Stochastic Control via Entropy Compression

TL;DR

This paper introduces a novel entropy-based analysis for stochastic control in noisy environments, extending Lovasz Local Lemma techniques to account for adversarial perturbations affecting state observations and evolution.

Contribution

It develops a new entropy-centered framework that enables success guarantees for stochastic control under noise, generalizing LLL conditions to noisy settings.

Findings

Entropy measures progress and noise impact effectively.

Established a sufficient condition balancing noise and system complexity.

Recovered LLL conditions in the absence of noise.

Abstract

We consider an agent trying to bring a system to an acceptable state by repeated probabilistic action. Several recent works on algorithmizations of the Lovasz Local Lemma (LLL) can be seen as establishing sufficient conditions for the agent to succeed. Here we study whether such stochastic control is also possible in a noisy environment, where both the process of state-observation and the process of state-evolution are subject to adversarial perturbation (noise). The introduction of noise causes the tools developed for LLL algorithmization to break down since the key LLL ingredient, the sparsity of the causality (dependence) relationship, no longer holds. To overcome this challenge we develop a new analysis where entropy plays a central role, both to measure the rate at which progress towards an acceptable state is made and the rate at which noise undoes this progress. The end result is a sufficient condition that allows a smooth tradeoff between the intensity of the noise and the amenability of the system, recovering an asymmetric LLL condition in the noiseless case.