We give another success story of using kernel-based methods to solve a dificult reinforcement learning problem, namely that of 3vs2 keepaway in RoboCup simulated soccer. Key challenges in keepaway are the high-dimensionality of the state space (rendering conventional grid-based function approximation like tilecoding infeasable) and the stochasticity due to noise and multiple learning agents needing to co- operate. We use approximate policy iteration with sparsified regular- ization networks to carry out policy evaluation. Preliminary results indicate that the behavior learned through our approach clearly out- performs the best results obtained with tilecoding by Stone et al.