Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice
نویسندگان
چکیده
We prove non-asymptotic lower bounds on the expectation of the maximum of d independent Gaussian variables and the expectation of the maximum of d independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (asymptotically optimal) non-asymptotic lower bound on the minimax regret of online learning with expert advice.
منابع مشابه
Towards Optimal Algorithms for Prediction with Expert Advice
We study the classical problem of prediction with expert advice in the adversarial setting with a geometric stopping time. In 1965, Cover gave the optimal algorithm for the case of 2 experts. In this paper, we design the optimal algorithm, adversary and regret for the case of 3 experts. Further, we show that the optimal algorithm for 2 and 3 experts is a probability matching algorithm (analogou...
متن کاملTowards Minimax Policies for Online Linear Optimization with Bandit Feedback
We address the online linear optimization problem with bandit feedback. Our contribution is twofold. First, we provide an algorithm (based on exponential weights) with a regret of order √ dn logN for any finite action set with N actions, under the assumption that the instantaneous loss is bounded by 1. This shaves off an extraneous √ d factor compared to previous works, and gives a regret bound...
متن کاملSmooth Online Learning of Expert Advice
This paper is concerned with algorithms for online learning of expert advice and contains both theoretical and empirical results. In the first part of the paper we present new online algorithms for combining expert opinions. Unlike most previous algorithms, our algorithms “smoothly” adjust their learning rates without forgetting past performance of the experts. Our analysis show that the propos...
متن کاملNear Minimax Optimal Players for the Finite-Time 3-Expert Prediction Problem
We study minimax strategies for the online prediction problem with expert advice. It has been conjectured that a simple adversary strategy, called COMB, is near optimal in this game for any number of experts. Our results and new insights make progress in this direction by showing that, up to a small additive term, COMB is minimax optimal in the finite-time three expert problem. In addition, we ...
متن کاملPoint Decisions for Interval-Identied Parameters
This paper considers a decision-maker who prefers to make a point decision when the object of interest is interval-identi ed with regular bounds. When the bounds are just identi ed along with known interval length, the local asymptotic minimax decision with respect to a symmetric convex loss function takes an obvious form: an e¢ cient lower bound estimator plus the half of the known interval le...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1511.02176 شماره
صفحات -
تاریخ انتشار 2015