Organizations: Department of Computer Science, University of Colorado, Colorado Springs, 1420 Austin Bluffs Pkwy, Colorado Springs, CO 80918, USA · Department of Computer Science, University of Iowa, 101 Jessup Hall, Iowa City, IA 52242, USA
Reinforcement learning trading systems published in the academic literature overwhelmingly rely on price-aggregate state representations (OHLCV bars) or limit-order-book depth features, leaving microstructure pattern theories from the practitioner literature, namely Auction Market Theory and Market Profile, without a peer-reviewed computational instantiation. We present ViperQ, a reinforcement learning system whose state representation is built explicitly from Auction Market Theory primitives: Volume Point of Control, Value Area position, Low Volume Node flags, Cumulative Volume Delta divergence, and tape-velocity signatures, assembled into a 20-dimensional Z-normalised vector. Two Proximal Policy Optimisation agents are trained with a prospect theory-grounded asymmetric reward function that penalises losing holds at a magnitude consistent with Kahneman and Tversky's loss-aversion coefficient. Evaluated on a held-out twelve-month partition of institutional tick data the agents have never seen, ViperQ achieves +163.6% ROI on TSLA (-27.5% max drawdown, 27,019 trades) and +116.5% ROI on NVDA (-47.8% max drawdown, 12,892 trades) under zero leverage. The results establish Auction Market Theory features as a tractable structured input modality for sequential decision-making on financial time series and motivate further work on microstructure-aware policy learning.
Figures & tables
Figure 1: Matching engine: aggressive market flow consumes passive resting liquidity; price moves only when the resting size at the touch is fully consumed. ViperQ observes the consumption rate via CVD slope, tape velocity, and imbalance ratio (Section 3.2 ).
Figure 2: Auction Market Theory: the market oscillates between balance and imbalance. The agent targets the transition from Value Area A to Value Area B, remaining flat during balance phases and holding through breakouts.
Dim
Name
Construct
Block A: AMT / microstructure patterns
1
z_price_vwap
Z(price − VWAP), gravity to fair value
2
z_price_vpoc
Z(price − VPOC), distance to Volume Point of Control
3
dist_to_wall
Normalised position within 300 s high–low range
4
cvd_slope
60 s first-difference of CVD
5
cvd_divergence
Binary flag on 300 s price–CVD correlation <−0.5
Table 1: The 20-dimensional state vector st . Block A encodes Auction Market Theory and microstructure patterns; Block B is injected at runtime from the agent’s position; Block C supplies short-horizon memory.
Constraint
TSLA agent
NVDA agent
Min. hold (s)
300
300
Drawdown shock
−2.0 /step
−2.0 /step
Trend bonus
none
+0.10 /step ( U_{t}>\100$ )
Table 2: Asset-specific training configurations. The same architecture and state vector yield two distinct profitable policies. All constants listed here, with their selection mechanism, appear in Table 3 .
Figure 3: ViperQ system architecture: pattern extraction (Layers 1–3), policy inference (Layer 4, dual PPO), and risk-bounded execution (Layer 5 and output).
Element
Value
Mech.
Source / rationale
Reward function (Eqs. 1 – 2 , items (3)–(6))
α (PnL scaling)
0.01
VAL
PPO gradient stability
fsyn
$0.50/share
VAL
suppresses sub-tick scalping (§ 6.3 )
Hold gain branch
+0.001⋅Ut
VAL
disposition-effect tuning
Hold loss branch
−0.05−0.005∣Ut∣
TH
Tversky–Kahneman λ≈2.25 [ 26 ]
Trend bonus
+0.10 /step
VAL
held-winner reinforcement
Table 3: Master hyperparameter table. Mech. : VAL = selected on the validation slice of the training partition; CONV = industry convention for intraday proprietary trading, taken without tuning; TH = theory-derived with literature anchor; LIT = library default (Stable-Baselines3).
Metric
TSLA
NVDA
Final balance
$26,364.87
$21,652.86
PnL
+ $16,364.87
+ $11,652.86
ROI
+163.6%
+116.5%
Maximum drawdown
−27.5%
−47.8%
Total trades
27,019
12,892
Test-set bars
33.4 M
16.5 M
Table 4: ViperQ performance on the held-out test partition (final 20% of data, never seen during training). Initial capital 10,000perasset;zeroleverage;0.0002/share regulatory fees applied.
System
Algorithm
Asset / Horizon
ROI %
MDD %
DeepLOB [ 30 ]
CNN sup.
