Processing big data sets for inference and decision making and the need to protect privacy of individuals' data have been two conflicting major challenges with growing importance over the last years. The notion of data privacy is gaining popularity among researchers with an increasing speed. We are interested in developing useful statistical inference and optimization methods while protecting privacy of individuals who contribute to the available data with their sensitive information.

Online optimization problems have a repetitive nature, and those that involve multiple agents entail user interaction.

Our goal is integrating the information gained through this interaction to the optimization process. This task requires utilizing machine learning tools to analyze the feedback data. Most of the problems we study learn the users’ utility functions through their preference feedback, such as determining price using the customers’ feedback on whether or not to buy, or learning the agents’ preferences based on the favorite option selected.