W. Z. Chang

William Chang, Yuanhao Lu

We consider a cooperative multiplayer bandit learning problem where the players are only allowed to agree on a strategy beforehand, but cannot communicate during the learning process. In this problem, each player simultaneously selects an action. Based on the actions selected by all players, the team of players receives a reward. The actions of all the players are commonly observed. However, each player receives a noisy version of the reward which cannot be shared with other players. Since players receive potentially different rewards, there is an asymmetry in the information used to select their actions. In this paper, we provide an algorithm based on upper and lower confidence bounds that the players can use to select their optimal actions despite the asymmetry in the reward information. We show that this algorithm can achieve logarithmic $O(\frac{\log T}{Δ_{\bm{a}}})$ (gap-dependent) regret as well as $O(\sqrt{T\log T})$ (gap-independent) regret. This is asymptotically optimal in $T$. We also show that it performs empirically better than the current state of the art algorithm for this environment.

Tianyuan Jin, Hao-Lun Hsu, William Chang et al.

We study the multi-agent multi-armed bandit (MAMAB) problem, where $m$ agents are factored into $ρ$ overlapping groups. Each group represents a hyperedge, forming a hypergraph over the agents. At each round of interaction, the learner pulls a joint arm (composed of individual arms for each agent) and receives a reward according to the hypergraph structure. Specifically, we assume there is a local reward for each hyperedge, and the reward of the joint arm is the sum of these local rewards. Previous work introduced the multi-agent Thompson sampling (MATS) algorithm \citep{verstraeten2020multiagent} and derived a Bayesian regret bound. However, it remains an open problem how to derive a frequentist regret bound for Thompson sampling in this multi-agent setting. To address these issues, we propose an efficient variant of MATS, the $ε$-exploring Multi-Agent Thompson Sampling ($ε$-MATS) algorithm, which performs MATS exploration with probability $ε$ while adopts a greedy policy otherwise. We prove that $ε$-MATS achieves a worst-case frequentist regret bound that is sublinear in both the time horizon and the local arm size. We also derive a lower bound for this setting, which implies our frequentist regret upper bound is optimal up to constant and logarithm terms, when the hypergraph is sufficiently sparse. Thorough experiments on standard MAMAB problems demonstrate the superior performance and the improved computational efficiency of $ε$-MATS compared with existing algorithms in the same setting.

William Chang, Mehdi Jafarnia-Jahromi, Rahul Jain

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. It's 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 can't 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.