We address the problem of automatic generation of features for value function
approximation. Bellman Error Basis Functions (BEBFs) have been shown to improve
the error of policy evaluation with function approximation, with a convergence
rate similar to that of value iteration. We propose a simple, fast and robust
algorithm based on random projections to generate BEBFs for sparse feature
spaces. We provide a finite sample analysis of the proposed method, and prove
that projections logarithmic in the dimension of the original space are enough
to guarantee contraction in the error. Empirical results demonstrate the
strength of this method
