Learn Continuously, Act Discretely: Hybrid Action-Space Reinforcement Learning For Optimal Execution
Learn Continuously, Act Discretely: Hybrid Action-Space Reinforcement Learning For Optimal Execution
This paper addresses the optimal execution problem with limit orders, focusing on the challenge of setting limit prices in a hybrid action space that is both continuous (percentage changes) and discrete (tick sizes). The authors propose HALOP (Hybrid Action-space Limit Order Placement), a two-stage reinforcement learning method. In Stage 1, a discretized Gaussian policy selects a target percentage change in price, scoping a subset of discrete actions for generalization across stocks. In Stage 2, a Gaussian-and-Softmax policy chooses a specific tick-based action from the subset, enabling specialization for individual stock characteristics. The method uses PPO for policy optimization and a neural network with 1D-CNN and self-attention for state representation. Experiments on CSI 300 data show that HALOP significantly outperforms market orders, vanilla PPO with continuous or discrete actions, and previous learning-based methods like ODP. It achieves an average excess return of 4.41 bps over TWAP with high statistical significance and improved stability. A grouping study confirms that HALOP balances generalization and specialization, particularly benefiting low-priced stocks. The work provides a practical framework for applying RL to real-world trading where action spaces have both continuous and discrete aspects.
Highlights
- 1Proposes a hybrid action-space reinforcement learning method (HALOP) for optimal execution with limit orders, combining continuous control for generalization and discrete control for specialization.
- 2Introduces discretized Gaussian and Gaussian-and-Softmax policies to bridge continuous and discrete action spaces.
- 3Achieves significant excess returns over TWAP benchmark (4.41 bps) with high statistical significance (t-value 123.2) and improved stability.
- 4Demonstrates superior generalization across stocks with different price levels and specialization for low-priced stocks.
- 5Outperforms vanilla PPO with Gaussian or Softmax policies and previous learning-based methods like ODP.
Methods
- MHybrid Action-Space Limit Order Placement (HALOP) with two stages: Stage 1 uses a discretized Gaussian policy for generalization; Stage 2 uses a Gaussian-and-Softmax policy for fine-grained discrete action selection.
- MProximal Policy Optimization (PPO) as the base RL algorithm.
- MSequence encoding with 1D convolutional neural networks and multi-head self-attention for state representation.
- MSimulation environment built from historical CSI 300 index data with realistic constraints (tick size, communication delay, order size limits).
Results
- RHALOP achieves an average excess return of 4.41 bps over TWAP with market orders, with a PnL of 2.98 bps and t-value of 123.2.
- RHALOP outperforms PPO-Gaussian (1.41 bps return, 4.61 Std) and PPO-Softmax (2.12 bps return, 35.88 Std) in both return and stability.
- RHALOP Stage-1 alone yields 3.69 bps return, showing strong generalization; adding Stage-2 improves to 4.41 bps, especially for low-priced stocks.
- RGrouping study shows HALOP improves returns across all price groups, with the largest gain for low-priced stocks (from ~3.5 to ~4.5 bps).
- RHALOP reduces standard deviation of returns compared to PPO-Softmax and improves PnL across different volume schedules (TWAP, VWAP, ODP).
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