C-GAIL: Stabilizing Generative Adversarial Imitation Learning with
  Control Theory
Tianjiao Luo Tim Pearce Huayu Chen Jianfei Chen Jun Zhu
Generative Adversarial Imitation Learning (GAIL) trains a generative policy
to mimic a demonstrator. It uses on-policy Reinforcement Learning (RL) to
optimize a reward signal derived from a GAN-like discriminator. A major
drawback of GAIL is its training instability - it inherits the complex training
dynamics of GANs, and the distribution shift introduced by RL. This can cause
oscillations during training, harming its sample efficiency and final policy
performance. Recent work has shown that control theory can help with the
convergence of a GAN's training. This paper extends this line of work,
conducting a control-theoretic analysis of GAIL and deriving a novel controller
that not only pushes GAIL to the desired equilibrium but also achieves
asymptotic stability in a 'one-step' setting. Based on this, we propose a
practical algorithm 'Controlled-GAIL' (C-GAIL). On MuJoCo tasks, our controlled
variant is able to speed up the rate of convergence, reduce the range of
oscillation and match the expert's distribution more closely both for vanilla
GAIL and GAIL-DAC.