Approximating Optimal Policies in Heterogeneous Asynchronous Multi-player Bandits

We study asynchronous distributed decision-making for scalable multi-agent bandit submodular maximization. We are motivated by distributed information-gathering tasks in unknown environments and under heterogeneous inter-agent communication delays. To enable scalability despite limited communication delays, existing approaches restrict each agent to coordinate only with its one-hop neighbors. But these approaches assume homogeneous communication delays among the agents and a synchronous global clock. In practice, however, delays are heterogeneous, and agents operate with mismatched local clocks. That is, each agent does not receive information from all neighbors at the same time, compromising decision-making. In this paper, we provide an asynchronous coordination algorithm to overcome the challenges. We establish a provable approximation guarantee against the optimal synchronized centralized solution, where the suboptimality gap explicitly depends on communication delays and clock mismatches. The bounds also depend on the topology of each neighborhood, capturing the effect of distributed decision-making via one-hop-neighborhood messages only. The clock-mismatch penalty is expressed through a bounded oscillation of the reward in the execution times, which, unlike a Lipschitz condition, is available for discrete-valued rewards such as target monitoring. We validate the approach through numerical simulations on multi-camera target monitoring through the lenses of two different reward structures and simulation setups.

We study multi-objective multi-agent multi-armed bandits (MO-MA-MAB) under stochastic rewards, where agents observe heterogeneous reward vectors and communicate over time-varying graphs. We formulate this emerging problem setting to address efficient learning, measured by Pareto regret, and incorporate fair learning as an additional goal, captured via social welfare. To measure efficiency, we formulate Pareto regret and develop Pareto UCB1 Gossip, whose novel exploration radius explicitly separates statistical uncertainty in Pareto-based inference from consensus error. To express the fairness constraint, we formulate a Nash Social Welfare objective over preference-scalarized rewards and propose Simulated NSW UCB Gossip, which integrates preference-based reward simulation, gossip-based utility estimation, and UCB-style exploration. We prove that Pareto UCB1 Gossip achieves $\mathcal{O}(\log T)$ regret and an instance-independent rate of $\mathcal{O}(\sqrt{T})$, while Simulated NSW UCB Gossip achieves an instance-independent regret bound of $\mathcal{O}(T^{3/4})$. This separation reveals the cost of imposing the fairness constraint to our efficiency objective: fairness limits information aggregation and slows convergence. Experiments show that our methods consistently outperform baselines, improving performance by approximately $100\%$ and $50\%$ in the efficiency and fairness settings, respectively.

We study the multiplayer multi-armed bandit problem with information asymmetry under Bernoulli rewards, for three information structures: asymmetry in actions, in rewards, and in both. Replacing the Hoeffding-style confidence intervals of prior work with Kullback--Leibler (KL) divergence-based bounds gives strictly tighter regret guarantees in each case. We propose mKL-UCB, mKL-UCB-Intervals and mKL-DSEE, and show that the improvement factor is at least two by Pinsker's inequality and far larger when reward means are near zero or one. For asymmetry in rewards we prove that two arms' KL intervals separate after a deterministic number of samples, and that $M$ independent players accelerate elimination further.