[Paper Review] Uniswap Liquidity Provision: An Online Learning Approach

Yogev Bar-On, Yishay Mansour|arXiv (Cornell University)|Feb 1, 2023

Advanced Bandit Algorithms ResearchDecision Sciences3 citations

TL;DR

This paper formulates Uniswap v3 liquidity provision as an online learning problem with non-stochastic rewards, proposing a dynamic strategy using regret-minimization and expert advice to guarantee a positive reward for liquidity providers when trading volume is sufficiently high. The key contribution is a theoretical lower bound on rewards that holds even under adversarial price changes, validated empirically using real 2022 Ethereum data.

ABSTRACT

Decentralized Exchanges (DEXs) are new types of marketplaces leveraging Blockchain technology. They allow users to trade assets with Automatic Market Makers (AMM), using funds provided by liquidity providers, removing the need for order books. One such DEX, Uniswap v3, allows liquidity providers to allocate funds more efficiently by specifying an active price interval for their funds. This introduces the problem of finding an optimal strategy for choosing price intervals. We formalize this problem as an online learning problem with non-stochastic rewards. We use regret-minimization methods to show a liquidity provision strategy that guarantees a lower bound on the reward. This is true even for non-stochastic changes to asset pricing, and we express this bound in terms of the trading volume.

Motivation & Objective

• To address the challenge of selecting optimal price intervals for liquidity provision in Uniswap v3, where poor interval choices lead to significant losses due to price misalignment.
• To formalize the liquidity provision problem as an online learning framework with non-stochastic rewards, enabling strategies that perform well even without assumptions about future price dynamics.
• To develop a dynamic, adaptive liquidity provision strategy that guarantees a positive reward for sufficiently high trading volume, regardless of price movement patterns.
• To validate the theoretical model using real-world Uniswap v3 data from 2022, demonstrating the practical viability of the proposed approach.

Proposed method

• The authors model liquidity provision as an online learning problem with expert advice, where each expert corresponds to a fixed price interval (concentration controller) for liquidity allocation.
• They introduce a dynamic strategy based on the Exponential Weights Algorithm (EWA), which adaptively combines the performance of multiple static strategies to minimize regret.
• The reward function is derived from the change in liquidity provider value, incorporating trading fees and impermanent loss, with a theoretical lower bound expressed in terms of average logarithmic price change and trading volume.
• The model assumes no stochastic assumptions on price evolution, making it robust to adversarial or non-stochastic market movements.
• Theoretical analysis establishes a lower bound on total reward that depends on the product of trading volume and the logarithmic price change magnitude.
• Empirical validation uses hourly data from Uniswap v3 pools (USDT/USDC and ETH/USDC) on Ethereum via Google BigQuery, simulating static and adaptive strategies over the full 2022 year.

Experimental results

Research questions

• RQ1 Can a liquidity provision strategy be designed that guarantees a positive reward even when asset prices change in a non-stochastic, adversarial manner?
• RQ2 What is the minimum required trading volume to ensure a positive reward in Uniswap v3 liquidity provision under adversarial price changes?
• RQ3 How does the performance of an adaptive strategy based on expert advice compare to static strategies across different liquidity pools and time periods?
• RQ4 To what extent do real-world trading volumes in Uniswap v3 pools satisfy the theoretical conditions for a positive reward?
• RQ5 Can the proposed online learning framework be effectively calibrated and validated using empirical blockchain data?

Key findings

• The Exponential Weights Adaptive (EWA) strategy achieved a total reward of 0.515 USDC per unit of liquidity in the USDT/USDC pool during 2022, outperforming all individual static strategies.
• In the ETH/USDC pool, the EWA strategy achieved a reward of -0.486 USDC, indicating negative performance under baseline conditions, but this turned positive with a 10% artificial increase in trading volume.
• The theoretical lower bound on reward is proportional to the product of the average logarithmic price change and the trading volume, with the benchmark term $ \frac{P \ln d}{\gamma} $ serving as a threshold for positive performance.
• Empirical data confirmed that $ d^{\left| \rho_t \right|} < 2 $ for all hourly intervals in 2022, validating the key assumption underlying the theoretical model.
• The EWA strategy’s performance closely tracked the best-performing static strategy in both USDT/USDC and ETH/USDC pools, demonstrating strong regret minimization.
• The model’s theoretical framework was empirically validated as a strong approximation of real-world liquidity provision dynamics, particularly when trading volume is high.