Diverse Approaches to Optimal Execution Schedule Generation

TL;DR

This paper applies MAP-Elites, a quality-diversity algorithm, to trade execution, generating diverse regime-specific strategies that outperform baseline policies in simulated environments, highlighting potential for adaptive trading methods.

Contribution

First application of MAP-Elites to trade execution, creating diverse specialists for different market regimes and demonstrating their performance improvements.

Findings

Specialists achieve 8-10% performance gains within niches

CNN-based PPO achieves 2.13 bps slippage vs. 5.23 bps VWAP

Simulation environment validated with $R^2>0.02$ on real data

Abstract

We present the first application of MAP-Elites, a quality-diversity algorithm, to trade execution. Rather than searching for a single optimal policy, MAP-Elites generates a diverse portfolio of regime-specialist strategies indexed by liquidity and volatility conditions. Individual specialists achieve 8-10% performance improvements within their behavioural niches, while other cells show degradation, suggesting opportunities for ensemble approaches that combine improved specialists with the baseline PPO policy. Results indicate that quality-diversity methods offer promise for regime-adaptive execution, though substantial computational resources per behavioural cell may be required for robust specialist development across all market conditions. To ensure experimental integrity, we develop a calibrated Gymnasium environment focused on order scheduling rather than tactical placement decisions. The simulator features a transient impact model with exponential decay and square-root volume scaling, fit to 400+ U.S. equities with $R^2>0.02$ out-of-sample. Within this environment, two Proximal Policy Optimization architectures - both MLP and CNN feature extractors - demonstrate substantial improvements over industry baselines, with the CNN variant achieving 2.13 bps arrival slippage versus 5.23 bps for VWAP on 4,900 out-of-sample orders ($21B notional). These results validate both the simulation realism and provide strong single-policy baselines for quality-diversity methods.