## 1 Introduction  
In recent years, the number of mobile users around the world has exploded, and so has the data traffic. A study found that the number of mobile terminal devices worldwide could reach tens of billions by 2023 [1]. At the same time, the rapid development of the mobile internet has also promoted the rapid popularization of mobile communication. As an important entrance to the mobile internet, the penetration rate of smart terminals has grown exponentially, which has greatly stimulated the development of the mobile internet and accelerated global users' demands for wireless data services. As the demand for wireless data services grows, existing network deployments cannot support the explosive growth of data services. In this context, Ultra-Dense Networks (UDN) technology, which increases the number of micropower base stations and reduces each base station's coverage radius, is an effective and affordable solution [2]. Dense deployment of small base stations could shorten distances as well as greatly improve link quality between mobile stations and base stations, improve signal coverage, and increase system capacity [3]. However, due to the complexity of terminal movement and the small-scale characteristics of a single base station, the coverage of most micro base stations is between 50 and 200 m. With the development of wireless access technology, this distance could even be reduced to 10 m [4]. This inevitably leads to more frequent handover of terminals between base stations, resulting in unprecedented signaling overhead. At the same time, due to the rapid changes in signal strength of the low-power micro-base station transmissions received by mobile users, the probability of handover failure and ping-pong handover also increases significantly, resulting in data packet loss and delay that damage network performance and user experience. Therefore, how to design a reasonable handover strategy to reduce the number of unexpected events during the user's mobility, such as ping-pong handover and handover failure, and ensure user experience has become an urgent problem to be solved [2]. At present, there have been a lot of research on cell handover, mainly by optimizing the trigger threshold and trigger time to improve the handover performance. The authors in [5] proposed a reduced early handover (REHO) scheme by adjusting the time to trigger (TTT) in the long-term evolution (LTE) system. The researchers in [6] presented a Markov-chain-based handover mechanism in the Fifth generation (5G) ultra-dense networks, which enables users to achieve early handover by predicting the next target base station. The authors in [7] proposed a deep Q-learning (DQN) algorithm to adaptively adjust the handover trigger time, based on the access rate and the signal to interference noise ratio (SINR). The authors in [8] proposed a long short term memory (LSTM)-based prediction method to find a proper handover point in advance through analyzing the historical reference signal receiving power (RSRP) and predicting the future changes of RSRP. The above studies mainly focus on optimizing the handover trigger point to reduce the handover failure rate and improve the stability of Quality of Service (QoS) during the handover process, but do not consider the resulting problem of ping-pong handover. In order to better optimize the handover problem, the handover failure rate and the handover ping-pong rate need to be considered jointly. The authors in [9] proposed a frequent handover mitigation algorithm to reduce the handover failure rate and ping-pang rate in UDN. The suggested algorithm monitors the serving cell history and the dwelling time of the users to detect fast mobile users or ping-pong users. Simulation results indicated that the suggested algorithm can reduce 79.56% of the overall handovers at the cost of high complexity. The authors in [10; 11] proposed several handover parameter optimization algorithms to overcome ping-pong problems, but only for the one-dimensional optimization of the hysteresis value (Hys).