Our selection is possiblefor settings. InconcurrentChatterjiet(2019) studied wherethefirstK constantd-dimensional class.

Consider An n= grad (r)+ A grad (r)+ C| 0 B @ 01 10 ... 1 C

Neural Information Processing Systems http://nips.cc/

How should a player who repeatedly plays a game against a no-regret learner strategize to maximize his utility?

We propose the first reduction-based approach to obtaining long-term memory guarantees for online learning in the sense of Bousquet and Warmuth[8], by reducing the problem to achieving typical switching regret.

This study considers online learning with general directed feedback graphs.

Quantile (and, more generally, KL) regret bounds, such as those achieved by NormalHedge (Chaudhuri, Freund, and Hsu 2009) and its variants, relax the goal of competing against the best individual expert to only competing against a majority of experts on adversarial data.

On the technical side, we show that the logarithmic loss and an informationtheoretic quantity called thetriangular discriminationplay a fundamental role in obtaining first-order guarantees, and we combine this observation with new refinements tothe regression oracle reduction framework ofFoster and Rakhlin [29].

LetT be the time horizon andPT be the path-length that essentially reflects the non-stationarity of environments, the state-of-the-art dynamicregretis O( p T(1+PT)).

Forthemulti-armed bandit problem, we also provide a nearly-tight lower bound up to a logarithmic factor.