# Borehole Trajectory Optimization Design Based on the SAC Algorithm with a Self-Attention Mechanism
## 1 Introduction
However, the Soft Actor-Critic (SAC) algorithm shows significant advantages in the field of reinforcement learning by virtue of its design based on the maximum entropy framework [15], especially in terms of exploration efficiency and learning stability. These characteristics make it an ideal choice to deal with complex control problems. However, challenges still exist when applied to problems such as wellbore trajectory design in complex geological environments. Such environments usually have high nonlinearity, strong coupling, and strong state history dependence. In the face of these characteristics, the traditional SAC algorithm has limitations in effectively capturing and utilizing the historical state information of long sequences, and it is difficult to accurately predict the dynamic changes of the environment. This deficiency also constitutes a key factor restricting the further improvement of the performance of the SAC algorithm in such complex scenes. Recent research has extended reinforcement learning applications in trajectory optimization by introducing more robust network architectures and domain adaptations. For instance, researchers have proposed using Transformer-based attention modules for long-term dependency capture in time-series control tasks [16], as well as advanced reward shaping techniques to handle sparse and delayed feedback [17]. Additionally, hybrid strategies combining SAC with other Actor-Critic variants such as TD3 or PPO have been successfully applied to geosteering, toolface orientation prediction, and adaptive bit path control [18; 19; 20; 21; 22]. These developments further validate the potential of reinforcement learning in trajectory design and offer technical references for our method integration. To solve the above problems, this paper deeply integrates the self-attention mechanism into the SAC algorithm framework. This mechanism can dynamically analyze the dependencies between input sequence elements and assign different weights to different time states. The SAC algorithm integrated into this mechanism can accurately capture long-term dependencies and identify and utilize key historical state information that is highly relevant to the current decision, focusing on the key signals in the evolution of geological environment in real time and improving the response and prediction ability to environmental dynamics; at the same time, a richer and more discriminative state feature representation is learned, thereby enhancing the state representation ability. In order to make the trajectory optimization design more suitable for the actual geological conditions and enhance the applicability of the model in different scenarios, the Wasserstein generative adversarial network (WGAN) technology is applied to the generation of 3D geological model data for the first time in the study. With the help of this technology, high-quality and highly realistic geological data are successfully created. These data show the complex spatial distribution and statistical characteristics of geological structures such as stratigraphic interface, fault strike, lithology distribution, and pore pressure field in the target area, which provides data support close to the real geological environment for algorithm training and makes the optimization results more valuable in practical engineering. During optimization goal setting, this study established a set of multi-objective weighted combinations of reward function systems. Each system takes into account a number of key factors: the first is the trajectory smoothness, which reduces the friction torque by reducing the dogleg to ensure drilling efficiency and string safety; the second is the safety of obstacle avoidance, strictly avoiding obstacles such as adjacent wells and geological risk areas to ensure the safety of drilling operations. The system strives to accurately reach the predetermined geological target point.