Abstract
The Bellman equation, with a resource-consuming solving process, plays a fundamental role in formulating and solving dynamic optimization problems. The realization of the Bellman solver with memristive computing-in-memory (MCIM) technology, is significant for implementing efficient dynamic decision-making. However, the iterative nature of the Bellman equation solving process poses a challenge for efficient implementation on MCIM systems, which excel at vector-matrix multiplication (VMM) operations but are less suited for iterative algorithms. In this work, by incorporating the temporal dimension and transforming the solution into recurrent dot product operations, a memristive Bellman solver (MBS) is proposed, facilitating the implementation of the Bellman equation solving process with efficient MCIM technology. The MBS effectively reduces the iteration numbers and which further enhanced by approximated solutions leveraging memristor noise. Finally, the path planning tasks are used to verify the feasibility of the proposed MBS. The theoretical derivation and experimental results demonstrate that the MBS effectively reduces the iteration cycles, facilitating the solving efficiency. This work could be a sound of choice for developing high-efficiency decision-making systems.