2019/11/22 by Erhan Bayraktar, Bayraktar, Erhan, Ibrahim Ekren +3 · 2 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Bandit Algorithms Research #Analysis of PDEs (math.AP) #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Probability (math.PR) #Reinforcement Learning in Robotics #cs.GT #cs.LG #math.AP #math.PR #stat.ML
paper · pdf · doi:10.48550/arxiv.1911.10936
Keywords: machine learning, expert advice framework, asymptotic expansion, inverse Laplace transform, regret minimization, Jacobi-theta function
openalex publication_date 2019/11/22 · arxiv created 2019/12/03 · arxiv updated 2019/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 C2, 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 and show that this conjecture in fact follows from the conjecture that the comb strategies are optimal.