Gittins' theorem under uncertainty

07/12/2019
by   Samuel N. Cohen, et al.
0

We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under strong independence of the bandits and with some relaxation in the definition of optimality, a Gittins allocation index gives optimal choices. This involves studying the interaction of our uncertainty with controls which determine the filtration. We also run a simple numerical example which illustrates the interaction between the willingness to explore and uncertainty aversion of the agent when making decisions.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/17/2020

Using Subjective Logic to Estimate Uncertainty in Multi-Armed Bandit Problems

The multi-armed bandit problem is a classical decision-making problem wh...
research
04/15/2019

Introduction to Multi-Armed Bandits

Multi-armed bandits a simple but very powerful framework for algorithms ...
research
04/12/2017

Value Directed Exploration in Multi-Armed Bandits with Structured Priors

Multi-armed bandits are a quintessential machine learning problem requir...
research
07/17/2013

From Bandits to Experts: A Tale of Domination and Independence

We consider the partial observability model for multi-armed bandits, int...
research
04/05/2019

Collaborative Learning with Limited Interaction: Tight Bounds for Distributed Exploration in Multi-Armed Bandits

Best arm identification (or, pure exploration) in multi-armed bandits is...
research
08/09/2021

Whittle Index for A Class of Restless Bandits with Imperfect Observations

We consider a class of restless bandit problems that finds a broad appli...
research
09/19/2022

Active Inference for Autonomous Decision-Making with Contextual Multi-Armed Bandits

In autonomous robotic decision-making under uncertainty, the tradeoff be...

Please sign up or login with your details

Forgot password? Click here to reset