  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.
