Computational Analysis of Intelligent Agents: Social and Strategic Settings

The central motif of this work is prediction and optimization in presence of multiple interacting intelligent agents. We use the phrase `intelligent agents' to imply in some sense, a `bounded rationality', the exact meaning of which varies depending on the setting. Our agents may not be `rational' in the classical game theoretic sense, in that they don't always optimize a global objective. Rather, they rely on heuristics, as is natural for human agents or even software agents operating in the real-world. Within this broad framework we study the problem of influence maximization in social networks where behavior of agents is myopic, but complication stems from the structure of interaction networks. In this setting, we generalize two well-known models and give new algorithms and hardness results for our models. Then we move on to models where the agents reason strategically but are faced with considerable uncertainty. For such games, we give a new solution concept and analyze a real-world game using out techniques. Finally, the richest model we consider is that of Network Cournot Competition which deals with strategic resource allocation in hypergraphs, where agents reason strategically and their interaction is specified indirectly via player's utility functions. For this model, we give the first equilibrium computability results. In all of the above problems, we assume that payoffs for the agents are known. However, for real-world games, getting the payoffs can be quite challenging. To this end, we also study the inverse problem of inferring payoffs, given game history. We propose and evaluate a data analytic framework and we show that it is fast and performant.

Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.

Trash: a local solution to a global problem

Gemstone Team GREEN JUSTICE