Online Learning

Online prediction and learning is omnipresent in the modern world, starting from ad placement in websites, to web caching for content distribution and many more online platforms. The principal problem here can be formulated to be one of minimizing a sequence of time varying functions over a convex constraint set. Unlike the offline version, the online optimization problems generally do not possess a unique minima because of the time varying functions involved. The fundamental notion of performance is therefore different than that of offline optimization. Indeed, the quantity of interest in online optimization is the regret of the online algorithm, which measures the relative performance of the online algorithm with respect to a clairvoyant oracle having hindsight of all the functions beforehand. Among the ocean of exciting new problems in this field, I am currently very interested in the amazingly simple yet elegant practical problem of online caching which can be formulated as an Online Linear Optimization (OLO) problem. A principled investigation of this problem and possible generalizations as well as connections with other fields of study are principle among my current topics of interest.

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