Mengfan Xu

Mengfan Xu, Liren Shan, Fatemeh Ghaffari et al.

We study a novel heterogeneous multi-agent multi-armed bandit problem with a cluster structure induced by stochastic block models, influencing not only graph topology, but also reward heterogeneity. Specifically, agents are distributed on random graphs based on stochastic block models - a generalized Erdos-Renyi model with heterogeneous edge probabilities: agents are grouped into clusters (known or unknown); edge probabilities for agents within the same cluster differ from those across clusters. In addition, the cluster structure in stochastic block model also determines our heterogeneous rewards. Rewards distributions of the same arm vary across agents in different clusters but remain consistent within a cluster, unifying homogeneous and heterogeneous settings and varying degree of heterogeneity, and rewards are independent samples from these distributions. The objective is to minimize system-wide regret across all agents. To address this, we propose a novel algorithm applicable to both known and unknown cluster settings. The algorithm combines an averaging-based consensus approach with a newly introduced information aggregation and weighting technique, resulting in a UCB-type strategy. It accounts for graph randomness, leverages both intra-cluster (homogeneous) and inter-cluster (heterogeneous) information from rewards and graphs, and incorporates cluster detection for unknown cluster settings. We derive optimal instance-dependent regret upper bounds of order $\log{T}$ under sub-Gaussian rewards. Importantly, our regret bounds capture the degree of heterogeneity in the system (an additional layer of complexity), exhibit smaller constants, scale better for large systems, and impose significantly relaxed assumptions on edge probabilities. In contrast, prior works have not accounted for this refined problem complexity, rely on more stringent assumptions, and exhibit limited scalability.

Mengfan Xu, Diego Klabjan

We study the challenging exploration incentive problem in both bandit and reinforcement learning, where the rewards are scale-free and potentially unbounded, driven by real-world scenarios and differing from existing work. Past works in reinforcement learning either assume costly interactions with an environment or propose algorithms finding potentially low quality local maxima. Motivated by EXP-type methods that integrate multiple agents (experts) for exploration in bandits with the assumption that rewards are bounded, we propose new algorithms, namely EXP4.P and EXP4-RL for exploration in the unbounded reward case, and demonstrate their effectiveness in these new settings. Unbounded rewards introduce challenges as the regret cannot be limited by the number of trials, and selecting suboptimal arms may lead to infinite regret. Specifically, we establish EXP4.P's regret upper bounds in both bounded and unbounded linear and stochastic contextual bandits. Surprisingly, we also find that by including one sufficiently competent expert, EXP4.P can achieve global optimality in the linear case. This unbounded reward result is also applicable to a revised version of EXP3.P in the Multi-armed Bandit scenario. In EXP4-RL, we extend EXP4.P from bandit scenarios to reinforcement learning to incentivize exploration by multiple agents, including one high-performing agent, for both efficiency and excellence. This algorithm has been tested on difficult-to-explore games and shows significant improvements in exploration compared to state-of-the-art.