Related papers: Decision Problems in Multilevel Linear Programming
In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ…
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…
We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply {\em only to linear codes.} Delsarte's LP is the weakest member of this family and our LP yields…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…
Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…
The System of Linear Equations Problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\kappa$ of $A$, a vector $b$, a Hermitian matrix $M$ and an accuracy $\epsilon$, and the task is to estimate $x^\dagger…
We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous…
We investigate universal bounds on spherical codes and spherical designs that could be obtained using Delsarte's linear programming methods. We give a lower estimate for the LP upper bound on codes, and an upper estimate for the LP lower…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of…
Optimal planning with respect to learned neural network (NN) models in continuous action and state spaces using mixed-integer linear programming (MILP) is a challenging task for branch-and-bound solvers due to the poor linear relaxation of…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We consider a bilevel optimization problem in which the ground set is partitioned between two decision makers, a leader and a follower, whose optimization problems are interleaved. We study the Bilevel Independent Set problem, and its…
Solving Markov Decision Processes (MDPs) is a recurrent task in engineering. Even though it is known that solutions for minimizing the infinite horizon expected reward can be found in polynomial time using Linear Programming techniques,…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
This paper considers program synthesis in the context of computational hardness, asking the question: How hard is it to determine whether a given synthesis problem has a solution or not? To answer this question, this paper studies program…
Hierarchical decision problems are often modeled as bilevel programs in which a leader commits to a policy and a follower responds optimally. When the follower's optimal response is nonunique, or when only near-optimal follower behavior can…
We investigate the satisfiability and finite satisfiability problem for probabilistic computation-tree logic (PCTL) where operators are not restricted by any step bounds. We establish decidability for several fragments containing…