"Spectrum is a key and scarce resource in wireless communication networks, and it remains tightly controlled by regulation authorities. Most of the frequency bands are exclusively allocated to a single system licensed to use it everywhere and for long periods of time. This rigid spectrum management model inevitably leads to significant inefficiencies in spectrum use. The explosion of demand for broadband wireless services also calls for more flexible models where much larger spectrum parts could be dynamically shared among users in a fluid manner. In such models, Dynamic Spectrum Access (DSA) techniques will play a major role. These techniques make it possible for radio devices to become frequency-agile, i.e. able to rapidly and dynamically access bands of a wide spectrum part.The success and spread of dynamic spectrum access strongly rely on the ability for many frequency-agile devices (or systems) to coexist peacefully and efficiently. With multiple interacting devices, the research agenda shifts from spectrum access problems to spectrum sharing problems, which raises original and challenging questions. There may be limited or no communication between the different devices or systems sharing spectrum. We further expect systems to be heterogeneous in their transmission capabilities, but also in the type of service they support. In that context, the design of spectrum access strategies resulting in an efficient and fair spectrum resource use constitutes a challenging puzzle. The broad objective of the proposed research is to develop original analytical and simulation tools to tackle dynamic spectrum sharing issues. The project leverages and marries techniques from distributed optimization and machine learning to design decentralized, efficient, and fair spectrum sharing algorithms. We believe that such algorithms are critical for the birth and rapid expansion of DSA technologies and hence for the development of future wireless broadband systems."