Samuel Resendez will present his MSE talk " Online Contention Resolution against Online Adversaries " on April 21, 2025 at 2:30 pm in CS 302. Committee: Matt Weinberg and Huacheng Yu Abstract: A framework called contention resolution schemes has been proposed as a way to unify algorithms for a relatively broad class of problems with similar combinatorial structures. A subset of this class comprises Bayesian online selection problems (BOSP). A BOSP describes an optimization problem that can be modeled as making an online selection of choices on a sequence of random variables, subject to some constraints. While the Bayesian online selection problem has been explored in many contexts we restrict ourselves to the k-uniform case. The k-uniform case describes settings where the only constraint on the selection of elements is the total cardinality of the set chosen. In particular, we are allowed to pick up to k elements from an arbitrarily large number of options. An online flavor of contention resolution schemes has been developed for BOSPs under k-uniform constraints. These schemes have been explored primarily in 2 settings. The first is the offline setting. In this setting, the ordering of elements is chosen before any of the elements are revealed. The other is the almighty setting. In this setting, we assume omnipotence for whoever is determining the element order - they are aware of all realizations of randomness, both of the elements and the algorithm, and are free to rearrange the order of elements shown at any moment. There is a third setting that lies between these two extremes - one that assumes that our opponent has a similar amount of power as us, in that they can rearrange elements arbitrarily after seeing what has been revealed, but do not know the realizations of any of the subsequent elements. This is known as the online setting. Our work demonstrates the hardness of online contention resolution against online adversaries. We develop tools to prove that the online case is more akin to the almighty case, and prove impossibility of restricted classes of algorithms against the online adversary.