Computing Complexity-aware Plans Using Kolmogorov Complexity

TL;DR

This paper proposes a novel complexity-aware planning method using Kolmogorov complexity to balance policy performance and simplicity in deterministic automata, with algorithms for low-complexity policy synthesis.

Contribution

It introduces a new planning objective based on Kolmogorov complexity and develops algorithms to find low-complexity policies balancing performance and simplicity.

Findings

Algorithms produce low-complexity policies consistent with intuition.

The approach effectively balances policy performance and complexity.

Evaluations on a navigation task demonstrate practical applicability.

Abstract

In this paper, we introduce complexity-aware planning for finite-horizon deterministic finite automata with rewards as outputs, based on Kolmogorov complexity. Kolmogorov complexity is considered since it can detect computational regularities of deterministic optimal policies. We present a planning objective yielding an explicit trade-off between a policy's performance and complexity. It is proven that maximising this objective is non-trivial in the sense that dynamic programming is infeasible. We present two algorithms obtaining low-complexity policies, where the first algorithm obtains a low-complexity optimal policy, and the second algorithm finds a policy maximising performance while maintaining local (stage-wise) complexity constraints. We evaluate the algorithms on a simple navigation task for a mobile robot, where our algorithms yield low-complexity policies that concur with intuition.