Stochastic Optimal Control via Measure Relaxations

TL;DR

This paper introduces a convex optimization approach over occupation measures for stochastic control problems, utilizing measure relaxations and Christoffel polynomials to learn cost functions from data, improving scalability over traditional methods.

Contribution

It presents a novel convex formulation for stochastic control using measure relaxations and demonstrates learning cost functions with Christoffel polynomials from data.

Findings

Successfully applied to synthetic and real-world scenarios

Achieved scalable solutions for long-horizon stochastic control problems

Provided open-source code for reproducibility

Abstract

The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic system as a convex optimization problem over occupation measures. We demonstrate our method on a set of synthetic and real-world scenarios, learning cost functions from data via Christoffel polynomials. The code for our experiments is available at https://github.com/ebuehrle/dpoc.