# Diverse Approaches to Optimal Execution Schedule Generation

arXiv: https://arxiv.org/abs/2601.22113 · HTML: https://mlsanity.com/paper/2601.22113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 28 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 9 of 9)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Quality-Diversity Optimization: a novel branch of stochastic optimization](https://mlsanity.com/paper/2012.04322/) (2020)
- [ABIDES-Gym: Gym Environments for Multi-Agent Discrete Event Simulation and Application to Financial Markets](https://mlsanity.com/paper/2110.14771/) (2021)
- [Accelerated Quality-Diversity through Massive Parallelism](https://mlsanity.com/paper/2202.01258/) (2022)
- [Synergizing Quality-Diversity with Descriptor-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2401.08632/) (2023)
- [Optimal Execution with Reinforcement Learning](https://mlsanity.com/paper/2411.06389/) (2024)
- [Extract-QD Framework: A Generic Approach for Quality-Diversity in Noisy, Stochastic or Uncertain Domains](https://mlsanity.com/paper/2502.06585/) (2025)

## Abstract (arXiv)

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 R2>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.