The K-Nearest Neighbour UCB algorithm for multi-armed bandits with covariates

نویسندگان

  • Henry WJ Reeve
  • Joe Mellor
  • Gavin Brown
چکیده

In this paper we propose and explore the k-Nearest Neighbour UCB algorithm for multiarmed bandits with covariates. We focus on a setting where the covariates are supported on a metric space of low intrinsic dimension, such as a manifold embedded within a high dimensional ambient feature space. The algorithm is conceptually simple and straightforward to implement. The k-Nearest Neighbour UCB algorithm does not require prior knowledge of the either the intrinsic dimension of the marginal distribution or the time horizon. We prove a regret bound for the k-Nearest Neighbour UCB algorithm which is minimax optimal up to logarithmic factors. In particular, the algorithm automatically takes advantage of both low intrinsic dimensionality of the marginal distribution over the covariates and low noise in the data, expressed as a margin condition. In addition, focusing on the case of bounded rewards, we give corresponding regret bounds for the k-Nearest Neighbour KL-UCB algorithm, which is an analogue of the KL-UCB algorithm adapted to the setting of multi-armed bandits with covariates. Finally, we present empirical results which demonstrate the ability of both the k-Nearest Neighbour UCB and k-Nearest Neighbour KL-UCB to take advantage of situations where the data is supported on an unknown sub-manifold of a high-dimensional feature space. c © 2018 H.W. Reeve, J. Mellor & G. Brown. ar X iv :1 80 3. 00 31 6v 1 [ cs .L G ] 1 M ar 2 01 8

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

UCB revisited: Improved regret bounds for the stochastic multi-armed bandit problem

ABSTRACT. In the stochastic multi-armed bandit problem we consider a modification of the UCB algorithm of Auer et al. [4]. For this modified algorithm we give an improved bound on the regret with respect to the optimal reward. While for the original UCB algorithm the regret in Karmed bandits after T trials is bounded by const · K log(T ) , where measures the distance between a suboptimal arm an...

متن کامل

A Survey on Contextual Multi-armed Bandits

4 Stochastic Contextual Bandits 6 4.1 Stochastic Contextual Bandits with Linear Realizability Assumption . . . . 6 4.1.1 LinUCB/SupLinUCB . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4.1.2 LinREL/SupLinREL . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.1.3 CofineUCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.1.4 Thompson Sampling with Linear Payoffs...

متن کامل

Regret Analysis of the Finite-Horizon Gittins Index Strategy for Multi-Armed Bandits

I prove near-optimal frequentist regret guarantees for the finite-horizon Gittins index strategy for multi-armed bandits with Gaussian noise and prior. Along the way I derive finite-time bounds on the Gittins index that are asymptotically exact and may be of independent interest. I also discuss computational issues and present experimental results suggesting that a particular version of the Git...

متن کامل

Weighted Bandits or: How Bandits Learn Distorted Values That Are Not Expected

Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the cost distributions: the classic K-armed bandit and the linearly parameterized bandit. In both settings, we propose algorithms that are inspired by Upper Confidence B...

متن کامل

On Bayesian Upper Confidence Bounds for Bandit Problems

Stochastic bandit problems have been analyzed from two different perspectives: a frequentist view, where the parameter is a deterministic unknown quantity, and a Bayesian approach, where the parameter is drawn from a prior distribution. We show in this paper that methods derived from this second perspective prove optimal when evaluated using the frequentist cumulated regret as a measure of perf...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2018