POSSP Problem with Task Failure Probability

The stochastic shortest path problem (SSP) is a standard model for sequential decision making under uncertainty[2]. In Otsubo’s paper[1], an SSP with task failure on a complete separable metric space was proposed, where states are perfectly observable. In this paper, we consider the partially observable stochastic shortest path problem (POSSP). This problem is transformed into an equivalent two-person zero-sum game, and we show that the order of maximizing and minimizing is interchangeable. Furthermore, we show that a good approximation to an optimal policy can be obtained by framing the problem in terms of the expected total discounted costs. From the above, we show that this problem can be addressed using a framework that combines two-person zero-sum games and partially observable Markov decision processes (POMDPs).