However, functions on such complex objects (e.g., point sets and graphs) are often

We provide online convex optimization algorithms that guarantee improved fullmatrix regret bounds. These algorithms extend prior work in several ways. First, we seamlessly allow for the incorporation of constraints without requiring unknown oracle-tuning for any learning rate parameters. Second, we improve the regret analysis of the full-matrix AdaGrad algorithm by suggesting a better learning rate value and showing how to tune the learning rate to this value on-the-fly. Third, all our bounds are obtained via a general framework for constructing regret bounds that depend on an arbitrary sequence of norms.

Weapplythisnovelformulation of inference as controlto the canonical problem of inferring the hidden scalar state of a linear dynamical system with Gaussian variability.

Inmicrobiome studies, we may wish to investigate the association between the overall composition of human microbiota, including hundreds of microbial taxa, and multiple host metabolites from aparticular metabolic pathway [3, 4].