We propose the use of kernel-based methods as underlying function approximator in the least-squares based policy evaluation framework of LSPE(λ) and LSTD(λ). In particular we present the 'kernelization' of model-free LSPE(λ). The 'kernelization' is computationally made possible by using the subset of regressors approximation, which approximates the kernel using a vastly reduced number of basis functions. The core of our proposed solution is an efficient recursive implementation with automatic

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... pervised selection of the relevant basis functions. The LSPE method is well-suited for optimistic policy iteration and can thus be used in the context of online reinforcement learning. We use the high-dimensional Octopus benchmark to demonstrate this.