Online Control in Population Dynamics
Fuente:
arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929375953289216 |
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| author | Golowich, Noah Hazan, Elad Lu, Zhou Rohatgi, Dhruv Sun, Y. Jennifer |
| author_facet | Golowich, Noah Hazan, Elad Lu, Zhou Rohatgi, Dhruv Sun, Y. Jennifer |
| contents | The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the problem of prediction rather than control. Existing mathematical models for control in population dynamics are often restricted to specific, noise-free dynamics, while real-world population changes can be complex and adversarial.
To address this gap, we propose a new framework based on the paradigm of online control. We first characterize a set of linear dynamical systems that can naturally model evolving populations. We then give an efficient gradient-based controller for these systems, with near-optimal regret bounds with respect to a broad class of linear policies. Our empirical evaluations demonstrate the effectiveness of the proposed algorithm for control in population dynamics even for non-linear models such as SIR and replicator dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01799 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Online Control in Population Dynamics Golowich, Noah Hazan, Elad Lu, Zhou Rohatgi, Dhruv Sun, Y. Jennifer Machine Learning Optimization and Control The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics. Most studies on population dynamics focus on the problem of prediction rather than control. Existing mathematical models for control in population dynamics are often restricted to specific, noise-free dynamics, while real-world population changes can be complex and adversarial. To address this gap, we propose a new framework based on the paradigm of online control. We first characterize a set of linear dynamical systems that can naturally model evolving populations. We then give an efficient gradient-based controller for these systems, with near-optimal regret bounds with respect to a broad class of linear policies. Our empirical evaluations demonstrate the effectiveness of the proposed algorithm for control in population dynamics even for non-linear models such as SIR and replicator dynamics. |
| title | Online Control in Population Dynamics |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2406.01799 |