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.

翻译：去中心化交易所（DEX）是利用区块链技术的新型市场平台。它们允许用户通过自动做市商（AMM）利用流动性提供者提供的资金进行资产交易，从而消除了对订单簿的需求。其中一种DEX——Uniswap v3允许流动性提供者通过指定其资金的活跃价格区间来更高效地分配资金。这就引出了如何为选择价格区间寻找最优策略的问题。我们将该问题形式化为一个具有非随机奖励的在线学习问题。我们使用遗憾最小化方法提出了一种流动性供应策略，该策略可保证奖励的下界。即使资产价格发生非随机变化，该结论依然成立，并且我们用交易量来表示该下界。