A universal approximator for the value function in continuous-state VI

William B. Haskell; Rahul Jain; Hiteshi Sharma; Pengqian Yu, TA Universal Empirical Dynamic Programming Algorithm for Continuous State MDPs, IEEE Transactions on Automatic Control ( Volume: 65, Issue: 1, Jan. 2020), DOI: 10.1109/TAC.2019.2907414.

We propose universal randomized function approximation-based empirical value learning (EVL) algorithms for Markov decision processes. The “empirical” nature comes from each iteration being done empirically from samples available from simulations of the next state. This makes the Bellman operator a random operator. A parametric and a nonparametric method for function approximation using a parametric function space and a reproducing kernel Hilbert space respectively are then combined with EVL. Both function spaces have the universal function approximation property. Basis functions are picked randomly. Convergence analysis is performed using a random operator framework with techniques from the theory of stochastic dominance. Finite time sample complexity bounds are derived for both universal approximate dynamic programming algorithms. Numerical experiments support the versatility and computational tractability of this approach.

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