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Submodular Maximization Through Barrier Functions
In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization.
High probability generalization bounds for uniformly stable algorithms with nearly optimal rate
Specifically, their bound on the estimation error of any $\gamma$-uniformly stable learning algorithm on $n$ samples and range in $[0, 1]$ is $O(\gamma \sqrt{n \log(1/\delta)} + \sqrt{\log(1/\delta)/n})$ with probability $\geq 1-\delta$.
Generalization Bounds for Uniformly Stable Algorithms
Specifically, for a loss function with range bounded in $[0, 1]$, the generalization error of a $\gamma$-uniformly stable learning algorithm on $n$ samples is known to be within $O((\gamma +1/n) \sqrt{n \log(1/\delta)})$ of the empirical error with probability at least $1-\delta$.
Information-theoretic lower bounds for convex optimization with erroneous oracles
We consider the problem of optimizing convex and concave functions with access to an erroneous zeroth-order oracle.
Tight Bounds on Low-degree Spectral Concentration of Submodular and XOS functions
This improves on previous approaches that all showed an upper bound of $O(1/\epsilon^2)$ for submodular and XOS functions.
Lazier Than Lazy Greedy
Is it possible to maximize a monotone submodular function faster than the widely used lazy greedy algorithm (also known as accelerated greedy), both in theory and practice?
Optimal Bounds on Approximation of Submodular and XOS Functions by Juntas
This is the first algorithm in the PMAC model that over the uniform distribution can achieve a constant approximation factor arbitrarily close to 1 for all submodular functions.
Representation, Approximation and Learning of Submodular Functions Using Low-rank Decision Trees
We show that these structural results can be exploited to give an attribute-efficient PAC learning algorithm for submodular functions running in time $\tilde{O}(n^2) \cdot 2^{O(1/\epsilon^{4})}$.
