This paper presents a novel and practical non-parametric approximate dynamic programming (ADP) algorithm that enjoys graceful, dimension-independent approximation and sample complexity guarantees. In particular, we establish both theoretically and computationally that our proposal can serve as a viable replacement to state of the art parametric ADP algorithms, freeing the designer from carefully specifying an approximation architecture. We accomplish this by "kernelizing" a recent mathematical program for ADP (the "smoothed" approximate LP) proposed by Desai et al. (2011). Our theoretical guarantees establish that the quality of the approximation produced by our procedure improves gracefully with sampling effort. Via a computational study on a controlled queueing network, we show that our non-parametric procedure outperforms the state of the art parametric ADP approaches and established heuristics.