Summary of Bisimulation Metrics Are Optimal Transport Distances, and Can Be Computed Efficiently, by Sergio Calo et al.
Bisimulation Metrics are Optimal Transport Distances, and Can be Computed Efficiently
by Sergio Calo, Anders Jonsson, Gergely Neu, Ludovic Schwartz, Javier Segovia-Aguas
First submitted to arxiv on: 6 Jun 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary The paper proposes a new framework for calculating optimal transport distances between Markov chains. The previous approaches focused on couplings between joint distributions, which led to inefficient algorithms. This work introduces discounted occupancy couplings and formulates the problem as a linear program (LP). The LP formulation enables entropy regularization and the calculation of optimal transport distances using Sinkhorn Value Iteration (SVI), a Sinkhorn-like method. The paper shows that SVI converges quickly to an optimal coupling, with a computational cost similar to vanilla Sinkhorn in each pair of states. This framework also exactly matches the common notion of bisimulation metrics between Markov chains and is more efficient than previous methods. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This research creates a new way to measure how close two random processes are. Right now, there are inefficient ways to do this. The new approach makes it easier by looking at a simplified version of the processes and solving a simple math problem. This allows for more efficient calculations and is useful for understanding complex systems. |
Keywords
» Artificial intelligence » Regularization
