UC Berkeley

This dissertation work combines two lines of work related to stochastic optimization, one focused on theoretical contributions to the field, and the other focused on modelling and philosophical contributions to the field. In the first line of work, we contribute to the theoretical underpinnings of two models that draw from data analysis, mathematical and statistical modeling, and optimization. In particular, there are several classes of machine learning problems which interface with stochastics and optimization, and, with the use of stochastic process theory and associated notions of complexity, we can recharacterize some of the theoretical expectations of these problems, which importantly model uncertainty. The improved results are gained from problem reformulations, improved analytical techniques, and a concerted effort to use the most recent advances in complexity analysis and their associated generalizations, and has implications for the construction and analysis of societal scale models. In the second line of work, we demonstrate why the techniques in stochastic optimization help form a mathematical and statistical basis that can solve large-scale societal problems over time, with precise engineering intervention focus. The main model researched is the Principal Agent Model (PAM). Considering sectors of the social economy as the principal and communities of people as the agents, we utilize development engineering and the associated economics of global poverty reduction to unveil the concept of Optimal Intervention Theory as a means to explore, adapt, and activate tractable solutions in specially-constrained environments. By tractable here, we mean interventions that last long beyond the intervention period, according to the education-, resource-, access-, and network-bases interventions afforded the impacted populations, especially those concerned with international development and global poverty alleviation.