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Causal MOT Benchmarks

The causal benchmark compares the exact multi-period martingale LP with the regularized causal Sinkhorn approximation on a three-step uniform chain:

[1, 3] -> [0.5, 3.5] -> [0, 4]

The benchmark payoff is additive across adjacent transitions:

|S2 - S1| + |S3 - S2|

Run it from a local checkout with the package on PYTHONPATH:

PYTHONPATH=src python scripts/benchmark_causal.py

The script evaluates n = 5, 10, 15, 20 atoms per step by default and prints a markdown table with:

  • exact causal upper bound from solve_exact_causal_mot
  • regularized expected payoff from causal_sinkhorn_mot
  • absolute objective gap
  • wall-clock time for each method
  • convergence status for the regularized solver

The exact LP scales over the full joint tensor and is intended as a small-grid benchmark. The Sinkhorn path is the practical approximation route for larger causal chains.