195 research outputs found
Borda Regret Minimization for Generalized Linear Dueling Bandits
Dueling bandits are widely used to model preferential feedback prevalent in
many applications such as recommendation systems and ranking. In this paper, we
study the Borda regret minimization problem for dueling bandits, which aims to
identify the item with the highest Borda score while minimizing the cumulative
regret. We propose a rich class of generalized linear dueling bandit models,
which cover many existing models. We first prove a regret lower bound of order
for the Borda regret minimization problem, where
is the dimension of contextual vectors and is the time horizon. To attain
this lower bound, we propose an explore-then-commit type algorithm for the
stochastic setting, which has a nearly matching regret upper bound
. We also propose an EXP3-type algorithm for the
adversarial linear setting, where the underlying model parameter can change at
each round. Our algorithm achieves an regret,
which is also optimal. Empirical evaluations on both synthetic data and a
simulated real-world environment are conducted to corroborate our theoretical
analysis.Comment: 33 pages, 5 figure. This version includes new results for dueling
bandits in the adversarial settin
Versatile Dueling Bandits: Best-of-both-World Analyses for Online Learning from Preferences
International audienceWe study the problem of -armed dueling bandit for both stochastic and adversarial environments, where the goal of the learner is to aggregate information through relative preferences of pair of decisions points queried in an online sequential manner. We first propose a novel reduction from any (general) dueling bandits to multi-armed bandits and despite the simplicity, it allows us to improve many existing results in dueling bandits. In particular, \emph{we give the first best-of-both world result for the dueling bandits regret minimization problem} -- a unified framework that is guaranteed to perform optimally for both stochastic and adversarial preferences simultaneously. Moreover, our algorithm is also the first to achieve an optimal regret bound against the Condorcet-winner benchmark, which scales optimally both in terms of the arm-size and the instance-specific suboptimality gaps . This resolves the long-standing problem of designing an instancewise gap-dependent order optimal regret algorithm for dueling bandits (with matching lower bounds up to small constant factors). We further justify the robustness of our proposed algorithm by proving its optimal regret rate under adversarially corrupted preferences -- this outperforms the existing state-of-the-art corrupted dueling results by a large margin. In summary, we believe our reduction idea will find a broader scope in solving a diverse class of dueling bandits setting, which are otherwise studied separately from multi-armed bandits with often more complex solutions and worse guarantees. The efficacy of our proposed algorithms is empirically corroborated against the existing dueling bandit methods
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)
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
Relative Upper Confidence Bound for the K-Armed Dueling Bandit Problem
This paper proposes a new method for the K-armed dueling bandit problem, a
variation on the regular K-armed bandit problem that offers only relative
feedback about pairs of arms. Our approach extends the Upper Confidence Bound
algorithm to the relative setting by using estimates of the pairwise
probabilities to select a promising arm and applying Upper Confidence Bound
with the winner as a benchmark. We prove a finite-time regret bound of order
O(log t). In addition, our empirical results using real data from an
information retrieval application show that it greatly outperforms the state of
the art.Comment: 13 pages, 6 figure
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