# Towards a Framework for Comparing the Complexity of Robotic Tasks

arXiv: https://arxiv.org/abs/2202.09892 · HTML: https://mlsanity.com/paper/2202.09892/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2022.

## Built on by (most cited first, 1 of 1)

- [Foundational World Models Accurately Detect Bimanual Manipulator Failures](https://mlsanity.com/paper/2603.06987/) (2026)

## Abstract (arXiv)

We are motivated by the problem of comparing the complexity of one robotic task relative to another. To this end, we define a notion of reduction that formalizes the following intuition: Task 1 reduces to Task 2 if we can efficiently transform any policy that solves Task 2 into a policy that solves Task 1. We further define a quantitative measure of the relative complexity between any two tasks for a given robot. We prove useful properties of our notion of reduction (e.g., reflexivity, transitivity, and antisymmetry) and relative complexity measure (e.g., nonnegativity and monotonicity). In addition, we propose practical algorithms for estimating the relative complexity measure. We illustrate our framework for comparing robotic tasks using (i) examples where one can analytically establish reductions, and (ii) reinforcement learning examples where the proposed algorithm can estimate the relative complexity between tasks.