DescriptionOptical networks-on-chips (NoCs) based on silicon photonics have been proposed as an emerging communication architecture for many-core chip multiprocessors. However, one of the key challenges is the thermal sensitivity of silicon photonic devices under on-chip temperature variations, which would result in significant thermal-induced optical power loss in optical NoCs. In this work, we propose an approximate Q-routing to find optimal low-loss paths in the presence of on-chip temperature variations. With the method of linear function approximation, the proposed approximate Q-routing does not require Q-tables which are necessary in traditional table-based Q-routing. Simulation results of an 8x8 mesh-based optical NoC under a set of synthetic traffic patterns and real applications show that the proposed approximate Q-routing can converge faster and its optimization effect is very close to the best optimization effect of the traditional table-based Q-routing.