  In this article, for the first time, we propose a transformer network-based
reinforcement learning (RL) method for power distribution network (PDN)
optimization of high bandwidth memory (HBM). The proposed method can provide an
optimal decoupling capacitor (decap) design to maximize the reduction of PDN
self- and transfer impedance seen at multiple ports. An attention-based
transformer network is implemented to directly parameterize decap optimization
policy. The optimality performance is significantly improved since the
attention mechanism has powerful expression to explore massive combinatorial
space for decap assignments. Moreover, it can capture sequential relationships
between the decap assignments. The computing time for optimization is
dramatically reduced due to the reusable network on positions of probing ports
and decap assignment candidates. This is because the transformer network has a
context embedding process to capture meta-features including probing ports
positions. In addition, the network is trained with randomly generated data
sets. Therefore, without additional training, the trained network can solve new
decap optimization problems. The computing time for training and data cost are
critically decreased due to the scalability of the network. Thanks to its
shared weight property, the network can adapt to a larger scale of problems
without additional training. For verification, we compare the results with
conventional genetic algorithm (GA), random search (RS), and all the previous
RL-based methods. As a result, the proposed method outperforms in all the
following aspects: optimality performance, computing time, and data efficiency.
