TY - GEN

T1 - A Near-Optimal Best-of-Both-Worlds Algorithm for Online Learning with Feedback Graphs

AU - Rouyer, Chloé

AU - van der Hoeven, Dirk

AU - Cesa-Bianchi, Nicolò

AU - Seldin, Yevgeny

PY - 2022

Y1 - 2022

N2 - We consider online learning with feedback graphs, a sequential decision-making framework where the learner's feedback is determined by a directed graph over the action set. We present a computationally efficient algorithm for learning in this framework that simultaneously achieves near-optimal regret bounds in both stochastic and adversarial environments. The bound against oblivious adversaries is O~(αT−−−√), where T is the time horizon and α is the independence number of the feedback graph. The bound against stochastic environments is O((lnT)2maxS∈I(G)∑i∈SΔ−1i) where I(G) is the family of all independent sets in a suitably defined undirected version of the graph and Δi are the suboptimality gaps. The algorithm combines ideas from the EXP3++ algorithm for stochastic and adversarial bandits and the EXP3.G algorithm for feedback graphs with a novel exploration scheme. The scheme, which exploits the structure of the graph to reduce exploration, is key to obtain best-of-both-worlds guarantees with feedback graphs. We also extend our algorithm and results to a setting where the feedback graphs are allowed to change over time.

AB - We consider online learning with feedback graphs, a sequential decision-making framework where the learner's feedback is determined by a directed graph over the action set. We present a computationally efficient algorithm for learning in this framework that simultaneously achieves near-optimal regret bounds in both stochastic and adversarial environments. The bound against oblivious adversaries is O~(αT−−−√), where T is the time horizon and α is the independence number of the feedback graph. The bound against stochastic environments is O((lnT)2maxS∈I(G)∑i∈SΔ−1i) where I(G) is the family of all independent sets in a suitably defined undirected version of the graph and Δi are the suboptimality gaps. The algorithm combines ideas from the EXP3++ algorithm for stochastic and adversarial bandits and the EXP3.G algorithm for feedback graphs with a novel exploration scheme. The scheme, which exploits the structure of the graph to reduce exploration, is key to obtain best-of-both-worlds guarantees with feedback graphs. We also extend our algorithm and results to a setting where the feedback graphs are allowed to change over time.

M3 - Article in proceedings

SP - 35035

EP - 35048

BT - Advances in Neural Information Processing Systems 35 (NeurIPS 2022)

PB - NeurIPS Proceedings

Y2 - 28 November 2022 through 9 December 2022

ER -