Can latent actions and environment dynamics be recovered from offline trajectories when actions are never observed? We study this question in a setting where trajectories are action-free but tagged with demonstrator identity. We assume that each demonstrator follows a distinct policy, while the environment dynamics are shared across demonstrators and identity affects the next observation only through the chosen action. Under these assumptions, the conditional next-observation distribution $p(o_{t+1}\mid o_t,e)$ is a mixture of latent action-conditioned transition kernels with demonstrator-specific mixing weights. We show that this induces, for each state, a column-stochastic nonnegative matrix factorization of the observable conditional distribution. Using sufficiently scattered policy diversity and rank conditions, we prove that the latent transitions and demonstrator policies are identifiable up to permutation of the latent action labels. We extend the result to continuous observation spaces via a Gram-determinant minimum-volume criterion, and show that continuity of the transition map over a connected state space upgrades local permutation ambiguities to a single global permutation. A small amount of labeled action data then suffices to fix this final ambiguity. These results establish demonstrator diversity as a principled source of identifiability for learning latent actions and dynamics from offline RL data.

翻译：摘要：当动作从未被观测到时，能否从离线轨迹中恢复潜在动作与环境动力学？本文研究轨迹不含动作但带有演示者身份标识的场景。假设每位演示者遵循不同的策略，而环境动力学在所有演示者间共享，且身份仅通过所选动作影响下一观测值。在此假设下，条件下一观测分布 $p(o_{t+1}\mid o_t,e)$ 是潜在动作条件转移核的混合，混合权重因演示者而异。我们证明，这导致每个状态下可观测条件分布可分解为列随机非负矩阵。利用充分分散的策略多样性与秩条件，我们证明潜在转移与演示者策略可在潜在动作标签置换意义下被识别。我们将结果扩展到连续观测空间，通过Gram行列式最小体积准则，并证明连通状态空间上转移映射的连续性可将局部置换歧义升级为单一全局置换。少量带标签动作数据即可消除最终歧义。这些结果确立了演示者多样性作为从离线强化学习数据中学习潜在动作与动力学的可识别性原理性来源。