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In real-world scenarios, arbitrary interactions with the environment canoften be costly, and actions of expert demonstrations are not always available.To reduce the need for both, Offline Learning from Observations (LfO) isextensively studied, where the agent learns to solve a task with only expertstates and \textit{task-agnostic} non-expert state-action pairs. Thestate-of-the-art DIstribution Correction Estimation (DICE) methods minimize thestate occupancy divergence between the learner and expert policies. However,they are limited to either $f$-divergences (KL and $\chi^2$) or Wassersteindistance with Rubinstein duality, the latter of which constrains the underlyingdistance metric crucial to the performance of Wasserstein-based solutions. Toaddress this problem, we propose Primal Wasserstein DICE (PW-DICE), whichminimizes the primal Wasserstein distance between the expert and learner stateoccupancies with a pessimistic regularizer and leverages a contrastivelylearned distance as the underlying metric for the Wasserstein distance.Theoretically, we prove that our framework is a generalization of thestate-of-the-art, SMODICE, and unifies $f$-divergence and Wassersteinminimization. Empirically, we find that PW-DICE improves upon severalstate-of-the-art methods on multiple testbeds.

Offline Imitation from Observation via Primal Wasserstein State Occupancy Matching