This thesis investigates the problem of time-varying function optimization. In particular, we study techniques to minimize the cumulative regret when optimizing a time-varying function in the Gaussian process setting. First, we introduce the problem and present a literature review of the current methods and results. Following this, we we propose enhancements to existing algorithms, demonstrating improved regret bounds. We discuss the applications of these algorithms and where they can provide a benefit compared to existing methods. With these applications in mind we introduce two new temporal models for time-varying functions and their associated algorithms. We test their performance in order to validate their effectiveness and potential benefits.

The purpose of this report is to design and iterate all the subsystems of a drone for Mars exploration. Based on a design option analysis and tradeoff, the vehicle is designed to be a VTOL tilt rotor. The mission need statement is: Enable largescale targeted exploration of the atmosphere and surface of currently inaccessible areas of Mars. This mission statement resulted in two expedition types: collect and return expeditions in which soil samples are collected, and remote sensing expeditions where visual mapping, height mapping, gas analyzing and dust composition data is collected and. The project objective statement is: Design a semiautonomous unpiloted atmospheric vehicle that can assist human Martian exploration by observing remote areas and collecting atmosphere and soil samples from difficulttoreach places...