  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.
