Stochastic Shortest Path Problem with Failure Probability

TL;DR

This paper introduces a novel approach to the stochastic shortest path problem that incorporates failure probabilities and dead-ends, using Bayesian MDPs and game theory to find less conservative policies for robot motion planning.

Contribution

It extends the stochastic shortest path framework to handle failure probabilities with dead-ends and develops a method to find policies within a failure threshold using Bayesian MDPs and game theory.

Findings

Effective in motion planning with obstacle avoidance

Balances failure risk and policy conservativeness

Demonstrates practical applicability in robotics

Abstract

We solve a sequential decision-making problem under uncertainty that takes into account the failure probability of a task. This problem cannot be handled by the stochastic shortest path problem, which is the standard model for sequential decision-making. This problem is addressed by introducing dead-ends. Conventionally, we only consider policies that minimize the probability of task failure, so the optimal policy constructed could be overly conservative. In this paper, we address this issue by expanding the search range to a class of policies whose failure probability is less than a desired threshold. This problem can be solved by treating it as a framework of a Bayesian Markov decision process and a two-person zero-sum game. Also, it can be seen that the optimal policy is expressed in the form of a probability distribution on a set of deterministic policies. We also demonstrate the effectiveness of the proposed methods by applying them to a motion planning problem with obstacle avoidance for a moving robot.