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Due to an increased amount of applications that can be modeled as large-scale, there has been growing interest in using simple methods for optimization that require low iteration cost as well as limited memory storage. We will be concerned with optimization problems for networked systems with high dimensions, focusing on applications in crowdsourcing and pandemic control. What makes these problems complex is that the objectives relate to aspects of the evolution of the dynamics of the system. We develop first-order optimization methods with low iteration complexity for such applications in this dissertation work. In the first part of this work, we consider the adversarial crowdsourcing problem. We reduce this problem to the robust rank-one matrix completion problem, and we propose a new first-order algorithm with theoretical guarantees. These results are then applied to the problem of classification from crowdsourced data under the assumption that while the majority of the workers are governed by the standard single-coin David-Skene model, some of the workers can deviate arbitrarily from this model. Extensive experimental results show our algorithm outperforms all other state-of-the-art methods in such an adversarial scenario. In the second part of the work, we consider the optimal lockdown problem for pandemic control. As a common strategy of contagious disease containment, lockdowns will inevitably weaken the economy. Here we propose a mathematical framework with first-order methods to achieve pandemic control through an optimal stabilizing non-uniform lockdown, where our goal is to reduce the economic activity as little as possible while decreasing the number of infected individuals at a prescribed rate. We demonstrate the power of this framework by analyzing a model of COVID-19 spread in the 62 counties of New York State. We find that an optimal stabilizing lockdown based on epidemic status in April 2020 would have reduced economic activity more stringently outside of New York City compared to within it, even though the epidemic was much more prevalent in New York City at that point. In the third part of the work, we consider the optimal vaccine allocation issue for pandemic control, where our goal is to send the infections to zero as soon as possible with a fixed number of vaccines. To achieve this, we propose a mathematical framework for classical epidemic models as well as a COVID-19 model. Moreover, we also analyzed the epidemic model used in [Bubar et al., 2021], and compared our method with the strategies in [Bubar et al., 2021]. We found that it is better to offer vaccines to younger people when the basic reproduction number R0 is moderately above one. |
