Necessary and Sufficient Conditions for the Optimization-Based Concurrent Execution of Learned Robotic Tasks

In this work, we consider the problem of executing multiple tasks encoded by value functions, each learned through Reinforcement Learning, using an optimization-based framework. Prior works develop this framework but did not address when learned value functions can be concurrently executed. This work's main contributions consist of theorems which provide necessary and sufficient conditions to concurrently execute sets of learned tasks within subsets of the state space using the previously proposed min-norm controller. These theorems provide insight into when learned control tasks can be made concurrently executable, when they may already be so, and when concurrent execution is not possible under the proposed framework. We also extend the proposed framework to account for value functions trained with a discount factor, making it more compatible with standard RL practices.