Online algorithms for submodular minimization with combinatorial constraints
نویسندگان
چکیده
Building on recent results for submodular minimization with combinatorial constraints, and on online submodular minimization, we address online approximation algorithms for submodular minimization with combinatorial constraints. We discuss two types of algorithms and outline approximation algorithms that integrate into those.
منابع مشابه
Online Prediction under Submodular Constraints
We consider an online prediction problem of combinatorial concepts where each combinatorial concept is represented as a vertex of a polyhedron described by a submodular function (base polyhedron). In general, there are exponentially many vertices in the base polyhedron. We propose polynomial time algorithms with regret bounds. In particular, for cardinality-based submodular functions, we give O...
متن کاملOnline Submodular Minimization for Combinatorial Structures
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...
متن کاملSize-constrained Submodular Minimization through Minimum Norm Base
A number of combinatorial optimization problems in machine learning can be described as the problem of minimizing a submodular function. It is known that the unconstrained submodular minimization problem can be solved in strongly polynomial time. However, additional constraints make the problem intractable in many settings. In this paper, we discuss the submodular minimization under a size cons...
متن کاملA Submodular Function Minimization Algorithm Based on the Minimum-Norm Base∗
We consider an application of the minimum-norm-point algorithm to submodular function minimization. Although combinatorial polynomial algorithms for submodular function minimization (SFM) have recently been obtained, there still remain (open) problems of reducing the complexity of the SFM algorithms and of constructing a practically fast SFM algorithms. We show some possible approach to the pro...
متن کاملCombinatorial Algorithms for Submodular Function Minimization and Related Problems
Submodular functions are common in combinatorics; examples include the cut capacity function of a graph and the rank function of a matroid. The submodular function minimization problem generalizes the classical minimum cut problem and also contains a number of other combinatorial optimization problems as special cases. In this thesis, we study submodular function minimization and two related pr...
متن کامل