Tommaso R. Cesari

Nicolò Cesa-Bianchi, Tommaso R. Cesari, Riccardo Della Vecchia

We study the interplay between communication and feedback in a cooperative online learning setting, where a network of communicating agents learn a common sequential decision-making task through a feedback graph. We bound the network regret in terms of the independence number of the strong product between the communication network and the feedback graph. Our analysis recovers as special cases many previously known bounds for cooperative online learning with expert or bandit feedback. We also prove an instance-based lower bound, demonstrating that our positive results are not improvable except in pathological cases. Experiments on synthetic data confirm our theoretical findings.

Nicolò Cesa-Bianchi, Tommaso R. Cesari, Claire Monteleoni

We study an asynchronous online learning setting with a network of agents. At each time step, some of the agents are activated, requested to make a prediction, and pay the corresponding loss. The loss function is then revealed to these agents and also to their neighbors in the network. Our results characterize how much knowing the network structure affects the regret as a function of the model of agent activations. When activations are stochastic, the optimal regret (up to constant factors) is shown to be of order $\sqrt{αT}$, where $T$ is the horizon and $α$ is the independence number of the network. We prove that the upper bound is achieved even when agents have no information about the network structure. When activations are adversarial the situation changes dramatically: if agents ignore the network structure, a $Ω(T)$ lower bound on the regret can be proven, showing that learning is impossible. However, when agents can choose to ignore some of their neighbors based on the knowledge of the network structure, we prove a $O(\sqrt{\overlineχ T})$ sublinear regret bound, where $\overlineχ \ge α$ is the clique-covering number of the network.