Query Optimization is considered to be one of the most important challenges in database management. Existing built-in query optimizers are very complex and rely on various approximations and hand-picked rules. The rise of deep learning and deep reinforcement learning has aided many scientific and industrial fields, providing an opportunity to develop a learnable query optimizer. In this paper, we analyse and improve the state-of-the-art learned query optimizer, Neo for the JOB benchmark on two database systems: PostgreSQL and Huawei GaussDB. We describe our methods, based on combination of Neo, Tree-Transformers, auxiliary tasks, reward weighting. Combinations of these methods improve latency of the found query execution plans. We also conduct a thorough analysis of the resulting execution plans and devise a set of decision-based rules to indicate the cases when the learned optimizer will outperform the built-in one. We also provide a source code for the proposed methods and experiments. Finally, we provide possible directions for further improvement in this field.