  This paper explores decentralized learning in a graph-based setting, where
data is distributed across nodes. We investigate a decentralized SGD algorithm
that utilizes a random walk to update a global model based on local data. Our
focus is on designing the transition probability matrix to speed up
convergence. While importance sampling can enhance centralized learning, its
decentralized counterpart, using the Metropolis-Hastings (MH) algorithm, can
lead to the entrapment problem, where the random walk becomes stuck at certain
nodes, slowing convergence. To address this, we propose the Metropolis-Hastings
with L\'evy Jumps (MHLJ) algorithm, which incorporates random perturbations
(jumps) to overcome entrapment. We theoretically establish the convergence rate
and error gap of MHLJ and validate our findings through numerical experiments.
