Boreiri, Amirhossein2024-05-142024-05-142024-05-142024-05-10http://hdl.handle.net/10012/20563A Real-Time Bidding (RTB) network is a real-time auction market, primarily used for advertising space sales. Within this environment, clients participate by bidding on preferred items and subsequently purchasing them upon winning. This thesis addresses the problem of optimal real-time bidding within a second-price Vickrey auction setting, where the distribution of prices is unknown. Our focus centers on second-price auction mechanisms, which offers unique properties that enable the development of compelling algorithms. We introduce the concept of a demand-side platform (DSP), acting as an intermediary representing clients in the auction market. With no prior knowledge of typical prices, the DSP must determine optimal bidding strategies for each item and distribute won items among clients to fulfill their contracts while minimizing expenses. When the distribution of the prices of items is known, this optimal bidding problem can be solved by classic convex optimization algorithms such as ADMM. However, market properties may vary over time, and access to competitor behavior or bidding information is limited. Consequently, the DSP must continually update its information about the price distribution, while adapting bidding estimations in real-time. Our primary contribution lies in devising efficient online optimization algorithms that accurately find the optimal bids. To tackle this, we employ tools from convex optimization analysis, including duality, along with stochastic optimization algorithms, notably stochastic approximation. Moreover, techniques such as projection and penalty term methods are utilized to enhance algorithm performance.enReal-time BiddingAuction TheoryConvex OptimizationStochastic ApproximationOnline LearningMaster Thesis