Imitation & Inverse RL

adversarial inverse RL (AIRL)

AIRL keeps GAIL's adversarial game but fixes what GAIL throws away: the reward function. GAIL learns a discriminator that, once the policy is trained, is discarded — you get a good imitator but no portable objective. AIRL structures the discriminator so that a meaningful, reusable reward falls out of it, recovering the why, not just the what.

It does this by parameterizing the discriminator in a special form: it judges an action by comparing a learned reward term against the policy's own probability of taking that action. Because the reward term sits in a fixed place in the equation, training the discriminator to spot the expert simultaneously fits a reward function. With an added shaping term, AIRL can even recover a reward that is disentangled from the environment's dynamics and so transfers to new dynamics.

That transferability is the prize: a robot can relearn the same goal under a different body or terrain, something a GAIL imitator, locked to the training environment, cannot do.

D_{\theta}(s,a)=\dfrac{\exp\!\big(f_{\theta}(s,a)\big)}{\exp\!\big(f_{\theta}(s,a)\big)+\pi(a\mid s)}

AIRL's discriminator compares a learned reward term f_θ against the policy's action probability; f_θ becomes the recovered reward.

Also called
AIRL