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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.
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This paper focuses on building personalized player models solely from player behavior in the context of adaptive games. We present two main contributions: The first is a novel approach to player modeling based on multi-armed bandits (MABs). This approach addresses, at the same time and in a principled way, both the problem of collecting data to model the characteristics of interest for the current player and the problem of adapting the interactive experience based on this model. Second, we present an approach to evaluating and fine-tuning these algorithms prior to generating data in a user study. This is an important problem, because conducting user studies is an expensive and labor-intensive process; therefore, an ability to evaluate the algorithms beforehand can save a significant amount of resources. We evaluate our approach in the context of modeling players social comparison orientation (SCO) and present empirical results from both simulations and real players.
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.
We study stochastic multi-armed bandits with many players. The players do not know the number of players, cannot communicate with each other and if multiple players select a common arm they collide and none of them receive any reward. We consider the static scenario, where the number of players remains fixed, and the dynamic scenario, where the players enter and leave at any time. We provide algorithms based on a novel `trekking approach that guarantees constant regret for the static case and sub-linear regret for the dynamic case with high probability. The trekking approach eliminates the need to estimate the number of players resulting in fewer collisions and improved regret performance compared to the state-of-the-art algorithms. We also develop an epoch-less algorithm that eliminates any requirement of time synchronization across the players provided each player can detect the presence of other players on an arm. We validate our theoretical guarantees using simulation based and real test-bed based experiments.
We introduce a framework for decentralized online learning for multi-armed bandits (MAB) with multiple cooperative players. The reward obtained by the players in each round depends on the actions taken by all the players. Its a team setting, and the objective is common. Information asymmetry is what makes the problem interesting and challenging. We consider three types of information asymmetry: action information asymmetry when the actions of the players cant be observed but the rewards received are common; reward information asymmetry when the actions of the other players are observable but rewards received are IID from the same distribution; and when we have both action and reward information asymmetry. For the first setting, we propose a UCB-inspired algorithm that achieves $O(log T)$ regret whether the rewards are IID or Markovian. For the second section, we offer an environment such that the algorithm given for the first setting gives linear regret. For the third setting, we show that a variation of the `explore then commit algorithm achieves almost log regret.
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.
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