Towards a Framework for Comparing the Complexity of Robotic Tasks
This work addresses the challenge of task complexity comparison in robotics, which is incremental as it builds on existing reduction concepts.
The paper tackles the problem of comparing the complexity of robotic tasks by defining a reduction notion and a quantitative measure, proving properties like reflexivity and transitivity, and proposing practical algorithms for estimation, illustrated with analytical and reinforcement learning examples.
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.