  Engineering change orders (ECOs) in late stages make minimal design fixes to
recover from timing shifts due to excessive IR drops. This paper integrates
IR-drop-aware timing analysis and ECO timing optimization using reinforcement
learning (RL). The method operates after physical design and power grid
synthesis, and rectifies IR-drop-induced timing degradation through gate
sizing. It incorporates the Lagrangian relaxation (LR) technique into a novel
RL framework, which trains a relational graph convolutional network (R-GCN)
agent to sequentially size gates to fix timing violations. The R-GCN agent
outperforms a classical LR-only algorithm: in an open 45nm technology, it (a)
moves the Pareto front of the delay-area tradeoff curve to the left and (b)
saves runtime over the classical method by running fast inference using trained
models at iso-quality. The RL model is transferable across timing
specifications, and transferable to unseen designs with zero-shot learning or
fine tuning.
