Marginal Price Optimization

TL;DR

This paper presents a novel boundary-restricted optimization framework for AMM markets that significantly enhances speed and robustness over traditional convex optimization methods, especially in high-dimensional and leveraged scenarios.

Contribution

It introduces a boundary-based reformulation of the optimal routing and arbitrage problem, reducing complexity and improving computational efficiency in AMM market optimization.

Findings

Achieves up to 200x speed improvement over existing solvers

Provides a robust solution for highly leveraged and high-dimensional cases

Offers an approximation method for infinitely concentrated liquidity scenarios

Abstract

We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can parameterize this boundary using a set of prices, and a potentially very high dimensional optimization problem (2 optimization variables per curve) gets reduced to a much lower dimensional root finding problem (1 optimization variable per token, regardless of the number of the curves). Our reformulation is similar to the dual problem of a reformulation of the original convex problem. We show our reformulation of the problem is equivalent to the original formulation except in the case of infinitely concentrated liquidity, where we provide a suitable approximation. Our formulation performs far better than the original one in terms of speed - we obtain an improvement of up to 200x against Clarabel, the new CVXPY default solver - and robustness, especially on levered curves.