Stochastic Bandits with Vector Losses: Minimizing ℓ^∞-Norm of Relative Losses

10/15/2020
by   Xuedong Shang, et al.
0

Multi-armed bandits are widely applied in scenarios like recommender systems, for which the goal is to maximize the click rate. However, more factors should be considered, e.g., user stickiness, user growth rate, user experience assessment, etc. In this paper, we model this situation as a problem of K-armed bandit with multiple losses. We define relative loss vector of an arm where the i-th entry compares the arm and the optimal arm with respect to the i-th loss. We study two goals: (a) finding the arm with the minimum ℓ^∞-norm of relative losses with a given confidence level (which refers to fixed-confidence best-arm identification); (b) minimizing the ℓ^∞-norm of cumulative relative losses (which refers to regret minimization). For goal (a), we derive a problem-dependent sample complexity lower bound and discuss how to achieve matching algorithms. For goal (b), we provide a regret lower bound of Ω(T^2/3) and provide a matching algorithm.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/09/2020

Streaming Algorithms for Stochastic Multi-armed Bandits

We study the Stochastic Multi-armed Bandit problem under bounded arm-mem...
research
05/28/2021

Asymptotically Optimal Bandits under Weighted Information

We study the problem of regret minimization in a multi-armed bandit setu...
research
07/14/2020

Quantum exploration algorithms for multi-armed bandits

Identifying the best arm of a multi-armed bandit is a central problem in...
research
05/15/2017

Bandit Regret Scaling with the Effective Loss Range

We study how the regret guarantees of nonstochastic multi-armed bandits ...
research
06/15/2023

Optimal Best-Arm Identification in Bandits with Access to Offline Data

Learning paradigms based purely on offline data as well as those based s...
research
09/19/2021

Generalized Translation and Scale Invariant Online Algorithm for Adversarial Multi-Armed Bandits

We study the adversarial multi-armed bandit problem and create a complet...
research
11/19/2018

Decentralized Exploration in Multi-Armed Bandits

We consider the decentralized exploration problem: a set of players coll...

Please sign up or login with your details

Forgot password? Click here to reset