Strategies for prediction under imperfect monitoring

• 成果类型: Article
• 署名作者: Lugosi, Gabor; Mannor, Shie; Stoltz, Gilles
• 署名单位: ICREA; Pompeu Fabra University; Pompeu Fabra University; McGill University; Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Hautes Etudes Commerciales (HEC) Paris
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1080.0312
• 发表日期: 2008
• 页码: 513-528
• 关键词: universal prediction; gradient; regret

摘要

We propose simple randomized strategies for sequential decision ( or prediction) under imperfect monitoring, that is, when the decision maker ( forecaster) does not have access to the past outcomes but rather to a feedback signal. The proposed strategies are consistent in the sense that they achieve, asymptotically, the best-possible average reward among all fixed actions. It was Rustichini [Rustichini, A. 1999. Minimizing regret: The general case. Games Econom. Behav. 29 224-243] who first proved the existence of such consistent predictors. The forecasters presented here offer the first constructive proof of consistency. Moreover, the proposed algorithms are computationally efficient. We also establish upper bounds for the rates of convergence. In the case of deterministic feedback signals, these rates are optimal up to logarithmic terms.