Submodularity is a fundamental concept in combinatorial optimization, usually associated with discrete setfunctions [Fujishige, 1991]. Assubmodular functions formalize theintuitivenotion of diminishing returns, and thus provide a useful structure, they appear in a wide range of modernmachine learning applications including various forms of data summarization [Lin and Bilmes,2012, Mirzasoleiman et al., 2013], influence maximization [Kempe et al., 2003], sparse and deeprepresentations [Balkanski etal.,2016,

A finite episodic Markov decision process (MDP) is a tuple (S,A,H,α,P,r) where S and A are the finite sets of states and actions withS = |S|,A = |A|, H is the (fixed) episode length andα is the initial state distribution.

For stochastic oracles, we provide a lower bound of Ω κ 2+κ1/3 4 .

When solving real-world problems, where contexts and actions are complex and high-dimensional (e.g., users' social graph, items' visual description), it is crucial to provide the bandit algorithm with a suitable representation of the context-action space.

This concept has been investigated extensively, but only through a worst-case lens. Instead, we study the expected distortion of voting rules with respect to an underlying distribution over voter utilities.

With applied quantum computing in its infancy, there already exist quantum machine learning models such as variational quantum eigensolvers which have been used e.g. in the context of energy minimization tasks.