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Register a new userDiversity-Preserving K-Armed Bandits, Revisited
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Hedi Hadiji
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We consider the bandit-based framework for diversity-preserving recommendations introduced by Celis et al. (2019), who approached it mainly by a reduction to the setting of linear bandits. We design a UCB algorithm using the specific structure of the setting and show that it enjoys a bounded distribution-dependent regret in the natural cases when the optimal mixed actions put some probability mass on all actions (i.e., when diversity is desirable). Simulations illustrate this fact. We also provide regret lower bounds and briefly discuss distribution-free regret bounds.
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Multi-player Multi-Armed Bandits (MAB) have been extensively studied in the literature, motivated by applications to Cognitive Radio systems. Driven by such applications as well, we motivate the introduction of several levels of feedback for multi-player MAB algorithms. Most existing work assume that sensing information is available to the algorithm. Under this assumption, we improve the state-of-the-art lower bound for the regret of any decentralized algorithms and introduce two algorithms, RandTopM and MCTopM, that are shown to empirically outperform existing algorithms. Moreover, we provide strong theoretical guarantees for these algorithms, including a notion of asymptotic optimality in terms of the number of selections of bad arms. We then introduce a promising heuristic, called Selfish, that can operate without sensing information, which is crucial for emerging applications to Internet of Things networks. We investigate the empirical performance of this algorithm and provide some first theoretical elements for the understanding of its behavior.
We consider nonstationary multi-armed bandit problems where the model parameters of the arms change over time. We introduce the adaptive resetting bandit (ADR-bandit), which is a class of bandit algorithms that leverages adaptive windowing techniques from the data stream community. We first provide new guarantees on the quality of estimators resulting from adaptive windowing techniques, which are of independent interest in the data mining community. Furthermore, we conduct a finite-time analysis of ADR-bandit in two typical environments: an abrupt environment where changes occur instantaneously and a gradual environment where changes occur progressively. We demonstrate that ADR-bandit has nearly optimal performance when the abrupt or global changes occur in a coordinated manner that we call global changes. We demonstrate that forced exploration is unnecessary when we restrict the interest to the global changes. Unlike the existing nonstationary bandit algorithms, ADR-bandit has optimal performance in stationary environments as well as nonstationary environments with global changes. Our experiments show that the proposed algorithms outperform the existing approaches in synthetic and real-world environments.
The paper proposes a novel upper confidence bound (UCB) procedure for identifying the arm with the largest mean in a multi-armed bandit game in the fixed confidence setting using a small number of total samples. The procedure cannot be improved in the sense that the number of samples required to identify the best arm is within a constant factor of a lower bound based on the law of the iterated logarithm (LIL). Inspired by the LIL, we construct our confidence bounds to explicitly account for the infinite time horizon of the algorithm. In addition, by using a novel stopping time for the algorithm we avoid a union bound over the arms that has been observed in other UCB-type algorithms. We prove that the algorithm is optimal up to constants and also show through simulations that it provides superior performance with respect to the state-of-the-art.
An online reinforcement learning algorithm is anytime if it does not need to know in advance the horizon T of the experiment. A well-known technique to obtain an anytime algorithm from any non-anytime algorithm is the Doubling Trick. In the context of adversarial or stochastic multi-armed bandits, the performance of an algorithm is measured by its regret, and we study two families of sequences of growing horizons (geometric and exponential) to generalize previously known results that certain doubling tricks can be used to conserve certain regret bounds. In a broad setting, we prove that a geometric doubling trick can be used to conserve (minimax) bounds in $R_T = O(sqrt{T})$ but cannot conserve (distribution-dependent) bounds in $R_T = O(log T)$. We give insights as to why exponential doubling tricks may be better, as they conserve bounds in $R_T = O(log T)$, and are close to conserving bounds in $R_T = O(sqrt{T})$.
We consider the best-arm identification problem in multi-armed bandits, which focuses purely on exploration. A player is given a fixed budget to explore a finite set of arms, and the rewards of each arm are drawn independently from a fixed, unknown distribution. The player aims to identify the arm with the largest expected reward. We propose a general framework to unify sequential elimination algorithms, where the arms are dismissed iteratively until a unique arm is left. Our analysis reveals a novel performance measure expressed in terms of the sampling mechanism and number of eliminated arms at each round. Based on this result, we develop an algorithm that divides the budget according to a nonlinear function of remaining arms at each round. We provide theoretical guarantees for the algorithm, characterizing the suitable nonlinearity for different problem environments described by the number of competitive arms. Matching the theoretical results, our experiments show that the nonlinear algorithm outperforms the state-of-the-art. We finally study the side-observation model, where pulling an arm reveals the rewards of its related arms, and we establish improved theoretical guarantees in the pure-exploration setting.
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