We study a two-sided market, wherein, price-sensitive heterogeneous customers and servers arrive and join their respective queues. A compatible customer-server pair can then be matched by the platform, at which point, they leave the system. Our objective is to design pricing and matching algorithms that maximize the platform's profit, while maintaining reasonable queue lengths. As the demand and supply curves governing the price-dependent arrival rates may not be known in practice, we design a novel online-learning-based pricing policy and establish its near-optimality. In particular, we prove a tradeoff among three performance metrics: OpT1 γq regret, OpTγ{2q average queue length, and OpTγq maximum queue length for γ P p0,1{6s, significantly improving over existing results [1]. Moreover, barring the permissible range of γ, we show that this trade-off between regret and average queue length is optimal up to logarithmic factors under a class of policies, matching the optimal one as in [2] which assumes the demand and supply curves to be known. Our proposed policy has two noteworthy features: a dynamic component that optimizes the tradeoff between low regret and small queue lengths; and a probabilistic component that resolves the tension between obtaining useful samples for fast learning and maintaining small queue lengths.

Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight

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Neither (i) nor (ii) are known for general RMABs. Therefore, to capture the scheduling problems addressed inthiswork,weintroduce anewsubclass ofRMABs,Collapsing Bandits, distinguished by the following feature: when an arm is played, the agent fully observes its state, "collapsing" any uncertainty, but when an arm is passive, no observation is made and uncertainty evolves.

"collapsing" any uncertainty, but when an arm is passive, no observation is made,

Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight

Imagine a large firm with multiple departments that plans a large recruitment. Candidates arrive one-by-one, and for each candidate the firm decides, based on her data (CV, skills, experience, etc), whether to summon her for an interview.

--In wireless networks characterized by dense connectivity, the significant signaling overhead generated by distributed link scheduling algorithms can exacerbate issues like congestion, energy consumption, and radio footprint expansion. T o mitigate these challenges, we propose a distributed link sparsification scheme employing graph neural networks (GNNs) to reduce scheduling overhead for delay-tolerant traffic while maintaining network capacity. A GNN module is trained to adjust contention thresholds for individual links based on traffic statistics and network topology, enabling links to withdraw from scheduling contention when they are unlikely to succeed. Our approach is facilitated by a novel offline constrained unsupervised learning algorithm capable of balancing two competing objectives: minimizing scheduling overhead while ensuring that total utility meets the required level. In simulated wireless multi-hop networks with up to 500 links, our link sparsification technique effectively alleviates network congestion and reduces radio footprints across four distinct distributed link scheduling protocols. Index T erms --Threshold, massive access, scalable scheduling, graph neural networks, constrained unsupervised learning. The proliferation of wireless devices and emerging machine-type communications (MTC) [2] has led to new requirements for next-generation wireless networks, including massive access in ultra-dense networks, spectrum and energy efficiencies, multi-hop connectivity, and scalability [3]-[6]. A promising solution to these challenges is self-organizing wireless multi-hop networks, which have been applied to scenarios where infrastructure is infeasible or overloaded, such as military communications, satellite communications, vehicular/drone networks, Internet of Things (IoT), and 5G/6G (device-to-device (D2D), wireless backhaul, integrated access and backhaul (IAB)) [3]-[10]. Received 27 February 2024; revised 20 January 2025, 17 June 2025, and 13 August 2025; accepted 1 September 2025. Research was sponsored by the DEVCOM ARL Army Research Office and was accomplished under Cooperative Agreement Number W911NF-19-2-0269. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. Zhongyuan Zhao and Santiago Segarra are with the Department of Electrical and Computer Engineering, Rice University, USA.