Thus, weaker models that give imprecise results quickly can be advantageous, provided inaccuracies can be resolved using few queries to a stronger model. In the fundamental problem of computing a maximum-weight basis of a matroid, a well-known generalization of many combinatorial optimization problems, algorithms have access to a clean oracle to query matroid information. We additionally equip algorithms with a fast but dirty oracle. We design and analyze practical algorithms that only use few clean queries w.r.t. the quality of the dirty oracle, while maintaining robustness against arbitrarily poor dirty oracles, approaching the performance of classic algorithms for the given problem. Notably, we prove that our algorithms are, in many respects, best-possible. Further, we outline extensions to other matroid oracle types, non-free dirty oracles and other matroid problems.

In our case, it boils down to: ' The smoothing effect induced by the average helps to reduce the visual noise, and hence improves the explanations. For the experiment, m and are the same as SmoothGrad. We start by deriving the closed form of Saliency (SA) and naturally Gradient-Input (GI): ' The case of V arGrad is specific, as the gradient of a linear system being constant, its variance is null. W We recall that for Gradient Input, Integrated Gradients, Occlusion, ' It was quickly realized that they unified properties of various domains such as graph theory, linear algebra or geometry. Later, in the '60s, a connection was made At each step, the insertion metric selects the concepts of maximum score given a cardinality constraint.

In this work, we undertake a variational inference approach and approximate these rich distributions with simpler ones that respect the combinatorial constraints but are fully tractable. These approximations posses very strong negativeassociation properties, which we utilize inour theory.

In this work, we extend the above direction to a combinatorial semi-bandit setting and study avariant of stochastic MAB, where arms are subject to matroid constraints and each arm becomes unavailable (blocked) for afixed number of rounds after each play. A natural common generalization of the state-of-the-art for blocking bandits, and that for matroid bandits, only guarantees a1/2-approximation for general matroids.

Real-world problems such as ad allocation and matching havebeen extensively studied under the lens of combinatorial optimization. In several applications, uncertainty in the input appears naturally and this has led to the study of online stochastic optimization models for such problems.

Matching based markets, like ad auctions, ride-sharing, and eBay, are inherently online and combinatorial, and therefore have been extensively studied under the lens of online stochastic combinatorial optimization models. The general framework that has emerged uses Contention Resolution Schemes (CRSs) introduced by Chekuri, Vondrák, and Zenklusen for combinatorial problems, where one first obtains a fractional solution to a (continuous) relaxation of the objective, and then proceeds to round it. When the order of rounding is controlled by an adversary, it is called an Online Contention Resolution Scheme (OCRSs), which has been successfully applied in online settings such as posted-price mechanisms, prophet inequalities and stochastic probing.The study of greedy OCRSs against an almighty adversary has emerged as one of the most interesting problems since it gives a simple-to-implement scheme against the worst possible scenario. Intuitively, a greedy OCRS has to make all its decisions before the online process starts.