Optimal Planning Over Long and Infinite Horizons for Achieving Independent Partially-Observable Tasks That Evolve Over Time

Theory and Analysis of Optimal Planning over Long and Infinite Horizons for Achieving Independent Partially-Observable Tasks that Evolve over Time

“…Similarly, the value of following a trajectory n, V n i (b i ), can be computed by iteratively applying the Bellman equation and following *This work was partially supported by Sony AI. 1 The authors are with School of Computer Science, Carnegie Mellon University {anahitam, mmv, maxim}@cs.cmu.edu. the remaining trajectory [2].…”

“…Using the mathematical definition of the independent tasks, the optimal value of an agent POMDP built from a set of independent client POMDPs P can be iteratively computed as follows where Pr(z|b, a) = k∈P Pr(z k |b k , a[k]) [1].…”

“…Our prior work exploits the observation that in some domains the number of tasks, k * , that the robot can attend to within H is limited [1]. Given this observation, if the robot optimally solves all possible sub-problems of size k * with different combinations of tasks, it can find the optimal solution to the agent POMDP.…”

“…We focus on the class of problems with N independent tasks that evolve over time, proposed in [1]. The robot should interleave its actions to find an optimal sequence of actions to attend to all the tasks.…”

“…To compute an optimal solution for all the tasks, one should solve the agent POMDP optimally. We briefly describe the client and agent POMDPs, and how [1] referred to as multi-task planner solves the agent POMDP efficiently.…”