Capability-Aware Imbalance in Composite Decision Systems: An Optimal Transport View

Authors: Hadi Sadoghi Yazdi
Status: Under review (JMLR 2026)

Overview

This work reframes structural imbalance in composite decision systems (Mixture-of-Experts, Boosting, hierarchical classifiers, distributed systems) as a natural and often optimal outcome rather than a flaw.

Using the lens of Optimal Transport, we prove that when task difficulty is heterogeneous, the cost-minimizing assignment is necessarily non-uniform — a phenomenon we call Constructive Imbalance.

Key Contributions

• Fundamental Theorem of Constructive Imbalance: Optimal routing is non-uniform whenever task difficulty is non-uniform.
• Effective Complexity as the primal transport cost.
• Complexity attenuation via rare specialization (highly complex experts add almost zero global cost if rarely used).
• Unified framework connecting MoE routing, Boosting reweighting, load balancing, and hierarchical decomposition.
• Theoretical link between transport-optimal routing and Rademacher generalization bounds.
• Empirical validation + corrections to previous claims (harmonic mean bound, marginal cost equalization).

Repository Contents

• run_experiments.py — Reproducible main script
• results.json — All raw experimental results

Reproducibility

```bash python run_experiments.py