Most results for online decision problems with structured concepts, such as trees or cuts, assume linear costs. In many settings, however, nonlinear costs are more realistic. Owing to their non-separability, these lead to much harder optimization problems. Going beyond linearity, we address online approximation algorithms for structured concepts that allow the cost to be submodular, i.e., nonse...

CMO Council reports that 71% of internet users in the U.S. were influenced by coupons and discounts when making their purchase decisions. It has also been shown that offering coupons to a small fraction of users (called seed users) may affect the purchase decisions of many other users in a social network. This motivates us to study the optimal coupon allocation problem, and our objective is to ...

We introduce and study minimax curriculum learning (MCL), a new method for adaptively selecting a sequence of training subsets for a succession of stages in machine learning. The subsets are encouraged to be small and diverse early on, and then larger, harder, and allowably more homogeneous in later stages. At each stage, model weights and training sets are chosen by solving a joint continuous-...

We study the problem of maximizing a monotone submodular function subject to a cardinality constraint k, with the added twist that a number of items τ from the returned set may be removed. We focus on the worst-case setting considered in (Orlin et al., 2016), in which a constant-factor approximation guarantee was given for τ = o( √ k). In this paper, we solve a key open problem raised therein, ...

We consider the monotone submodular k-set packing problem in the context of the more general problem of maximizing a monotone submodular function in a k-exchange system. These systems, introduced by Feldman et al. [9], generalize the matroid k-parity problem in a wide class of matroids and capture many other combinatorial optimization problems. We give a deterministic, non-oblivious local searc...

Submodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function f . We focus on stochastic functions that are given as an expectation of functions over a distribution P . In practice, we often have only a limited set of samples fi from P . The standard approach indirectly optimizes f by maximizing the sum of fi. H...

In this paper we consider the problem of maximizing a separable concave function over a polymatroid. More specifically, we study the submodularity of its optimal objective value in the parameters of the objective function. This question is interesting in its own right and is encountered in many applications. But our research has been mainly motivated by a cooperative game associated with the we...

Discrete energy minimization is a ubiquitous task in computer vision, yet is NP-hard in most cases. In this work we propose a multiscale framework for coping with the NP-hardness of discrete optimization. Our approach utilizes algebraic multiscale principles to efficiently explore the discrete solution space, yielding improved results on challenging, non-submodular energies for which current me...

It is becoming increasingly evident that many machine learning problems may be reduced to submodular optimization. Previous work addresses generic discrete approaches and specific relaxations. In this work, we take a generic view from a relaxation perspective. We show a relaxation formulation and simple rounding strategy that, based on the monotone closure of relaxed constraints, reveals analog...