PDE Approaches to A Problem from Prediction with Expert Advice

Nadejda Drenska
University of Minnesota
School of Mathematics

Prediction with expert advice is an area of online machine learning, which aims to synthesize advice from different experts. We consider the case of a stock prediction problem with an investor who relies on history-dependent experts, and an adversarial market. This forms a two-person game, and we are interested in the optimal strategies of the market and the player when the game is played over a long time. We prove that the discrete value function converges to the unique solution of a nonlinear parabolic PDE, which determines asymptotically optimal strategies.

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