The Stochastic Shortest Path (SSP) problem models probabilistic sequential-decision problems where an agent must pursue a goal while minimizing a cost function. Because of the probabilistic dynamics, it is desired to have a cost function that considers risk. Conditional Value at Risk (CVaR) is a criterion that allows modeling an arbitrary level of risk by considering the expectation of a fraction $\alpha$ of worse trajectories. Although an optimal policy is non-Markovian, solutions of CVaR-SSP can be found approximately with Value Iteration based algorithms such as CVaR Value Iteration with Linear Interpolation (CVaRVIQ) and CVaR Value Iteration via Quantile Representation (CVaRVILI). These type of solutions depends on the algorithm's parameters such as the number of atoms and $\alpha_0$ (the minimum $\alpha$). To compare the policies returned by these algorithms, we need a way to exactly evaluate stationary policies of CVaR-SSPs. Although there is an algorithm that evaluates these policies, this only works on problems with uniform costs. In this paper, we propose a new algorithm, Forward-PECVaR (ForPECVaR), that evaluates exactly stationary policies of CVaR-SSPs with non-uniform costs. We evaluate empirically CVaR Value Iteration algorithms that found solutions approximately regarding their quality compared with the exact solution, and the influence of the algorithm parameters in the quality and scalability of the solutions. Experiments in two domains show that it is important to use an $\alpha_0$ smaller than the $\alpha$ target and an adequate number of atoms to obtain a good approximation.

本文提出了一种新的算法Forward-PECVaR，用于确切评估具有非均匀成本的CVaR-SSPs的稳态策略，并通过实证评估CVaR Value Iteration算法的质量以及算法参数对解决方案的质量和可伸缩性的影响。

Forward-PECVaR算法：CVaR SSPs的精确评估