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| Model-free method for LQ mean-field social control problems with one-dimensional state space |
| ZhenhuiXu1,TielongShen2 |
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| (1 School of Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan;2 Department of Engineering and Applied Sciences, Sophia University, Tokyo 102-8554, Japan) |
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| 摘要: |
| This paper presents a novel model-free method to solve linear quadratic (LQ) mean-field control problems with onedimensional
state space and multiplicative noise. The focus is on the infinite horizon LQ setting, where the conditions
for solution either stabilization or optimization can be formulated as two algebraic Riccati equations (AREs). The proposed
approach leverages the integral reinforcement learning technique to iteratively solve the drift-coefficient-dependent stochastic
ARE (SARE) and other indefinite ARE, without requiring knowledge of the system dynamics. A numerical example is given
to demonstrate the effectiveness of the proposed algorithm. |
| 关键词: Mean-field control · Social optima · Infinite horizon · Reinforcement learning |
| DOI：https://doi.org/10.1007/s11768-024-00210-0 |
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| 基金项目: |
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| Model-free method for LQ mean-field social control problems with one-dimensional state space |
| Zhenhui Xu1,Tielong Shen2 |
| (1 School of Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan;2 Department of Engineering and Applied Sciences, Sophia University, Tokyo 102-8554, Japan) |
| Abstract: |
| This paper presents a novel model-free method to solve linear quadratic (LQ) mean-field control problems with onedimensional
state space and multiplicative noise. The focus is on the infinite horizon LQ setting, where the conditions
for solution either stabilization or optimization can be formulated as two algebraic Riccati equations (AREs). The proposed
approach leverages the integral reinforcement learning technique to iteratively solve the drift-coefficient-dependent stochastic
ARE (SARE) and other indefinite ARE, without requiring knowledge of the system dynamics. A numerical example is given
to demonstrate the effectiveness of the proposed algorithm. |
| Key words: Mean-field control · Social optima · Infinite horizon · Reinforcement learning |
