Memristive Bellman solver for decision-making

Zhe Feng, Zuheng Wu (), Jianxun Zou, Lingli Cheng, Xiaolong Zhao, Xumeng Zhang, Jian Lu, Cong Wang, Yilin Wang, Haochen Wang, Wenbin Guo, Zhibin Qian, Yunlai Zhu, Zuyu Xu, Yuehua Dai () and Qi Liu ()
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Zhe Feng: Anhui University
Zuheng Wu: Anhui University
Jianxun Zou: Anhui University
Lingli Cheng: Fudan University
Xiaolong Zhao: University of Science and Technology of China
Xumeng Zhang: Fudan University
Jian Lu: Zhejiang Laboratory
Cong Wang: Nanjing University
Yilin Wang: University of Science and Technology of China
Haochen Wang: Anhui University
Wenbin Guo: Anhui University
Zhibin Qian: Anhui University
Yunlai Zhu: Anhui University
Zuyu Xu: Anhui University
Yuehua Dai: Anhui University
Qi Liu: Fudan University

Nature Communications, 2025, vol. 16, issue 1, 1-11

Abstract: 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.

Date: 2025
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DOI: 10.1038/s41467-025-60085-w

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