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Explore a technical lecture that delves into optimal prediction strategies and the Randomized Littlestone Dimension in online learning scenarios. Learn about classical online learning problems through the lens of daily weather forecasting and cat/dog image classification, discovering how these challenges connect to binary tree depth calculations. Gain insights into new complexity measures derived from the Littlestone dimension, including breakthrough findings on optimal randomized learners and their expected mistake bounds. The presentation covers joint research with Yuval Filmus, Steve Hanneke, and Shay Moran, demonstrating how the optimal expected regret in learning scenarios with Littlestone dimension relates to classification function performance. Delivered by Idan Mehalel, a PhD student at the Technion's computer science department, this 59-minute talk offers valuable perspectives on learning theory and online learning theory applications.