Abstract: This talk focuses on expert prediction problem with finite horizon, which is formulated as a zero sum game between a player and an adversary. By considering a scaled game, the value function of discrete games converges to the viscosity solution of a PDE. We explicitly solve this nonlinear PDE with N = 4 experts. By showing that the solution is C^2, we are able to show that the comb strategies, as conjectured in “Towards Optimal Algorithms for Prediction with Expert Advice” by Peres et al., form an asymptotic Nash equilibrium. We also prove the “Finite vs Geometric regret” conjecture proposed in Peres et al. for N = 4, and show that this conjecture in fact follows from the conjecture that the comb strategies are optimal. This talk is based on a joint work with Erhan Bayraktar and Ibrahim Ekren.

Der Vortrag wurde auf 3. Februar 2022 verschoben!