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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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Algorithms & Randomness Center (ARC)
Nick Harvey (Univ. of British Columbia, Vancouver)
Monday, October 26, 2020
Virtual via Bluejeans - 11:00 am
Title: Optimal anytime regret with two experts
Abstract: A central problem in online learning is regret minimization in the expert setting. The famous multiplicative weights method achieves the optimal regret asymptotically if the number of experts is large, and the time horizon is known in advance. Optimal algorithms are also known if there are exactly two, three or four experts, and the time horizon is known in advance.
In the “anytime” setting, where the time horizon is not known in advance, algorithms can be obtained by the “doubling trick”, but they are not optimal, let alone practical. No minimax optimal algorithm was previously known in the anytime setting, regardless of the number of experts. We design the first minimax optimal algorithm for minimizing regret in the anytime setting. We consider the case of two experts, and prove that the optimal regret is \gamma \sqrt{t}/2 at all time steps t, where \gamma is a natural constant that arose 35 years ago in studying fundamental properties of Brownian motion. The algorithm is designed by considering a continuous analogue of the regret problem, which is solved using ideas from stochastic calculus.
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