Title: Optimal Control under Multiplicative and Internal Noise with Model Mismatch
Primary area: applications to neuroscience & cognitive science
Keywords: Stochastic Optimal Control, Motor Control, Neural Population Control, Partial Observability, Multiplicative Noise, Internal Process Noise

Abstract: Natural agents interact with their environment through noisy and continuous sensorimotor loops. Stochastic optimal control provides a principled framework for this problem, but existing analytical solutions are restricted to linear dynamics with Gaussian observations and additive noise. They cannot address scenarios with multiplicative noise in control or observations, and with internal noise affecting estimation — features central to biological and robotic systems.
We provide a provably convergent algorithm that computes fixed-point controller–filter solutions for linear dynamics with quadratic costs under multiplicative and internal noise. Our method overcomes the limitations of prior analytical approaches and improves the efficiency of state-of-the-art gradient-based methods by more than three orders of magnitude in realistic tasks. Importantly, it also optimizes internal dynamics, relaxing the classical assumption that internal models must match external dynamics. Allowing such model mismatch yields substantially better performance under internal noise.
In sum, we provide the first full solution to stochastic optimal linear control with multiplicative and internal noise, covering both matched and mismatched internal models.

TL;DR: We present a novel and efficient analytical method for solving stochastic optimal control problems with multiplicative and internal noise, enabling state-of-the-art performance and optimization of internal dynamics.