Online Convex Optimization in Changing Environments and its Application to Resource Allocation

In the era of the big data, we create and collect lots of data from all different kinds of sources: the Internet, the sensors, the consumer market, and so on. Many of the data are coming sequentially, and would like to be processed and understood quickly. One classic way of analyzing data is based on batch processing, in which the data is stored and analyzed in an offline fashion. However, when the volume of the data is too large, it is much more difficult and time-consuming to do batch processing than sequential processing. What's more, sequential data is usually changing dynamically, and needs to be understood on-the-fly in order to capture the changes. Online Convex Optimization (OCO) is a popular framework that matches the above sequential data processing requirement. Applications using OCO include online routing, online auctions, online classification and regression, as well as online resource allocation. Due to the general applicability of OCO to the sequential data and the rigorous theoretical guarantee, it has attracted lots of researchers to develop useful algorithms to fulfill different needs. In this thesis, we show our contributions to OCO's development by designing algorithms to adapt to changing environments.