Droplet-microfluidic devices are a means of realizing programmable and flexible devices used to perform diverse laboratory operations on a single chip. These microchips are also capable of reducing reaction times that take hours to mere seconds in discrete droplets. Recent developments have incorporated basic functionalities in droplet-based devices such as droplet sorting, sequencing, synchronization, etc. Still, most of them are useful only for a few droplets. The devices are also developed based on a narrowly defined objective or functionality, where the device or framework needs to be changed when the functionality changes. In this work, a unified droplet-microfluidic framework is developed that can cater to many droplets. The framework includes an optimal network architecture that can perform a given functionality by passively routing droplets through several interconnected channels. The optimal network, which is essentially a certain combination of channels, is identified using reinforcement learning techniques, a promising tool for searching large dimensional spaces. The framework also puts forward a novel approach of injecting droplets into the network, which leads to a huge computational advantage and reduced complexity across varying functionalities.