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Register a new userOnline Learning for Cooperative Multi-Player Multi-Armed Bandits
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William Chang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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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.
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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.
During online decision making in Multi-Armed Bandits (MAB), one needs to conduct inference on the true mean reward of each arm based on data collected so far at each step. However, since the arms are adaptively selected--thereby yielding non-iid data--conducting inference accurately is not straightforward. In particular, sample averaging, which is used in the family of UCB and Thompson sampling (TS) algorithms, does not provide a good choice as it suffers from bias and a lack of good statistical properties (e.g. asymptotic normality). Our thesis in this paper is that more sophisticated inference schemes that take into account the adaptive nature of the sequentially collected data can unlock further performance gains, even though both UCB and TS type algorithms are optimal in the worst case. In particular, we propose a variant of TS-style algorithms--which we call doubly adaptive TS--that leverages recent advances in causal inference and adaptively reweights the terms of a doubly robust estimator on the true mean reward of each arm. Through 20 synthetic domain experiments and a semi-synthetic experiment based on data from an A/B test of a web service, we demonstrate that using an adaptive inferential scheme (while still retaining the exploration efficacy of TS) provides clear benefits in online decision making: the proposed DATS algorithm has superior empirical performance to existing baselines (UCB and TS) in terms of regret and sample complexity in identifying the best arm. In addition, we also provide a finite-time regret bound of doubly adaptive TS that matches (up to log factors) those of UCB and TS algorithms, thereby establishing that its improved practical benefits do not come at the expense of worst-case suboptimality.
We study the problem of stochastic bandits with adversarial corruptions in the cooperative multi-agent setting, where $V$ agents interact with a common $K$-armed bandit problem, and each pair of agents can communicate with each other to expedite the learning process. In the problem, the rewards are independently sampled from distributions across all agents and rounds, but they may be corrupted by an adversary. Our goal is to minimize both the overall regret and communication cost across all agents. We first show that an additive term of corruption is unavoidable for any algorithm in this problem. Then, we propose a new algorithm that is agnostic to the level of corruption. Our algorithm not only achieves near-optimal regret in the stochastic setting, but also obtains a regret with an additive term of corruption in the corrupted setting, while maintaining efficient communication. The algorithm is also applicable for the single-agent corruption problem, and achieves a high probability regret that removes the multiplicative dependence of $K$ on corruption level. Our result of the single-agent case resolves an open question from Gupta et al. [2019].
We consider a fully decentralized multi-player stochastic multi-armed bandit setting where the players cannot communicate with each other and can observe only their own actions and rewards. The environment may appear differently to different players, $textit{i.e.}$, the reward distributions for a given arm are heterogeneous across players. In the case of a collision (when more than one player plays the same arm), we allow for the colliding players to receive non-zero rewards. The time-horizon $T$ for which the arms are played is emph{not} known to the players. Within this setup, where the number of players is allowed to be greater than the number of arms, we present a policy that achieves near order-optimal expected regret of order $O(log^{1 + delta} T)$ for some $0 < delta < 1$ over a time-horizon of duration $T$. This paper is currently under review at IEEE Transactions on Information Theory.
We introduce a new class of reinforcement learning methods referred to as {em episodic multi-armed bandits} (eMAB). In eMAB the learner proceeds in {em episodes}, each composed of several {em steps}, in which it chooses an action and observes a feedback signal. Moreover, in each step, it can take a special action, called the $stop$ action, that ends the current episode. After the $stop$ action is taken, the learner collects a terminal reward, and observes the costs and terminal rewards associated with each step of the episode. The goal of the learner is to maximize its cumulative gain (i.e., the terminal reward minus costs) over all episodes by learning to choose the best sequence of actions based on the feedback. First, we define an {em oracle} benchmark, which sequentially selects the actions that maximize the expected immediate gain. Then, we propose our online learning algorithm, named {em FeedBack Adaptive Learning} (FeedBAL), and prove that its regret with respect to the benchmark is bounded with high probability and increases logarithmically in expectation. Moreover, the regret only has polynomial dependence on the number of steps, actions and states. eMAB can be used to model applications that involve humans in the loop, ranging from personalized medical screening to personalized web-based education, where sequences of actions are taken in each episode, and optimal behavior requires adapting the chosen actions based on the feedback.
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