Non-stochastic Bandits With Evolving Observations

We introduce a novel online learning framework that unifies and generalizes pre-established models, such as delayed and corrupted feedback, to encompass adversarial environments where action feedback evolves over time. In this setting, the observed loss is arbitrary and may not correlate with the true loss incurred, with each round updating previous observations adversarially. We propose regret minimization algorithms for both the full-information and bandit settings, with regret bounds quantified by the average feedback accuracy relative to the true loss. Our algorithms match the known regret bounds across many special cases, while also introducing previously unknown bounds.

Uniswap Liquidity Provision: An Online Learning Approach

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.

Individual Regret in Cooperative Nonstochastic Multi-Armed Bandits

We study agents communicating over an underlying network by exchanging messages, in order to optimize their individual regret in a common nonstochastic multi-armed bandit problem. We derive regret minimization algorithms that guarantee for each agent $v$ an individual expected regret of \[ \widetilde{O}\left(\sqrt{\left(1+\frac{K}{\left|\mathcal{N}\left(v\right)\right|}\right)T}\right), \] where $T$ is the number of time steps, $K$ is the number of actions and $\mathcal{N}\left(v\right)$ is the set of neighbors of agent $v$ in the communication graph. We present algorithms both for the case that the communication graph is known to all the agents, and for the case that the graph is unknown. When the graph is unknown, each agent knows only the set of its neighbors and an upper bound on the total number of agents. The individual regret between the models differs only by a logarithmic factor. Our work resolves an open problem from [Cesa-Bianchi et al., 2019b].