Inverse Stochastic Optimal Control for Linear-Quadratic Gaussian and Linear-Quadratic Sensorimotor Control Models

TL;DR

This paper develops an iterative method to solve inverse stochastic optimal control problems for LQG and LQS models, estimating unknown parameters from observed human movement data.

Contribution

It introduces a novel bi-level optimization approach to identify cost and noise parameters in LQG and LQS models from real trajectories.

Findings

Algorithm accurately recovers parameters matching observed data.

Method effectively estimates covariance matrices of noise processes.

Simulation results validate the approach's ability to replicate human movement statistics.

Abstract

In this paper, we define and solve the Inverse Stochastic Optimal Control (ISOC) problem of the linear-quadratic Gaussian (LQG) and the linear-quadratic sensorimotor (LQS) control model. These Stochastic Optimal Control (SOC) models are state-of-the-art approaches describing human movements. The LQG ISOC problem consists of finding the unknown weighting matrices of the quadratic cost function and the covariance matrices of the additive Gaussian noise processes based on ground truth trajectories observed from the human in practice. The LQS ISOC problem aims at additionally finding the covariance matrices of the signal-dependent noise processes characteristic for the LQS model. We propose a solution to both ISOC problems which iteratively estimates cost function and covariance matrices via two bi-level optimizations. Simulation examples show the effectiveness of our developed algorithm. It finds parameters that yield trajectories matching mean and variance of the ground truth data.