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Designing Ambiguity Sets for Distributionally Robust Optimization Using Structural Causal Optimal Transport

AAAI 2025 · Probabilistic and scientific modeling › Causal discovery · approach: Latent-variable causal estimation · 1 citations (OpenAlex)

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Proposes structural causal optimal transport, which restricts transport plans to those respecting an SCM's structural equations, and a relaxed entropic version solved by DC programming plus Sinkhorn, with finite-sample and dimension-free radius guarantees for DRO ambiguity sets.

Problem

Classical Wasserstein ambiguity sets ignore causal structure and produce overly conservative DRO models; existing causal OT variants (adapted OT, G-causal OT) use only the causal graph and not the structural equations, and G-causal OT lacks a computational method.

Approach

Define structural causal OT whose plans and distributions are constrained to be F-compatible: after pushing forward through the inverse reduced-form mapping, the measures and plans factorize over independent exogenous noises. A relaxed version replaces the hard constraints by a KL penalty to a factorized projection, solvable via DC programming with Sinkhorn steps.

Key results

• On the simulated Age-Education SCM, the G-causal ambiguity set yields higher worst-case loss than the structural causal set for all tested functions and radii, e.g. (x-y)^2 at radius 0.1 gives +5.54% and at radius 0.4 gives +29.6%.
• The concentration bound for the exogenous-space empirical construction removes the N^{-1/d} dimension dependence, giving rate roughly N^{-1/(2p)} for the structural causal ambiguity set (stated as a corollary under d_i=1 and d>=2p+1).
• The relaxed structural causal OT converges to W^F as epsilon goes to infinity and to classical W as epsilon goes to zero, and the structural causal set is contained in the relaxed set.

Measured effects reported in the paper

Limitations

• Experiments are limited to a single simple two-variable linear SCM; no real-world DRO evaluation.
• The G-causal distance lacks a direct computational method, so its ambiguity set was approximated by random Gaussian sampling.
• No strong duality result converting the DRO problem into a tractable form is provided.

Experimental setup

Datasets: simulated linear SCM (Age, Education) with standard normal noise

Benchmarks: simulated linear SCM worst-case loss comparison

Metrics: worst-case expected loss relative to structural causal ambig

Baselines: classical Wasserstein ambiguity set adapted optimal transport G-causal optimal transport

Builds on: adapted optimal transport G-causal optimal transport CO-OT Sinkhorn algorithm

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