When an object with mass accelerates, it produces Gravitational Waves (GWs) that are not easily absorbed or scattered. GW is the only means to study some extreme astronomical phenomena. To overcome the limitations from seismic gravity-gradient noise in ground-based GW observatories, several spaced-based GW observatory projects: LISA, DECIGO, Taiji, and TianQin, have been initiated world widely in the past two decades, aiming to detect GWs in the frequency range from 0.1 mHz to 1 Hz (science band).Spaced-based GW observatory is essentially a laser interferometer consisting of three spacecrafts. Because GW is extremely weak, the frequency noise of the lasers inside the interferometer needs to be suppressed by at least 8 to 10 orders of magnitude to meet the detection requirements. To achieve this goal, three techniques are typically employed. The laser's frequency is first prestabilized to a fixed-length ultrastable optical cavity using Pound-Drever-Hall (PDH) locking method; then the arm length of the constellation, which is much more stable than the laser's frequency in the science band, is used as a reference to further reduce the laser's phase noise, and this is called arm locking technique; finally, the residual laser frequency noise can be canceled by Time Delay Interferometry (TDI), with the help of virtual delays introduced in data postprocessing.Despite significant advances in arm locking techniques over the past two decades, all arm locking controllers reported so far have been based on the traditional forward design approach: first giving the concrete form of the controller and then fine-tuning a small number of parameters. This method has a very limited degree of freedom for optimization, which severely limits the noise suppression performance of the arm locking system.In this paper, for the first time, the inverse design idea is employed for the design of the arm locking controller. A layer structure is used for the controller optimization. The data input layer is responsible for modeling noise, gravitational wave signal and controller parameters; the control architecture layer determines the structure of the arm locking system; and the optimization output layer is responsible for parameter optimization and output. During the optimization, several key characteristics, such as laser frequency noise suppression ratio, peak gain of other noises, gravitational wave sensitivity and zeros and poles of the closed-loop system, are firstly obtained by analyzing the data collected by the phase meter. These characteristics are then combined linearly or nonlinearly to obtain a figure of merit (FoM) function whose independent variables are the feedback controller parameters in the data input layer. Finally, a specific optimization algorithm, such as gradient descent algorithm, is used to obtain the optimal value of the FoM function, and the corresponding controller parameters are returned to the data input layer, thus updating the controller structure in the control architecture layer.Using the method above, the controllers of three noise-coupled architectures, single arm locking, dual arm locking and common arm locking systems, are optimized respectively. The optimization parameters are obtained by searching the local minimal of the FoM function, under the constrains of the arm locking stability criterions we summarized recently.After optimization, the laser phase noise suppression ratio of noise-coupled single arm locking system is above 75.9 dB within the full scientific band, except for those frequencies near the dead zone of the interferometer, and the maximum suppression ratio exceeds 112.7 dB. The laser phase noise suppression ratio for dual arm locking is more than 74.0 dB within the full science band (no dead zones), and approaches 234.0 dB at 0.1 mHz. And for common arm locking this suppression ratio is more than 75.5 dB in the full science band (except for a few frequencies around the dead zones) and can exceed 196 dB at 0.1 mHz. In all the three systems, the GW and technical noise at low frequency range can be amplified, therefore, the signal-to-noise ratio of GW relative to laser phase noise are significantly improved. To verify the performance of the optimized controllers, time domain MATLAB/Simulink simulation is performed for all the three noise-coupled architectures, respectively. By choosing appropriate out-of-loop measurement ports, the technical noise can be well suppressed while GW is still amplified by the locking system. The experimental results show that the signal-to-noise ratio of GW relative to all other noises can be increased by 149.05 dB, 179.62 dB and 171.20 dB, for single arm locking, dual arm locking and common arm locking system, respectively. This work can be generalized to different kinds of arm locking controller design and will effectively improve the sensitivity of the space-based GW observatories.