We explicitly solve the nonlinear PDE that is the continuous limit of dynamic programming equation of the 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 C2, we are able to show that the comb strategies, as conjectured in Peres et al., form an asymptotic Nash equilibrium. We also prove the "Finite vs Geometric regret" conjecture proposed by Peres et al. for N = 4, and show that this conjecture in fact follows from the conjecture that the comb strategies are optimal for all N.

Joint work with Erhan Bayraktar and Ibrahim Ekren. Speaker(s): Xin Zhang (UM)