Finite-Time 4-Expert Prediction Problem
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We explicitly solve the nonlinear PDE that is the continuous limit of dynamic programming of expert prediction problem in finite horizon setting with N=4 experts. The expert prediction problem is formulated as a zero sum game between a player and an adversary. By showing that the solution is C^2, we are able to show that the strategies conjectured in arXiv:1409.3040G form an asymptotic Nash equilibrium. We also prove the "Finite vs Geometric regret" conjecture proposed in arXiv:1409.3040G for N=4, and we give a stronger conjecture which characterizes the relation between the finite and geometric stopping.
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