UC San Diego

As highly nonlinear continuous functions become the prevalent model of computation, NP-hard optimization problems over the continuous domain pose significant challenges to AI/ML algorithms and systems, especially in terms of their robustness and safety. The key to nonlinear optimization is to efficiently search through input regions with potentially widely varying numerical properties to achieve low-regret descent and fast progress toward the optima. Monte Carlo Tree Search (MCTS) methods have recently been introduced to improve global optimization by computing better partitioning of the search space that balances exploration and exploitation.

This dissertation investigates the application of Monte Carlo tree methods for nonlinear optimization (encompassing black-box and non-convex optimization) to identify the global optimum, and the crafting of training datasets designed to boost transferability and reduce dataset size in computational molecular dynamics. To tackle global optimization challenges, the study integrates sampling strategies with MCTS frameworks, employing diverse local optimization techniques to highlight promising samples. These techniques span stochastic search, Gaussian Processes regression, numerical overapproximation of the objective function, and analysis of first- and second-order information. In the realm of training dataset development, computational simulations of water serve as a practical case study. An active learning framework is introduced to efficiently condense the size of the training dataset while preserving its quality and comprehensiveness. The research further explores model transferability by assessing various subsets for training set inclusion to the simulation of water molecules, thereby uncovering the model's adaptability challenges across different scenarios.

The findings affirm that Monte Carlo tree methods provide cost-effective strategies for managing the complexities inherent in state space exploration. By applying these methods to a range of application areas, the dissertation underscores the robustness and utility of sampling techniques in advancing machine learning research.