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We propose a principled kernel-based policy iteration algorithm to solve thecontinuous-state Markov Decision Processes (MDPs). In contrast to mostdecision-theoretic planning frameworks, which assume fully known statetransition models, we design a method that eliminates such a strong assumption,which is oftentimes extremely difficult to engineer in reality. To achievethis, we first apply the second-order Taylor expansion of the value function.The Bellman optimality equation is then approximated by a partial differentialequation, which only relies on the first and second moments of the transitionmodel. By combining the kernel representation of value function, we then designan efficient policy iteration algorithm whose policy evaluation step can berepresented as a linear system of equations characterized by a finite set ofsupporting states. We have validated the proposed method through extensivesimulations in both simplified and realistic planning scenarios, and theexperiments show that our proposed approach leads to a much superiorperformance over several baseline methods.

Kernel Taylor-Based Value Function Approximation for Continuous-State Markov Decision Processes