Summary of On the Uniqueness Of Solution For the Bellman Equation Of Ltl Objectives, by Zetong Xuan et al.
On the Uniqueness of Solution for the Bellman Equation of LTL Objectives
by Zetong Xuan, Alper Kamil Bozkurt, Miroslav Pajic, Yu Wang
First submitted to arxiv on: 7 Apr 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: Robotics (cs.RO)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper proposes a new approach to surrogate rewards for linear temporal logic (LTL) objectives in planning problems. The authors demonstrate that the widely-adopted method of using two discount factors can lead to inaccurate evaluation of the expected return due to multiple solutions to the Bellman equation. They propose a condition for the Bellman equation to have the expected return as the unique solution, requiring solutions for states inside a rejecting bottom strongly connected component (BSCC) to be 0. The authors prove this condition is sufficient by showing that the solutions for the states with discounting can be separated from those for the states without discounting under this condition. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper talks about how to make sure that rewards in planning problems are accurate. They show a problem with an old way of doing things and then propose a new way to fix it. This new way helps us get the right answer by making sure that certain parts of the plan don’t affect others. |
