Related papers: Efficient Minimization of Decomposable Submodular …

Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. However, in large-scale applications, solving Submodular Function Minimization (SFM)…

We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding…

Submodular functions, as well as the sub-class of decomposable submodular functions, and their optimization appear in a wide range of applications in machine learning, recommendation systems, and welfare maximization. However, optimization…

We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…

Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we…

Minimax optimization has been central in addressing various applications in machine learning, game theory, and control theory. Prior literature has thus far mainly focused on studying such problems in the continuous domain, e.g.,…

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…

We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…

Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…

Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…

Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer…

Few-shot prompting is a surprisingly powerful way to use Large Language Models (LLMs) to solve various tasks. However, this approach struggles as the task complexity increases or when the individual reasoning steps of the task themselves…

The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular…

We consider learning of submodular functions from data. These functions are important in machine learning and have a wide range of applications, e.g. data summarization, feature selection and active learning. Despite their combinatorial…

A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. Unfortunately, the resulting submodular optimization…

Combinatorial algorithms for minimization of functions of many variables, which take their values in finite totally ordered sets, are developed. For that the decomposition of the functions by Boolean polynomials is used. The modified SFM…

Continuous submodular functions are a category of generally non-convex/non-concave functions with a wide spectrum of applications. The celebrated property of this class of functions - continuous submodularity - enables both exact…