# Optimal adaptive control with separable drift uncertainty

arXiv: https://arxiv.org/abs/2309.07091 · HTML: https://mlsanity.com/paper/2309.07091/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2023.

## Built on by (most cited first, 3 of 3)

- [Deep Hilbert--Galerkin Methods for Infinite-Dimensional PDEs and Optimal Control](https://mlsanity.com/paper/2603.19463/) (2026)
- [Universal Approximation of Nonlinear Operators and Their Derivatives](https://mlsanity.com/paper/2605.15285/) (2026)
- [Sharp Critical Minimax Laws and No-Learning Thresholds in Continuous-Time Adaptive Control](https://mlsanity.com/paper/2609.33154/) (2026)

## Abstract (arXiv)

We consider a problem of stochastic optimal control with separable drift uncertainty in strong formulation on a finite horizon. The drift coefficient of the state Yu is multiplicatively influenced by an unknown random variable λ, while admissible controls u are required to be adapted to the observation filtration. Choosing a control actively influences the state and information acquisition simultaneously and comes with a learning effect. The problem, initially non-Markovian, is embedded into a higher-dimensional Markovian, full information control problem with control-dependent filtration and noise. To that problem, we apply the stochastic Perron method to characterize the value function as the unique viscosity solution to the HJB equation, explicitly construct varepsilon-optimal controls and show that the values of strong and weak formulations agree. Numerical illustrations show a significant difference between the adaptive control and the certainty equivalence control.