Real-Time Bidding (RTB) has become a relevant paradigm in display advertising. It mimics stock exchanges and utilizes computer algorithms to buy and sell ads in real-time automatically. Imagine that you have to participate in N ≫ 1 of those online ad auctions with a limited bidding budget. The task is to create such a bidding strategy that you can win some of them, and that the placed ads generate at least Nc clicks. That should be done by spending as little money as possible. In the following, we will look at a possible solution to this problem.

1. Real-Time Bidding ecosystem

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Illustration of a Real-time bidding ecosystem. The schema is taken from [1].

A brief description of the RTB ecosystem is given in the figure above. When a user visits an ad-supported site each ad placement will trigger an auction. Bid requests will be sent via the ad exchange to the different bidding agents. Upon receiving a bid request, every bidding agent calculates a bid that is sent together with an ad to the Ad exchange. Finally, the winner’s ad will be shown to the visitor along with the regular content of the website. The whole process should be completed within a fraction of the second. A more detailed introduction to RTB could be found in [1,2]. …

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Federated learning is a machine learning technique that trains a model across multiple decentralized devices, each of them holding a local data sample, without exchanging these data samples. Let’s imagine that by using this technique you have trained a binary classification model. You want to test it on the data of several devices by calculating the model ROC-AUC score on each one of them and then by averaging the results. The following questions arise:

  • How much does this score differ from the ROC-AUC score that could have been obtained if all the data was located on the same device?
  • Under which conditions are both scores equal? Are they equal only in the case when the data is identically distributed among all devices? …

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We will look at the problem of navigating through a dynamically changing map. It can be represented as a sequence of optimization problems for every time step and in the end, it will reduce to a specific case of the Bellman equation. A solution will be discussed and applied to a particular realization of the problem.

We will consider a map with impenetrable (dynamic) obstacles like the moving brick walls, the cactus or the animal bones, and points through which you can pass but it is not preferable to do so (the blue monster). …

Anton Ivanov

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