As explained in the paper, because we know that the true value function is convex with respect to the belief space fo the uncertain regions, we can compute an upper bound of the value function by interpolating.
Note that this would only be an upper bound related to the approximation errors made in the belief space. That is it bounds the value function for the current roadmap with the current losses over its transitions. Thus it is not a general upper bound for any possible roadmap.
As explained in the paper, because we know that the true value function is convex with respect to the belief space fo the uncertain regions, we can compute an upper bound of the value function by interpolating. Note that this would only be an upper bound related to the approximation errors made in the belief space. That is it bounds the value function for the current roadmap with the current losses over its transitions. Thus it is not a general upper bound for any possible roadmap.