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Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading prices in these pools often trail behind those in more dynamic, centralized exchanges, leading to potential arbitrage losses for LPs. This issue is tackled by adapting market maker bonding curves to trader behavior, based on the classical market microstructure model of Glosten and Milgrom. Our approach ensures a zero-profit condition for the market maker’s prices. We derive the differential equation that an optimal adaptive curve should follow to minimize arbitrage losses while remaining competitive. Solutions to this optimality equation are obtained for standard Gaussian and Lognormal price models using Kalman filtering. A key feature of our method is its ability to estimate the external market price without relying on price or loss oracles. We also provide an equivalent differential equation for the implied dynamics of canonical static bonding curves and establish conditions for their optimality. Our algorithms demonstrate robustness to changing market conditions and adversarial perturbations, and we offer an on-chain implementation using Uniswap v4 alongside off-chain AI co-processors. 

Decentralized finance (DeFi) borrowing and lending platforms are crucial to the decentralized economy, involving two main participants: lenders who provide assets for interest and borrowers who offer collateral exceeding their debt and pay interest. Collateral volatility necessitates over-collateralization to protect lenders and ensure competitive returns. Traditional DeFi platforms use a fixed interest rate curve based on the utilization rate (the fraction of available assets borrowed) and determine over-collateralization offline through simulations to manage risk. This method doesn't adapt well to dynamic market changes, such as price fluctuations and evolving user needs, often resulting in losses for lenders or borrowers. In this paper, we introduce an adaptive, data-driven protocol for DeFi borrowing and lending. Our approach includes a high-frequency controller that dynamically adjusts interest rates to maintain market stability and competitiveness with external markets. Unlike traditional protocols, which rely on user reactions and often adjust slowly, our controller uses a learning-based algorithm to quickly find optimal interest rates, reducing the opportunity cost for users during periods of misalignment with external rates. Additionally, we use a low-frequency planner that analyzes user behavior to set an optimal over-collateralization ratio, balancing risk reduction with profit maximization over the long term. This dual approach is essential for adaptive markets: the short-term component maintains market stability, preventing exploitation, while the long-term planner optimizes market parameters to enhance profitability and reduce risks. We provide theoretical guarantees on the convergence rates and adversarial robustness of the short-term component and the long-term effectiveness of our protocol. Empirical validation confirms our protocol’s theoretical benefits.