Loop invariant generation has long been a challenging problem. Black-box learning has recently emerged as a promising method for inferring loop invariants. However, the performance depends heavily on the quality of collected examples. In many cases, only after tens or even hundreds of constraint queries, can a feasible invariant be successfully inferred.

To reduce the gigantic number of constraint queries and improve the performance of black-box learning, we introduce interval counterexamples into the learning framework. Each interval counterexample represents a set of counterexamples from constraint solvers. We propose three different generalization techniques to compute interval counterexamples. The existing decision tree algorithm is also improved to adapt interval counterexamples. We evaluate our techniques and report over $40%$ improvement on learning rounds and verification time over the state-of-the-art approach.