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Register a new userStochastic Optimal Control of Epidemic Processes in Networks
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Lars Lorch
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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We approach the development of models and control strategies of susceptible-infected-susceptible (SIS) epidemic processes from the perspective of marked temporal point processes and stochastic optimal control of stochastic differential equations (SDEs) with jumps. In contrast to previous work, this novel perspective is particularly well-suited to make use of fine-grained data about disease outbreaks and lets us overcome the shortcomings of current control strategies. Our control strategy resorts to treatment intensities to determine who to treat and when to do so to minimize the amount of infected individuals over time. Preliminary experiments with synthetic data show that our control strategy consistently outperforms several alternatives. Looking into the future, we believe our methodology provides a promising step towards the development of practical data-driven control strategies of epidemic processes.
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In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost functional, in general, the value function is not differentiable in the domain. Then, we characterize the value function as a viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation. Based on the result, we derive a necessary and sufficient condition for the $L^0$ optimality, which immediately gives the optimal feedback map. Especially for control-affine systems, we consider the relationship with $L^1$ optimal control problem and show an equivalence theorem.
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a maximum condition, we reformulate the original control problem as a new one. Three algorithms are proposed to solve the new control problem. Numerical results for different examples demonstrate the effectiveness of our proposed algorithms, especially in high dimensional cases. And an important application of this method is to calculate the sub-linear expectations, which correspond to a kind of fully nonlinear PDEs.
In stochastic dynamic environments, team stochastic games have emerged as a versatile paradigm for studying sequential decision-making problems of fully cooperative multi-agent systems. However, the optimality of the derived policies is usually sensitive to the model parameters, which are typically unknown and required to be estimated from noisy data in practice. To mitigate the sensitivity of the optimal policy to these uncertain parameters, in this paper, we propose a model of robust team stochastic games, where players utilize a robust optimization approach to make decisions. This model extends team stochastic games to the scenario of incomplete information and meanwhile provides an alternative solution concept of robust team optimality. To seek such a solution, we develop a learning algorithm in the form of a Gauss-Seidel modified policy iteration and prove its convergence. This algorithm, compared with robust dynamic programming, not only possesses a faster convergence rate, but also allows for using approximation calculations to alleviate the curse of dimensionality. Moreover, some numerical simulations are presented to demonstrate the effectiveness of the algorithm by generalizing the game model of social dilemmas to sequential robust scenarios.
We study the problem of optimal inside control of an SPDE (a stochastic evolution equation) driven by a Brownian motion and a Poisson random measure. Our optimal control problem is new in two ways: (i) The controller has access to inside information, i.e. access to information about a future state of the system, (ii) The integro-differential operator of the SPDE might depend on the control. In the first part of the paper, we formulate a sufficient and a necessary maximum principle for this type of control problem, in two cases: (1) When the control is allowed to depend both on time t and on the space variable x. (2) When the control is not allowed to depend on x. In the second part of the paper, we apply the results above to the problem of optimal control of an SDE system when the inside controller has only noisy observations of the state of the system. Using results from nonlinear filtering, we transform this noisy observation SDE inside control problem into a full observation SPDE insider control problem. The results are illustrated by explicit examples.
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