On the asymptotic optimality of the comb strategy for prediction with expert advice

DOI10.1214/20-AAP1565arXiv1902.02368MaRDI QIDQ6313706

Ibrahim Ekren, Yi-li Zhang, Erhan Bayraktar

Publication date: 6 February 2019

Abstract: For the problem of prediction with expert advice in the adversarial setting with geometric stopping, we compute the exact leading order expansion for the long time behavior of the value function. Then, we use this expansion to prove that as conjectured in Gravin et al. [12], the comb strategies are indeed asymptotically optimal for the adversary in the case of 4 experts.

Mathematics Subject Classification ID

Decision theory (91B06) Learning and adaptive systems in artificial intelligence (68T05) Dynamic programming in optimal control and differential games (49L20) Nonlinear elliptic equations (35J60) Optimal stochastic control (93E20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Optimality conditions for problems involving randomness (49K45) First-order hyperbolic equations (35L02)

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