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.

Blockchains implement decentralized monetary systems and applications. Recent advancements enable what we call tethering a blockchain to a primary blockchain, securing the tethered chain by nodes that post primary-chain tokens as collateral. The collateral ensures nodes behave as intended, until they withdraw it. Unlike a Proof of Stake blockchain which uses its own token as collateral, using primary-chain tokens shields the tethered chain from the volatility of its own token. State-of-the-art tethered blockchains either rely on centralization, or make extreme assumptions: that all communication is synchronous, that operators remain correct even post-withdrawal, or that withdrawals can be indefinitely delayed by tethered-chain failures. We prove that with partial synchrony, there is no solution to the problem. However, under the standard assumptions that communication with the primary chain is synchronous and communication among the tethered chain nodes is partially synchronous, there is a solution. We present a tethered-chain protocol called Aegis. Aegis uses references from its blocks to primary blocks to define committees, checkpoints on the primary chain to perpetuate decisions, and resets to establish new committees when previous ones become obsolete. It ensures safety at all times and rapid progress when latency among Aegis nodes is low.

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].