Approximate Information States for Worst-Case Control and Learning in Uncertain Systems

TL;DR

This paper develops a framework for decision-making in uncertain, partially observed systems using approximate information states, enabling strategies with bounded performance loss without full system knowledge.

Contribution

It introduces a novel approach to define and learn approximate information states for worst-case control and learning in uncertain systems.

Findings

Framework for decision-making with approximate information states

Strategies with bounded performance loss derived from data

Numerical examples demonstrating control and reinforcement learning applications

Abstract

In this paper, we investigate discrete-time decision-making problems in uncertain systems with partially observed states. We consider a non-stochastic model, where uncontrolled disturbances acting on the system take values in bounded sets with unknown distributions. We present a general framework for decision-making in such problems by using the notion of the information state and approximate information state, and introduce conditions to identify an uncertain variable that can be used to compute an optimal strategy through a dynamic program (DP). Next, we relax these conditions and define approximate information states that can be learned from output data without knowledge of system dynamics. We use approximate information states to formulate a DP that yields a strategy with a bounded performance loss. Finally, we illustrate the application of our results in control and reinforcement learning using numerical examples.