  Multiplication is a fundamental operation in many applications, and
multipliers are widely adopted in various circuits. However, optimizing
multipliers is challenging and non-trivial due to the huge design space. In
this paper, we propose RL-MUL, a multiplier design optimization framework based
on reinforcement learning. Specifically, we utilize matrix and tensor
representations for the compressor tree of a multiplier, based on which the
convolutional neural networks can be seamlessly incorporated as the agent
network. The agent can learn to optimize the multiplier structure based on a
Pareto-driven reward which is customized to accommodate the trade-off between
area and delay. Additionally, the capability of RL-MUL is extended to optimize
the fused multiply-accumulator (MAC) designs. Experiments are conducted on
different bit widths of multipliers. The results demonstrate that the
multipliers produced by RL-MUL can dominate all baseline designs in terms of
area and delay. The performance gain of RL-MUL is further validated by
comparing the area and delay of processing element arrays using multipliers
from RL-MUL and baseline approaches.
