Many insect herbivores are specialists, eating only a certain group of related plants, such as plants in the same species, genus, or family, or plants in a series of related species, genera, or families.
Many invasive plants have close native relatives. Although initially, many invasive plants are eaten by few or no native insect specialists, there is a phenomenon in which insects "jump host", from one plant to a new plant that they did not previously eat.
An example of this, the Ailanthus webworm moth is a moth native to South Florida and the American tropics, which originally ate trees of the Simaroubaceae family, such as Simarouba glauca and Simarouba amara. The Ailanthus altissima tree, or "tree of heaven", was introduced into North America from East Asia, and it became invasive, spreading throughout the continent. Ailanthus has rapid growth and is strongly allelopathic, and these two factors combine to result in it causing extensive harm to some ecosystems.
Although few native insects originally ate the Ailanthus altissima tree, the tree is a member of the Simaroubaceae family, and where its range came to overlap with the native trees of this family in South Florida, the Ailanthus webworm moth jumped host, and started eating the Ailanthus altissima trees as well. This moth has now expanded its range far north into North America, following the distribution of the invasive tree, and under certain conditions it can hugely limit the growth of these trees, sometimes even killing full-grown trees.
By planting native plants that are closely related to invasive plants that are common in your area, you can help attract native insects that specialize on those families, genera, or other groupings of plants. As more people do this, it will increase the populations of these insects, and increase the amount of contact between these insects and the invasive plants, which will increase the likelihood with which these insects will jump host and begin eating invasive plants.