In this paper, we study the problem of designing adaptive Medium Access Control (MAC) solutions for wireless sensor networks (WSNs) under the Irregular Repetition Slotted ALOHA (IRSA) protocol. In particular, we optimize the degree distribution employed by IRSA for finite frame sizes. Motivated by characteristics of WSNs, such as the restricted computational resources and partial observability, we model the design of IRSA as a Decentralized Partially Observable Markov Decision Process (Dec-POMDP). We have theoretically analyzed our solution in terms of optimality of the learned IRSA design and derived guarantees for finding near-optimal policies. These guarantees are generic and can be applied in resource allocation problems that exhibit the waterfall effect, which in our setting manifests itself as a severe degradation in the overall throughput of the network above a particular channel load. Furthermore, we combat the inherent non-stationarity of the learning environment in WSNs by advancing classical Q-learning through the use of virtual experience (VE), a technique that enables the update of multiple state-action pairs per learning iteration and, thus, accelerates convergence. Our simulations confirm the superiority of our learning-based MAC solution compared to traditional IRSA and provide insights into the effect of WSN characteristics on the quality of learned policies.