## 6 Discussion  
In this study, we encountered a challenging scenario involving a high 64-dimensional continuous action space and a low-dimensional 2 \(\times\) 2 observation space in quasi-static atmospheric turbulence. This situation could potentially hinder the effectiveness of RL algorithms. However, the successful performance of our RL algorithms in a quasi-static environment has demonstrated that their effectiveness does not solely depend on the limited dimensions of the photodetector and the deformable mirror. Instead, it arises from a combination of factors, including the robustness of the reward function, the quality of the employed photodetector, and the correlation within the action space. In other words, the Strehl ratio reward function used in a quasi-static environment offers a significant advantage due to its ability to provide high-quality rewards, which are calculated prior to the wavefront propagating through the photodetector, which had a higher pixel count (128 \(\times\) 128 as opposed to 2 \(\times\) 2) and resolution. Consequently, by employing a proficient function approximator and a robust reward function, the agent can effectively generalize over related actions. Given the large number of degrees of freedom in the mirror, there are numerous possible paths to focus the light and the agent only needs to cover one of these paths. While increasing the dimension of the observation space and reducing the dimension of the action space was not necessary in quasi-static atmospheric turbulence, it became crucial in semi-dynamic atmospheric turbulence. For this reason, the observation-space dimension was changed to 5 \(\times\) 5 and the action-space dimension was reduced to a first six modes (second radial orders) of Zernike polynomials. The reward function was changed from the Strehl ratio to Equation (2)) since the Strehl ratio cannot be accurately calculated using a 5 \(\times\) 5 detection array, and to better correspond to coupling efficiency into a single-mode fiber. The new reward function is designed to perform calculations utilizing only a 5 \(\times\) 5 pixel observation space. The results of a quasi-static environment indicate that, while it is possible for the PPO, SAC, and DDPG RL models to determine an accurate set of deformable mirror actions, the results generally underperform the output of the Shack-Hartmann wavefront sensor. PPO outperforms the SAC and DDPG models, converging on a Strehl ratio of over 60% after hundreds of training episodes. One of the main limitations of these results is the applicability to a dynamic atmosphere with limited deformable mirror speeds. The 3 dB bandwidth of the fastest mechanical deformable mirrors is limited to <10 kHz, which implies that less than 10 action-measurement loop iterations are required for the quasi-static turbulence condition to hold. For most deformable mirrors, this requirement cannot be met. However, some faster deformable mirrors possess sufficient speed, and photonic chip-based phase corrector arrays are capable of speeds well in excess of 20 kHz [33] and can make use of a model requiring tens of action steps to converge. Despite this limitation, we expect such simplifications to be reasonable as an RL-based system may still outperform a Shack-Hartmann wavefront sensor with its corresponding photon count requirements which are not considered in our comparisons. For existing and planned optical ground stations, AO may not be considered at all due to the cost, complexity, calibration, wavefront steps, aliasing, and latencies involved in Shack-Hartmann wavefront sensing. Therefore, any improvement to the wavefront beyond an uncorrected case is still of value. Furthermore, the application of models trained on quasi-static and semi-dynamic turbulence profiles may be of value to RL environments with dynamically changing turbulence profiles for improvement to signal re-acquisition times.