Constrained Policy Optimization for Provably Fair Order Matching

TL;DR

This paper introduces CPO-FOAM, a novel constrained policy optimization method for fair order matching that ensures provable fairness and stability while maintaining high throughput across diverse market regimes.

Contribution

It formulates fair order matching as a Constrained Markov Decision Process and develops a scalable, stable optimization algorithm with proven fairness and efficiency guarantees.

Findings

Recovers 95.9% of unconstrained throughput with 2.5% violation frequency on NASDAQ data.

Achieves 98.4% reward envelope capture at 3.2% CVF on crypto-asset data.

Scales sub-linearly to 8 constraints and improves reward by 2.1X on 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.