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Acceleration through Optimistic No-Regret Dynamics

Neural Information Processing Systems

Zero-sum games can be solved using online learning dynamics, where a classical technique involves simulating two no-regret algorithms that play against each other and, afterT rounds, the average iterate is guaranteed to solve the original optimization problem with error decaying asO(logT/T). In this paper we show that the technique can be enhanced to a rate ofO(1/T2) by extending recent work [22, 25] that leverages optimistic learning to speed upequilibrium computation.



A Theory of Optimistically Universal Online Learnability for General Concept Classes

Neural Information Processing Systems

Haussler et al. [1994], Ryabko [2006] researched the online learning problem with a mix of both restrictions. There are also substantial amount of papers investigating online learnability with all measurable functions but restricted data processes.




Universal Online Learning with Gradient Variations: A Multi-layer Online Ensemble Approach

Neural Information Processing Systems

In this paper, we propose an online convex optimization approach with two different levels of adaptivity. On a higher level, our approach is agnostic to the unknown types and curvatures of the online functions, while at a lower level, it can exploit the unknown niceness of the environments and attain problem-dependent guarantees.