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The Bellman operator constitutes the foundation of dynamic programming (DP).An alternative is presented by the Gauss-Seidel operator, whose evaluation,differently from that of the Bellman operator where the states are allprocessed at once, updates one state at a time, while incorporating into thecomputation the interim results. The provably better convergence rate of DPmethods based on the Gauss-Seidel operator comes at the price of an inherentsequentiality, which prevents the exploitation of modern multi-core systems. Inthis work we propose a new operator for dynamic programming, namely, therandomized mini-batch operator, which aims at realizing the trade-off betweenthe better convergence rate of the methods based on the Gauss-Seidel operatorand the parallelization capability offered by the Bellman operator. After theintroduction of the new operator, a theoretical analysis for validating itsfundamental properties is conducted. Such properties allow one to successfullydeploy the new operator in the main dynamic programming schemes, such as valueiteration and modified policy iteration. We compare the convergence of the DPalgorithm based on the new operator with its earlier counterparts, sheddinglight on the algorithmic advantages of the new formulation and the impact ofthe batch-size parameter on the convergence. Finally, an extensive numericalevaluation of the newly introduced operator is conducted. In accordance withthe theoretical derivations, the numerical results show the competitiveperformance of the proposed operator and its superior flexibility, which allowsone to adapt the efficiency of its iterations to different structures of MDPsand hardware setups.

Parallel and Flexible Dynamic Programming via the Randomized Mini-Batch Operator