Differentiating Bisimulation Metrics: A Framework for Parametric Markov Chain Fitting via Bicausal Optimal Transport
Many problems in sequential decision-making, such as imitation learning from observations, state-space compression, world-model learning, and sim-to-real transfer, can be reduced to learning a model such that a notion of distance with respect to the target process is minimized. We consider this general framework and consider the bisimulation metric, equivalently Bicausal Optimal Transport (BOT), as the notion of distance to minimize. We show that BOT, since it can be formulated as a linear program (LP), is differentiable with respect to the model dynamics. We then derive an exact closed-form gradient via the envelope theorem applied to the LP saddle point. The result is a general algorith...
| Authors | Sergio Calo, Amy Zhang, Javier Segovia-Aguas et al. |
|---|---|
| Primary category | cs.LG |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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