Multiply Accelerated Value Iteration for NonSymmetric Affine Fixed Point Problems and Application to Markov Decision Processes

We analyze a modified version of the Nesterov accelerated gradient algorithm, which applies to affine fixed point problems with non-self-adjoint matrices, such as ones appearing in theory Markov decision processes discounted or mean payoff criteria. characterize spectra matrices for this algorithm does converge an asymptotic rate. also introduce $d$th-order and show that it yields multiply rate under more demanding conditions on spectrum. subsequently apply these methods develop schemes nonlinear arising from processes. This is illustrated by numerical experiments.