Structural Properties of Bayesian Bandits with Exponential Family Distributions

Details Structural Properties of Bayesian Bandits with Exponential Family Distributions Structural Properties of Bayesian Bandits with Exponential Family Distributions

2011-03-16

arxiv.org/abs/1103.3089v1

Mathematics

Statistics Theory

Scientific paper

We study a bandit problem where observations from each arm have an exponential family distribution and different arms are assigned independent conjugate priors. At each of n stages, one arm is to be selected based on past observations. The goal is to find a strategy that maximizes the expected discounted sum of the $n$ observations. Two structural results hold in broad generality: (i) for a fixed prior weight, an arm becomes more desirable as its prior mean increases; (ii) for a fixed prior mean, an arm becomes more desirable as its prior weight decreases. These generalize and unify several results in the literature concerning specific problems including Bernoulli and normal bandits. The second result captures an aspect of the exploration-exploitation dilemma in precise terms: given the same immediate payoff, the less one knows about an arm, the more desirable it becomes because there remains more information to be gained when selecting that arm. For Bernoulli and normal bandits we also obtain extensions to nonconjugate priors.

Affiliated with

Also associated with

No associations

Rating

Structural Properties of Bayesian Bandits with Exponential Family Distributions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Structural Properties of Bayesian Bandits with Exponential Family Distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Structural Properties of Bayesian Bandits with Exponential Family Distributions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-262226