311 research outputs found
Multi-dueling Bandits with Dependent Arms
The dueling bandits problem is an online learning framework for learning from pairwise preference feedback, and is particularly well-suited for modeling settings that elicit subjective or implicit human feedback. In this paper, we study the problem of multi-dueling bandits with dependent arms, which extends the original dueling bandits setting by simultaneously dueling multiple arms as well as modeling dependencies between arms. These extensions capture key characteristics found in many real-world applications, and allow for the opportunity to develop significantly more efficient algorithms than were possible in the original setting. We propose the selfsparring algorithm, which reduces the multi-dueling bandits problem to a conventional bandit setting that can be solved using a stochastic bandit algorithm such as Thompson Sampling, and can naturally model dependencies using a Gaussian process prior. We present a no-regret analysis for multi-dueling setting, and demonstrate the effectiveness of our algorithm empirically on a wide range of simulation settings
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
Reducing Dueling Bandits to Cardinal Bandits
We present algorithms for reducing the Dueling Bandits problem to the
conventional (stochastic) Multi-Armed Bandits problem. The Dueling Bandits
problem is an online model of learning with ordinal feedback of the form "A is
preferred to B" (as opposed to cardinal feedback like "A has value 2.5"),
giving it wide applicability in learning from implicit user feedback and
revealed and stated preferences. In contrast to existing algorithms for the
Dueling Bandits problem, our reductions -- named \Doubler, \MultiSbm and
\DoubleSbm -- provide a generic schema for translating the extensive body of
known results about conventional Multi-Armed Bandit algorithms to the Dueling
Bandits setting. For \Doubler and \MultiSbm we prove regret upper bounds in
both finite and infinite settings, and conjecture about the performance of
\DoubleSbm which empirically outperforms the other two as well as previous
algorithms in our experiments. In addition, we provide the first almost optimal
regret bound in terms of second order terms, such as the differences between
the values of the arms
Tsallis-INF: An Optimal Algorithm for Stochastic and Adversarial Bandits
We derive an algorithm that achieves the optimal (within constants)
pseudo-regret in both adversarial and stochastic multi-armed bandits without
prior knowledge of the regime and time horizon. The algorithm is based on
online mirror descent (OMD) with Tsallis entropy regularization with power
and reduced-variance loss estimators. More generally, we define an
adversarial regime with a self-bounding constraint, which includes stochastic
regime, stochastically constrained adversarial regime (Wei and Luo), and
stochastic regime with adversarial corruptions (Lykouris et al.) as special
cases, and show that the algorithm achieves logarithmic regret guarantee in
this regime and all of its special cases simultaneously with the adversarial
regret guarantee.} The algorithm also achieves adversarial and stochastic
optimality in the utility-based dueling bandit setting. We provide empirical
evaluation of the algorithm demonstrating that it significantly outperforms
UCB1 and EXP3 in stochastic environments. We also provide examples of
adversarial environments, where UCB1 and Thompson Sampling exhibit almost
linear regret, whereas our algorithm suffers only logarithmic regret. To the
best of our knowledge, this is the first example demonstrating vulnerability of
Thompson Sampling in adversarial environments. Last, but not least, we present
a general stochastic analysis and a general adversarial analysis of OMD
algorithms with Tsallis entropy regularization for and explain
the reason why works best
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