  We study the problem of Inverse Reinforcement Learning (IRL) with an
average-reward criterion. The goal is to recover an unknown policy and a reward
function when the agent only has samples of states and actions from an
experienced agent. Previous IRL methods assume that the expert is trained in a
discounted environment, and the discount factor is known. This work alleviates
this assumption by proposing an average-reward framework with efficient
learning algorithms. We develop novel stochastic first-order methods to solve
the IRL problem under the average-reward setting, which requires solving an
Average-reward Markov Decision Process (AMDP) as a subproblem. To solve the
subproblem, we develop a Stochastic Policy Mirror Descent (SPMD) method under
general state and action spaces that needs $\mathcal{{O}}(1/\varepsilon)$ steps
of gradient computation. Equipped with SPMD, we propose the Inverse Policy
Mirror Descent (IPMD) method for solving the IRL problem with a
$\mathcal{O}(1/\varepsilon^2)$ complexity. To the best of our knowledge, the
aforementioned complexity results are new in IRL. Finally, we corroborate our
analysis with numerical experiments using the MuJoCo benchmark and additional
control tasks.
