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Federated Online and Bandit Convex Optimization
Kumar Kshitij Patel · Lingxiao Wang · Aadirupa Saha · Nati Srebro

Thu Jul 27 01:30 PM -- 03:00 PM (PDT) @ Exhibit Hall 1 #440
We study the problems of *distributed online and bandit convex optimization* against an adaptive adversary. We aim to minimize the average regret on $M$ machines working in parallel over $T$ rounds with $R$ intermittent communications. Assuming the underlying cost functions are convex and can be generated adaptively, our results show that *collaboration is not beneficial when the machines have access to the first-order gradient information at the queried points*. This is in contrast to the case for stochastic functions, where each machine samples the cost functions from a fixed distribution. Furthermore, we delve into the more challenging setting of *federated online optimization with bandit (zeroth-order) feedback*, where the machines can only access values of the cost functions at the queried points. The key finding here is *identifying the high-dimensional regime where collaboration is beneficial and may even lead to a linear speedup in the number of machines*. We further illustrate our findings through federated adversarial linear bandits by developing novel distributed single and two-point feedback algorithms. Our work is the first attempt towards a systematic understanding of federated online optimization with limited feedback, and it attains tight regret bounds in the intermittent communication setting for both first and zeroth-order feedback. Our results thus bridge the gap between stochastic and adaptive settings in federated online optimization.

Author Information

Kumar Kshitij Patel (Toyota Technological Institute at Chicago)
Lingxiao Wang (TTI-Chicago)
Aadirupa Saha (TTIC)

Bio: Aadirupa Saha is currently a visiting faculty at Toyota Technological Institute at Chicago (TTIC). She obtained her PhD from the Department of Computer Science, Indian Institute of Science, Bangalore, advised by Aditya Gopalan and Chiranjib Bhattacharyya. She spent two years at Microsoft Research New York City as a postdoctoral researcher. During her PhD, Aadirupa interned at Microsoft Research, Bangalore, Inria, Paris, and Google AI, Mountain View. Her research interests include Bandits, Reinforcement Learning, Optimization, Learning theory, Algorithms. She has organized various workshops, tutorials and also served as a reviewer in top ML conferences. Research Interests: Machine Learning Theory (specifically Online Learning, Bandits, Reinforcement Learning), Optimization, Game Theory, Algorithms. She is recently interested in exploring ML problems at the intersection of Fairness, Privacy, Game theory and Mechanism design.

Nati Srebro (Toyota Technological Institute at Chicago)

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