Adap-tivity to the problem's structure is essential in order to obtain optimal regret upper

"juntas" [Blum and Langley, 1997]), that is functions that depend only on a small number

We conclude that equality in Lemma 3.1 holds if and only if w

Many high-dimensional statistical inference problems are believed to possess inherent computational hardness. Various frameworks have been proposed to give rigorous evidence for such hardness, including lower bounds against restricted models of computation (such as low-degree functions), as well as methods rooted in statistical physics that are based on free energy landscapes. This paper aims to make a rigorousconnectionbetween the seeminglydifferent low-degreeand free-energybased approaches. We define a free-energybasedcriterionfor hardnessand formallyconnectit to the well-establishednotionof low-degree hardness for a broad class of statistical problems, namely all Gaussian additive models and certain models with a sparse planted signal.

However,mostexistingworkspropose to solve these convex reformulations by general-purpose solvers, which are not well-suited for tackling large-scale problems. In this paper, we focus on a family of Wasserstein distributionally robust support vector machine (DRSVM) problems and propose two novel epigraphical projection-based incremental algorithms to solve them.

RL-as-inference (see discussion in Section 4.3), they differ crucially in how the objective is interpreted.