PAC Best Arm Identification Under a Deadline

06/06/2021
by   Brijen Thananjeyan, et al.
2

We study (ϵ, δ)-PAC best arm identification, where a decision-maker must identify an ϵ-optimal arm with probability at least 1 - δ, while minimizing the number of arm pulls (samples). Most of the work on this topic is in the sequential setting, where there is no constraint on the time taken to identify such an arm; this allows the decision-maker to pull one arm at a time. In this work, the decision-maker is given a deadline of T rounds, where, on each round, it can adaptively choose which arms to pull and how many times to pull them; this distinguishes the number of decisions made (i.e., time or number of rounds) from the number of samples acquired (cost). Such situations occur in clinical trials, where one may need to identify a promising treatment under a deadline while minimizing the number of test subjects, or in simulation-based studies run on the cloud, where we can elastically scale up or down the number of virtual machines to conduct as many experiments as we wish, but need to pay for the resource-time used. As the decision-maker can only make T decisions, she may need to pull some arms excessively relative to a sequential algorithm in order to perform well on all possible problems. We formalize this added difficulty with two hardness results that indicate that unlike sequential settings, the ability to adapt to the problem difficulty is constrained by the finite deadline. We propose Elastic Batch Racing (EBR), a novel algorithm for this setting and bound its sample complexity, showing that EBR is optimal with respect to both hardness results. We present simulations evaluating EBR in this setting, where it outperforms baselines by several orders of magnitude.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

12/09/2020

Streaming Algorithms for Stochastic Multi-armed Bandits

We study the Stochastic Multi-armed Bandit problem under bounded arm-mem...
11/19/2018

Best-arm identification with cascading bandits

We consider a variant of the problem of best arm identification in multi...
07/09/2017

Nonlinear Sequential Accepts and Rejects for Identification of Top Arms in Stochastic Bandits

We address the M-best-arm identification problem in multi-armed bandits....
10/31/2020

Resource Allocation in Multi-armed Bandit Exploration: Overcoming Nonlinear Scaling with Adaptive Parallelism

We study exploration in stochastic multi-armed bandits when we have acce...
10/09/2018

Bridging the gap between regret minimization and best arm identification, with application to A/B tests

State of the art online learning procedures focus either on selecting th...
08/24/2019

Optimal best arm selection for general distributions

Given a finite set of unknown distributions or arms that can be sampled ...
04/20/2020

Collaborative Top Distribution Identifications with Limited Interaction

We consider the following problem in this paper: given a set of n distri...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.