Designing for Decentralized Finance through Differentiable Optimization, and a Study of Bayesian Optimization

Abstract

Decentralized finance (DeFi) is the concept of building financial infrastructures without relying on centralized intermediaries. A notable development in DeFi is the creation of decentralized exchanges (DEXs), which operate as smart contracts on a blockchain. Due to the high cost of on-chain operations, automated market makers (AMMs) such as Uniswap v3 have emerged as the prevailing model of liquidity provision on DEXs. Two closely related research questions arise in the DeFi space: (1) What are the optimal strategies of liquidity providers given an AMM design such as Uniswap v3? (2) How should the design of AMMs be optimized to achieve objectives such as profit maximization? This thesis addresses these two central research questions using computational methods, in particular, through differentiable optimization. Chapters 2 and 3 study the optimal strategies of liquidity providers (LPs) in Uniswap v3. In both chapters' formulations, the expected utility of an LP is differentiable with respect to its liquidity allocation under any exogenous price sequence, enabling differentiable optimization of LP strategies. With the formulation of a convex stochastic optimization problem that can be solved in a differentiable manner, Chapter 2 explores optimal static LP strategies in economic settings with varying factors such as an LP's belief about price dynamics, risk aversion, and for different specifications of the Uniswap v3 liquidity pool. Understanding LP strategies also leads to insights into the design of Uniswap v3 liquidity pools. Under a similar optimization framework, Chapter 3 extends from static LP strategies to dynamic LP strategies, specifically LP strategies that reallocate liquidity whenever the price movement reaches a certain threshold. These proposed dynamic strategies—particularly context-dependent variants modeled by a neural network, which adapt the shape of liquidity allocation to contextual information such as price and moving average of non-arbitrage trade volume at the time of reallocation—are shown to lead to significant gains compared to static LP strategies. Taking a broader perspective on AMM design, Chapter 4 optimizes market-making mechanisms for a single trade in settings with multiple traded goods, seeking market maker profit maximization under adverse selection. Conjectures of optimal mechanisms are generated using tools of differentiable economics, which uses differentiable optimization for economic design. To prove the optimality of proposed mechanisms, a duality theorem is established between the market-making mechanism design problem and an optimal transport problem. This approach of combining differentiable economics with theoretical analysis is used to develop a parameterized class of optimal market-making mechanisms. These results also establish that, in some cases, the optimal market maker across multiple goods must use complex bundling. Additional conjectures about the structure of optimal mechanisms are presented, and an empirical optimality bound is established for some conjectures by approximately solving the dual with linear programming. The second part of this thesis studies transfer learning of the Gaussian process (GP) prior in Bayesian optimization (BO), a widely used black-box function optimization method. Previous GP-based transfer learning methods for BO are limited to utilizing historical data collected from black-box functions with the same domain as the new black-box function to be optimized. The proposed method, model pre-training on heterogeneous domains (MPHD), employs a neural network that maps from domain-specific contextual information to specifications of hierarchical GPs for a given domain. As a result, MPHD is able to transfer knowledge across heterogeneous domains such as hyperparameter-tuning for different machine learning models. It is shown through theoretical analysis and empirical results that MPHD is a practical transfer learning method for BO, with demonstrations of competitive performance on challenging real-world hyperparameter-tuning tasks.Engineering and Applied Sciences - Computer Scienc