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algorithm of Koller and Parr (2000). As we discussed in Section 6.4, the L2 **projections in**
factored MDPs by Koller and Parr are difficult and time consuming; hence, we were only able to compare the two algorithms for smaller problems, where an equivalent L2**-projection**
can be implemented using an explicit state space formulation. Results for both algorithms are presented in Figure 15(a), showing the relative error of **the approximate solutions to** the true value function for increasing problem sizes. The results indicate that, for larger problems, the max-norm formulation generates a better approximation of the true optimal value function V
∗than the L2**-projection. Here, we used two types of basis functions: the**
same single variable functions, and pairwise basis functions. The pairwise basis functions contain indicators for neighboring pairs of machines (i.e.**, functions of two variables). As** expected, the use of pairwise basis functions resulted in better approximations.