LOB / events
n.a.
n.a.
DRL-Trade [ 31 ]
DQN/PG/A2C
50 fut / daily
pos. Sharpe
n.r.
FinRL [ 29 ]
Ensemble
Dow 30 / daily
≈30
−10.2
PPO-Exec [ 15 ]
PPO/LSTM
LOB / per-step
beats TWAP
n.r.
TDQN [ 23 ]
DQN
30 eq / daily
beats pass.
n.r.
HFT-PPO [ 1 ]
PPO
INTC / events
stable +
n.r.
Table 5: ViperQ vs. recently published RL trading systems with retrievable performance numbers. Typical published range [ 20 ] : ROI [5%,40%] , MDD [−5%,−25%] . “n.r.” = not reported; “n.a.” = not applicable.
Figure 4: ViperQ in the ROI/MDD plane against published RL trading systems with concrete numbers. The shaded region marks the typical published range surveyed in [ 20 ] .
Market making under realistic order-flow dynamics is challenging due to the clustered, self-exciting nature of order arrivals, which are naturally modeled by non-Markovian Hawkes processes. We propose a model-free reinforcement learning (RL) framework for market making with general Hawkes order-flow dynamics. We first establish non-asymptotic performance bounds that quantify the loss incurred by approximating the infinite-dimensional Hawkes state using a finite collection of exponentially weighted features. Guided by this analysis, we introduce the Hawkes-Structured Network (HSN), a novel neural architecture that encodes historical order flow through a learnable mixture-of-exponentials filter. HSN is trained end-to-end using model-free RL, jointly optimizing the feature representation and quoting policy directly from reward feedback. Experiments on single- and multi-asset market-making problems with mixture-of-exponentials, power-law, and regime-switching kernels demonstrate that HSN outperforms general-purpose neural architectures, achieving higher trading rewards while implicitly recovering the underlying order-flow intensities.
Fernando Acero, Philipp Plank, Yufei Zhang
Department of Mathematics, Imperial College London, United Kingdom
This paper studies reinforcement learning for high-frequency trading on limit order books by pairing an Order-Flow-based state model with policy-gradient methods. Instead of value-based RL techniques like tabular Q-learning, our approach deploys policy-based methods like vanilla PPO and DeepSeekMath-inspired variants like GRPO and GSPO, that use group-normalized updates and downside-aware shaping. On backtests with financial assets AMZN, AAPL, and GOOG under a simplified backtesting setup based on spread-scaled rewards, these new policies improve net average PnL, profitability, and drawdown over the Q-Learning baseline. Our results show that (1) Order-Flow signals are an adequate state for policy RL and (2) group-aware PPO surrogates are preferable over value-based baselines.
Sayak Charabarty, Souradip Pal
Department of Computer Science Northwestern University Evanston, IL 60208, USA · School of Electrical and Computer Engineering Purdue University West Lafayette, IN 47906, USA
Market-making strategies in real limit order book markets face substantial model uncertainty and regime-shift risk. Existing adversarial reinforcement learning approaches improve robustness by formulating the Avellaneda--Stoikov market-making problem as a zero-sum game between a market maker and an environmental adversary. However, these approaches typically rely on Poisson order arrivals and neglect trade-induced price impact, limiting their ability to capture important high-frequency market microstructure effects such as clustered order flow, self-excitation, and post-trade price feedback. We extend adversarial reinforcement learning for market making to a more complex environment with Hawkes self-exciting order arrivals and trade-induced price impact. To mitigate the increased non-stationarity introduced by the expanded regime space, we incorporate an LSTM module that explicitly models the temporal structure of recent observations. We further characterize the equilibrium properties of the proposed framework through both game-theoretic analysis and numerical experiments, and introduce a robustness evaluation protocol focused on improvements in the left tail of the return distribution. Experimental results across a range of market regimes show that the proposed method achieves improved left-tail performance in most complex microstructure environments. In particular, the gains are pronounced in regimes with strong Hawkes excitation and low-to-moderate price impact. Bootstrap tests provide no evidence that these improvements are obtained through a stronger terminal directional inventory bias. These results suggest that combining adversarial training with temporal state representation can improve the robustness of reinforcement-learning-based market-making strategies under order-flow self-excitation, price impact, and regime uncertainty.
Hao Yang, Zhenguo Xu
North China Institute of Computer System Engineering, Beijing, China · University of Science and Technology of China, Hefei, China