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MEAN-FIELD APPROXIMATIONS FOR STOCHASTIC POPULATION PROCESSES WITH HETEROGENEOUS INTERACTIONS.
- Source :
-
SIAM Journal on Control & Optimization . 2023, Vol. 61 Issue 6, p3442-3466. 25p. - Publication Year :
- 2023
-
Abstract
- This paper studies a general class of stochastic population processes in which agents interact with one another over a network. Agents update their behaviors in a random and decentralized manner according to a policy that depends only on the agent's current state and an estimate of the macroscopic population state, given by a weighted average of the neighboring states. When the number of agents is large and the network is a complete graph (has all-to-all information access), the macroscopic behavior of the population can be well-approximated by a set of deterministic differential equations called a mean-field approximation. For incomplete networks such characterizations remained previously unclear, i.e., in general whether a suitable mean-field approximation exists for the macroscopic behavior of the population. The paper addresses this gap by establishing a generic theory describing when various mean-field approximations are accurate for arbitrary interaction structures. Our results are threefold. Letting W be the matrix describing agent interactions, we first show that a simple mean-field approximation that incorrectly assumes a homogeneous interaction structure is accurate provided W has a large spectral gap. Second, we show that a more complex mean-field approximation which takes into account agent interactions is accurate as long as the Frobenius norm of W is small. Finally, we compare the predictions of the two mean-field approximations through simulations, highlighting cases where using mean-field approximations that assume a homogeneous interaction structure can lead to inaccurate qualitative and quantitative predictions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03630129
- Volume :
- 61
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Control & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 174808607
- Full Text :
- https://doi.org/10.1137/22M1488922