.