Adversarial Bandits with Knapsacks

Symposium on Foundations of Computer Science (FOCS)


We consider Bandits with Knapsacks (henceforth, BwK), a general model for multi-armed bandits under supply/budget constraints. In particular, a bandit algorithm needs to solve a well-known knapsack problem: find an optimal packing of items into a limited-size knapsack. The BwK problem is a common generalization of numerous motivating examples, which range from dynamic pricing to repeated auctions to dynamic ad allocation to network routing and scheduling. While the prior work on BwK focused on the stochastic version, we pioneer the other extreme in which the outcomes can be chosen adversarially. This is a considerably harder problem, compared to both the stochastic version and the “classic” adversarial bandits, in that regret minimization is no longer feasible. Instead, the objective is to minimize the competitive ratio: the ratio of the benchmark reward to algorithm’s reward.

We design an algorithm with competitive ratio O(log T) relative to the best fixed distribution over actions, where T is the time horizon; we also prove a matching lower bound. The key conceptual contribution is a new perspective on the stochastic version of the problem. We suggest a new algorithm for the stochastic version, which builds on the framework of regret minimization in repeated games and admits a substantially simpler analysis compared to prior work. We then analyze this algorithm for the adversarial version, and use it as a subroutine to solve the latter.

Our algorithm is the first “black-box reduction” from bandits to BwK: it takes an arbitrary bandit algorithm and uses it as a subroutine. We use this reduction to derive several extensions.

Related Publications

All Publications

COLING - December 8, 2020

Best Practices for Data-Efficient Modeling in NLG: How to Train Production-Ready Neural Models with Less Data

Ankit Arun, Soumya Batra, Vikas Bhardwaj, Ashwini Challa, Pinar Donmez, Peyman Heidari, Hakan Inan, Shashank Jain, Anuj Kumar, Shawn Mei, Karthik Mohan, Michael White

NeurIPS - December 1, 2020

Continuous Surface Embeddings

Natalia Neverova, David Novotny, Vasil Khalidov, Marc Szafraniec, Patrick Labatut, Andrea Vedaldi

NeurIPS - November 25, 2020

Ridge Rider: Finding Diverse Solutions by Following Eigenvectors of the Hessian

Jack Parker-Holder, Luke Metz, Cinjon Resnick, Hengyuan Hu, Adam Lerer, Alistair Letcher, Alex Peysakhovich, Aldo Pacchiano, Jakob Foerster

NeurIPS - November 30, 2020

Adversarial Attacks on Linear Contextual Bandits

Evrard Garcelon, Baptiste Roziere, Laurent Meunier, Jean Tarbouriech, Olivier Teytaud, Alessandro Lazaric, Matteo Pirotta

To help personalize content, tailor and measure ads, and provide a safer experience, we use cookies. By clicking or navigating the site, you agree to allow our collection of information on and off Facebook through cookies. Learn more, including about available controls: Cookies Policy