We show the convergence of Wasserstein inverse reinforcement learning (WIRL) for multi-objective optimizations with the projective subgradient method by formulating an inverse problem of the optimization problem that is equivalent to WIRL for multi-objective optimizations. In addition, we prove convergence of inverse reinforcement learning (maximum entropy inverse reinforcement learning, guid cost learning) for multi-objective optimization with the projective subgradient method.

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