RAmmStein: Regime Adaptation in Mean-reverting Markets with Stein Thresholds -- Optimal Impulse Control in Concentrated AMMs

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 evaluate the framework using high-frequency 1Hz Coinbase trade data comprising over 6.8M trades. Experimental results show that RAmmStein achieves a superior net ROI of 0.72% compared to both passive and aggressive strategies. Notably, the agent reduces rebalancing frequency by 67% compared to a greedy rebalancing strategy while maintaining 88% active time. 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.