In unmanned aerial vehicle (UAV) networks, the high mobility of nodes leads to frequent changes in network topology, which brings challenges to the neighbor discovery (ND) for UAV networks. Integrated sensing and communication (ISAC), as an emerging technology in 6G mobile networks, has shown great potential in improving communication performance with the assistance of sensing information. ISAC obtains the prior information about node distribution, reducing the ND time. However, the prior information obtained through ISAC may be imperfect. Hence, an ND algorithm based on reinforcement learning is proposed. The learning automaton (LA) is applied to interact with the environment and continuously adjust the probability of selecting beams to accelerate the convergence speed of ND algorithms. Besides, an efficient ND algorithm in the neighbor maintenance phase is designed, which applies the Kalman filter to predict node movement. Simulation results show that the LA-based ND algorithm reduces the ND time by up to 32% compared with the Scan-Based Algorithm (SBA), which proves the efficiency of the proposed ND algorithms.