Formalize the no‑regret connection for target weight mechanisms in PDLPs

Formalize the connection between target weight mechanisms for Perpetual Demand Lending Pools—defined by minimizing deviation between the pool’s price‑weighted asset composition and a target weight via a discount function F—and no‑regret online learning algorithms on the simplex (such as the Hedge algorithm), and ascertain conditions under which target‑weight update rules enjoy no‑regret guarantees.

Background

The paper introduces target weight mechanisms (TWMs) that incentivize liquidity providers to rebalance a PDLP’s portfolio toward a specified target weight by offering discounts/subsidies via a function F. This mechanism indirectly attempts to solve an optimization problem that minimizes deviation between current and target price‑weighted asset compositions under pool constraints.

The authors observe that the incentive structure resembles online learning on the simplex (e.g., the Hedge algorithm) and suggest that appropriately designed weight‑update rules may be no‑regret. However, they explicitly state that formalizing this connection is left for future work.