Mathematics
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Item Adversarial Robustness and Robust Meta-Learning for Neural Networks(2020) Goldblum, Micah; Czaja, Wojciech; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Despite the overwhelming success of neural networks for pattern recognition, these models behave categorically different from humans. Adversarial examples, small perturbations which are often undetectable to the human eye, easily fool neural networks, demonstrating that neural networks lack the robustness of human classifiers. This thesis comprises a sequence of three parts. First, we motivate the study of defense against adversarial examples with a case study on algorithmic trading in which robustness may be critical for security reasons. Second, we develop methods for hardening neural networks against an adversary, especially in the low-data regime, where meta-learning methods achieve state-of-the-art results. Finally, we discuss several properties of the neural network models we use. These properties are of interest beyond robustness to adversarial examples, and they extend to the broad setting of deep learning.Item MULTI-AGENT UNMANNED UNDERWATER VEHICLE VALIDATION VIA ROLLING-HORIZON ROBUST GAMES(2019) Quigley, Kevin J; Gabriel, Steven A.; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Autonomy in unmanned underwater vehicle (UUV) navigation is critical for most applications due to inability of human operators to control, monitor or intervene in underwater environments. To ensure safe autonomous navigation, verification and validation (V&V) procedures are needed for various applications. This thesis proposes a game theory-based benchmark validation technique for trajectory optimization for non-cooperative UUVs. A quadratically constrained nonlinear program formulation is presented, and a "perfect-information reality" validation framework is derived by finding a Nash equilibrium to various two-player pursuit-evasion games (PEG). A Karush-Kuhn-Tucker (KKT) point to such a game represents a best-case local optimum, given perfect information available to non-cooperative agents. Rolling-horizon foresight with robust obstacles are incorporated to demonstrate incomplete information and stochastic environmental conditions. A MATLAB-GAMS interface is developed to model the rolling-horizon game, and is solved via a mixed complementarity problem (MCP), and illustrative examples show how equilibrium trajectories can serve as benchmarks for more practical real-time path planners.