Paper: arXiv 2602.19419

Authors: Pranay Anchuri

Abstract

Concentrated liquidity provision in decentralized exchanges presents a fundamental Impulse Control problem. Liquidity Providers (LPs) face a non-trivial trade-off between maximizing fee accrual through tight price-range concentration and minimizing the friction costs of rebalancing, including gas fees and swap slippage. Existing methods typically employ heuristic or threshold strategies that fail to account for market dynamics. This paper formulates liquidity management as an optimal control problem and derives the corresponding Hamilton-Jacobi-Bellman quasi-variational inequality (HJB-QVI). We present an approximate solution RAmmStein, a Deep Reinforcement Learning method that incorporates the mean-reversion speed (theta) of an Ornstein-Uhlenbeck process among other features as input to the model. We demonstrate that the agent learns to separate the state space into regions of action and inaction. We further extend the framework with RAmmStein-Width, which jointly optimizes rebalancing timing and position width via a 6-action DDQN. We evaluate the framework using high-frequency 1Hz Coinbase trade data comprising over 6.8M trades on a realistic environment (10M TVL, 1% default width). Experimental results show that RAmmStein achieves a net ROI of 1.60%, the highest among all realistic (non-omniscient) strategies, while greedy strategies lose up to -8.4% to gas costs. Notably, the agent reduces rebalancing frequency by 85% compared to greedy rebalancing. RAmmStein-Width discovers extreme parsimony on its own, executing only 9 rebalances and $40 in gas, and degrades more slowly than all active strategies at elevated gas costs. Our results demonstrate that regime-aware laziness can significantly improve capital efficiency by preserving the returns that would otherwise be eroded by the operational costs.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong combination of theoretical mathematical rigor (HJB-QVI formulation for optimal impulse control) and extensive empirical evaluation on high-frequency market data (6.8M+ trades). Incorporating Ornstein-Uhlenbeck mean-reversion dynamics directly into a reinforcement learning framework presents an impactful and original solution to the LP rebalancing paradox in concentrated AMMs.

Research Flowchart

  flowchart TD
    A["Research Goal: Optimize CLMM Liquidity Provision via Impulse Control"] --> B["Formulate HJB-QVI & Modeled Market via OU Process"]
    B --> C["Data Input: 6.8M 1Hz Coinbase Trades & Market Dynamics"]
    C --> D["Train DRL Agents: RAmmStein & RAmmStein-Width DDQN"]
    D --> E["Action Space Segmentation: Action vs. Inaction Regions Learned"]
    E --> F["Outcomes: 1.60% Net ROI, 85% Rebalance Reduction & High Gas Efficiency"]