2,156 research outputs found
Factored Bandits
We introduce the factored bandits model, which is a framework for learning
with limited (bandit) feedback, where actions can be decomposed into a
Cartesian product of atomic actions. Factored bandits incorporate rank-1
bandits as a special case, but significantly relax the assumptions on the form
of the reward function. We provide an anytime algorithm for stochastic factored
bandits and up to constants matching upper and lower regret bounds for the
problem. Furthermore, we show that with a slight modification the proposed
algorithm can be applied to utility based dueling bandits. We obtain an
improvement in the additive terms of the regret bound compared to state of the
art algorithms (the additive terms are dominating up to time horizons which are
exponential in the number of arms)
Calibrated Fairness in Bandits
We study fairness within the stochastic, \emph{multi-armed bandit} (MAB)
decision making framework. We adapt the fairness framework of "treating similar
individuals similarly" to this setting. Here, an `individual' corresponds to an
arm and two arms are `similar' if they have a similar quality distribution.
First, we adopt a {\em smoothness constraint} that if two arms have a similar
quality distribution then the probability of selecting each arm should be
similar. In addition, we define the {\em fairness regret}, which corresponds to
the degree to which an algorithm is not calibrated, where perfect calibration
requires that the probability of selecting an arm is equal to the probability
with which the arm has the best quality realization. We show that a variation
on Thompson sampling satisfies smooth fairness for total variation distance,
and give an bound on fairness regret. This complements
prior work, which protects an on-average better arm from being less favored. We
also explain how to extend our algorithm to the dueling bandit setting.Comment: To be presented at the FAT-ML'17 worksho
A Relative Exponential Weighing Algorithm for Adversarial Utility-based Dueling Bandits
We study the K-armed dueling bandit problem which is a variation of the
classical Multi-Armed Bandit (MAB) problem in which the learner receives only
relative feedback about the selected pairs of arms. We propose a new algorithm
called Relative Exponential-weight algorithm for Exploration and Exploitation
(REX3) to handle the adversarial utility-based formulation of this problem.
This algorithm is a non-trivial extension of the Exponential-weight algorithm
for Exploration and Exploitation (EXP3) algorithm. We prove a finite time
expected regret upper bound of order O(sqrt(K ln(K)T)) for this algorithm and a
general lower bound of order omega(sqrt(KT)). At the end, we provide
experimental results using real data from information retrieval applications
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