相关论文: A Truthful Randomized Mechanism for Combinatorial …

Consider costly and time-consuming tasks that add up to the success of a project, and must be fitted into a given time-frame. This is an instance of the classic budgeted maximization (knapsack) problem, which admits an FPTAS. Now assume an…

Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints,…

Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large…

A practical challenge in reinforcement learning are combinatorial action spaces that make planning computationally demanding. For example, in cooperative multi-agent reinforcement learning, a potentially large number of agents jointly…

In combinatorial auctions, a designer must decide how to allocate a set of indivisible items amongst a set of bidders. Each bidder has a valuation function which gives the utility they obtain from any subset of the items. Our focus is…

Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…

The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable…

We consider distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as Linear Matrix Inequalities (LMIs). We propose a decentralized and computationally inexpensive…

We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…

We consider the maximization problem of monotone submodular functions under an uncertain knapsack constraint. Specifically, the problem is discussed in the situation that the knapsack capacity is not given explicitly and can be accessed…

Motivated by real-world applications, we study the fair allocation of graphical resources, where the resources are the vertices in a graph. Upon receiving a set of resources, an agent's utility equals the weight of a maximum matching in the…

We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…

The problem of maximizing nonnegative monotone submodular functions under a certain constraint has been intensively studied in the last decade, and a wide range of efficient approximation algorithms have been developed for this problem.…

A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG (Vickrey, Clarke, Groves). When applying this method to complex problems such as combinatorial auctions, a difficulty…

In machine learning and big data, the optimization objectives based on set-cover, entropy, diversity, influence, feature selection, etc. are commonly modeled as submodular functions. Submodular (function) maximization is generally NP-hard,…

We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower…

We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…

We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is…

In this paper, we demonstrate a formulation for optimizing coupled submodular maximization problems with provable sub-optimality bounds. In robotics applications, it is quite common that optimization problems are coupled with one another…

In this paper, we consider combinatorial reinforcement learning with preference feedback, where a learning agent sequentially offers an action--an assortment of multiple items to--a user, whose preference feedback follows a multinomial…