Multi-player Bandit Research Articles

Decentralized Scheduling with QoS Constraints: Achieving O(1) QoS Regret of Multi-Player Bandits

We consider a decentralized multi-player multi-armed bandit (MP-MAB) problem where players cannot observe the actions and rewards of other players and no explicit communication or coordination between players is possible. Prior studies mostly focus on maximizing the sum of rewards of the players over time. However, the total reward maximization learning may lead to imbalanced reward among players, leading to poor Quality of Service (QoS) for some players. In contrast, our objective is to let each player n achieve a predetermined expected average reward over time, i.e., achieving a predetermined level of QoS. We develop a novel decentralized MP-MAB algorithm to accomplish this objective by leveraging the methodology of randomized matching. We prove that our decentralized algorithm can ensure that all players have an O(1) QoS regret. We also reveal an analog between our MP-MAB model and the online wireless queuing systems, which builds a connection between QoS in MP-MAB learning and stability in queuing theory.

Two-Stage Resource Allocation in Reconfigurable Intelligent Surface Assisted Hybrid Networks via Multi-player Bandits

This paper considers a resource allocation problem where several Internet-of-Things (IoT) devices send data to a base station (BS) with or without the help of the reconfigurable intelligent surface (RIS) assisted cellular network. The objective is to maximize the sum rate of all IoT devices by finding the optimal RIS and spreading factor (SF) for each device. Since these IoT devices lack prior information of the RISs or the channel state information (CSI), a distributed resource allocation framework with low complexity and learning features is required to achieve this goal. Therefore, we model this problem as a two-stage multi-player multi-armed bandit (MPMAB) framework to learn the optimal RIS and SF sequentially. Then, we put forth an exploration and exploitation boosting (E2Boost) algorithm to solve this two-stage MPMAB problem by combining the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -greedy algorithm, Thompson sampling (TS) algorithm, and non-cooperation game method. We derive an upper regret bound for the proposed algorithm, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}(\log ^{1+\delta }_{2} T)$ </tex-math></inline-formula> , increasing logarithmically with the time horizon <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> . Numerical results show that the E2Boost algorithm has the best performance among the existing methods and exhibits a fast convergence rate. More importantly, the proposed algorithm is not sensitive to the number of combinations of the RISs and SFs thanks to the two-stage allocation mechanism, which can benefit the high-density networks.

One for All and All for One: Distributed Learning of Fair Allocations With Multi-Player Bandits

Consider N cooperative but non-communicating players where each plays one out of M arms for T turns. Players have different utilities for each arm, represented as an N×M matrix. These utilities are unknown to the players. In each turn, players select an arm and receive a noisy observation of their utility for it. However, if any other players selected the same arm in that turn, all colliding players will receive zero utility due to the conflict. No communication between the players is possible. We propose two distributed algorithms which learn fair matchings between players and arms while minimizing the regret. We show that our first algorithm learns a max-min fairness matching with near- O(logT) regret (up to a loglogT factor). However, if one has a known target Quality of Service (QoS) (which may vary between players) then we show that our second algorithm learns a matching where all players obtain an expected reward of at least their QoS with constant regret, given that such a matching exists. In particular, if the max-min value is known, a max-min fairness matching can be learned with O(1) regret.

Multiplayer Bandits: A Trekking Approach

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.

Game of Thrones: Fully Distributed Learning for Multiplayer Bandits

We consider an N-player multiarmed bandit game in which each player chooses one out of M arms for T turns. Each player has different expected rewards for the arms, and the instantaneous rewards are independent and identically distributed or Markovian. When two or more players choose the same arm, they all receive zero reward. Performance is measured using the expected sum of regrets compared with optimal assignment of arms to players that maximizes the sum of expected rewards. We assume that each player only knows that player’s own actions and the reward that player received each turn. Players cannot observe the actions of other players, and no communication between players is possible. We present a distributed algorithm and prove that it achieves an expected sum of regrets of near-[Formula: see text]. This is the first algorithm to achieve a near order optimal regret in this fully distributed scenario. All other works have assumed that either all players have the same vector of expected rewards or that communication between players is possible.

Learning to Coordinate in a Decentralized Cognitive Radio Network in Presence of Jammers

Efficient utilization of licensed spectrum in the cognitive radio network is challenging due to lack of coordination among the Secondary Users (SUs). Distributed algorithms proposed in the literature aim to maximize the network throughput by ensuring orthogonal channel allocation for the SUs. However, these algorithms work under the assumption that all the SUs faithfully follow the algorithms which may not always hold due to the decentralized nature of the network. In this paper, we study distributed algorithms that are robust against malicious behavior (jamming attack). We consider both the cases of jammers launching coordinated and uncoordinated attacks. In the coordinated attack, the jammers select non-overlapping channels to attack in each time slot and can significantly increase the number of collisions for SUs. We setup the problem in each scenario as a multi-player bandit and develop algorithms. The analysis shows that when the SUs faithfully implement proposed algorithms, the regret is constant with high probability. We validate our claims through exhaustive synthetic experiments and also through a realistic USRP based experiment.

Multi-Player Bandits: The Adversarial Case

We consider a setting where multiple players sequentially choose among a common set of actions (arms). Motivated by a cognitive radio networks application, we assume that players incur a loss upon colliding, and that communication between players is not possible. Existing approaches assume that the system is stationary. Yet this assumption is often violated in practice, e.g., due to signal strength fluctuations. In this work, we design the first Multi-player Bandit algorithm that provably works in arbitrarily changing environments, where the losses of the arms may even be chosen by an adversary. This resolves an open problem posed by Rosenski, Shamir, and Szlak (2016).