## 1 Introduction  
Hearing impairment is the third most frequent chronic disease [1]. Furthermore, hearing rehabilitation is expected to face more severe challenges due to the ageing of the global population [2, 3]. Currently, the use of hearing aids is one of the most effective means of hearing rehabilitation [4]. However, even in developed countries, only one in five people has hearing aids [5]. Due to more limited medical conditions and lower health-care consciousness, this proportion is much lower in developing countries [6]. One factor that affects the penetration rate of hearing aids is a lack of hearing professionals [7, 8], whose skills directly affect the hearing aid fitting process and after-sale service quality. To this end, teleaudiology is a solution to the problem of the shortage of hearing professionals [5]. This technology is primarily applied in remote hearing diagnosis, hearing testing, regulation and consultation for hearing aids and can effectively overcome certain shortcomings, such as long distance, high cost, and lack of professional institutions in remote areas and thus increase access to hearing services [9]. Surveys show that 75% of hearing-impaired patients with moderate to extremely severe hearing loss are more willing to use remote hearing services [10]. Unfortunately, because doctors and patients represent different countries, many urgent problems remain to be solved, such as qualification, responsibility, reimbursement, and quality control, among others. From design conception, self-fitting is the best choice for solving the problem of a shortage of hearing professionals [11]. The essence of self-fitting is that the installation, fitting and use of hearing aids are completed by the user alone, without any hearing experts or equipment [12]. In 1984, [PERSON], [PERSON], et al. proposed this concept [13], but it has not yet been fully achieved. Certain similar products called user-programmable hearing aids have been introduced. However, the design of user-programmable hearing aids is relatively simple. The user manually adjusts the hearing aid using the configuration switch according to his/her subjective judgment of the environment. Studies show that in different environments, the patient can control four parameters [14; 15] to realize the optimal configuration or use four independent memories to adjust the algorithm gain, noise reduction mode, microphone mode and spectral enhancement extent [16]. The design concept of the user-programmable hearing aid is similar to that of the self-fitting hearing aid, i.e., the user manually adjusts the parameters of the hearing aid to compensate for the deterioration of speech with changes in the environment. The difference between these two categories of hearing aids is that the number and extent of change of the adjustable parameters for the user-programmable hearing aid are limited, whereas those of the self-fitting hearing aid are not. Currently, in the commercialization of self-fitting hearing aids, the design of professional instruction materials [17], research on ear moulds, batteries and distribution models, among other activities, are performed simultaneously. With respect to the self-fitting algorithm, parameter optimization of the loudness compensation algorithm was initially realized by [PERSON] in 2007 based on an interactive evolutionary computation (IEC) [18] algorithm. This study delivered a feasible approach to realizing the hearing aid self-fitting algorithm. [PERSON] et al. designed a two-dimensional Gaussian distribution optimization model and set the model parameter as the chromosome. Once the model parameters are determined by the IEC algorithm, the fitting model is determined. Because this algorithm has a large solution population and searches for the optimal solution in the global three-dimensional space, the convergence time is inevitably long. Therefore, it is difficult to meet the needs of patients in practical applications. In 2015, a self-fitting algorithm based on Gaussian Processes (GP) and active learning was proposed [19].