Constrained Policy Optimization for Provably Fair Order Matching

2026-04-07

AI Summary

This work addresses systemic execution unfairness in automated matching engines arising from latency, order size, and market access disparities by unifying group fairness notions—demographic parity and equalized odds—with individual Lipschitz fairness within a constrained Markov decision process (CMDP) framework. It introduces a dual-loop optimization mechanism: the inner loop computes analytical trust-region steps on the Fisher information manifold, while the outer loop employs a PID controller to dynamically tighten safety margins, mitigating sawtooth oscillations of Lagrange multipliers in non-stationary environments, complemented by spectral normalization for deterministic fairness guarantees. Theoretically, the system is proven BIBO stable with asymptotically vanishing constraint violations. Empirically, the method recovers 95.9% of unconstrained throughput with only 2.5% constraint violation on NASDAQ LOBSTER data, captures 98.4% of the reward upper bound under MEV attacks in crypto order books at 3.2% violation, scales sublinearly to eight constraints, fits within a single Ethereum block, and achieves a 2.1× reward improvement in Safety-Gymnasium.

Abstract

Automated matching engines execute millions of orders per session, yet systematic asymmetries in latency, order size, and market access compound into persistent execution disparities that erode participant trust. We formulate provably fair order matching as a Constrained Markov Decision Process and propose CPO-FOAM (Constrained Policy Optimization with Feedback-Optimized Adaptive Margins). An inner loop computes an analytic trust-region step on the Fisher information manifold; a PID-controlled outer loop dynamically tightens safety margins, suppressing the sawtooth oscillations endemic to Lagrangian methods under non-stationary dynamics. Group fairness (demographic parity, equalized odds) enters the CMDP cost vector while individual Lipschitz fairness is enforced deterministically via spectral normalization. We prove BIBO stability and that the integral term drives steady-state violations to zero. On LOBSTER NASDAQ data across six market regimes, CPO-FOAM recovers 95.9% of unconstrained throughput at 2.5% constraint violation frequency; on crypto-asset LOB data under MEV injection it captures 98.4% of the reward envelope at 3.2% CVF. The method scales sub-linearly to M=8 constraints, settles on-chain within one Ethereum block, and yields a 2.1X reward improvement on Safety-Gymnasium, confirming domain-agnostic generalization.

Problem

• fair order matching
• execution disparity
• constrained optimization
• market fairness
• algorithmic trading

Innovation

• Constrained Policy Optimization
• Fair Order Matching
• Fisher Information Manifold
• Spectral Normalization
• PID-Controlled Safety Margins