Wasserstein-robust contraction certification achieves 2.2x improvement under spike disturbances
Streaming data certification withstands heavy-tailed noise and coupling without joint models.
A new paper from Faegheh K Moazeni tackles two critical challenges in real-time control certification: shifting disturbance distributions and the lack of a joint model for coupled subsystems. The proposed Wasserstein-robust certificate uses an online estimate of the empirical excess kurtosis of recent residuals to adapt the safety margin, ensuring it degrades gracefully under distributional shift instead of failing catastrophically.
On a five-node G5 benchmark tested under Gaussian, heavy-tailed Laplace, and spike event noise regimes, the Wasserstein certificate remains valid in 73% of spike-regime timesteps compared to just 33% for the standard Gaussian baseline—a 2.2x improvement. Critically, the Gaussian certificate never authorizes deployment during the spike window.
For interconnected systems, the method composes local certificates beta_A and beta_B into a network-level guarantee via a simple formula: beta_net = (beta_A+beta_B)/2 - sqrt[(beta_A-beta_B)^2/4 + gamma^2] > 0 whenever gamma < sqrt(beta_A*beta_B). This requires no joint model. The framework correctly identifies all three coupling regimes from local data alone, with gamma_warn accurately predicting network-level contraction loss.
- Wasserstein-robust certificate uses online kurtosis estimates to adapt safety margins under distribution shifts.
- Achieves 73% validity in spike regimes vs 33% for Gaussian baseline (2.2x improvement).
- Composes local subsystem certificates into network guarantee without joint model, with gamma_warn ≈ 0.98 precisely predicting contraction loss.
Why It Matters
Enables safe real-time control in autonomous systems where sensor noise and coupling shift unpredictably.