Related papers: Algorithmic Thresholds in Mean Field Spin Glasses
This paper considers stochastic convex optimization problems with smooth functional constraints arising in constrained estimation and robust signal recovery. We operate in the high-dimensional and highly-constrained setting, where oracle…
In this paper, we tackle the resolution of chance-constrained problems reformulated via Sample Average Approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program cursed with…
The full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The averaged physical quantities are to be represented via…
This study focuses on the problem of finding ground states of random instances of the Sherrington-Kirkpatrick (SK) spin-glass model with Gaussian couplings. While the ground states of SK spin-glass instances can be obtained with branch and…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
We propose a new iterative construction of solutions of the classical TAP equations for the Sherrington-Kirkpatrick model, i.e. with finite-size Onsager correction. The algorithm can be started in an arbitrary point, and converges up to the…
Let A be a matrix, c be any linear objective function and x be a fractional vector, say an LP solution to some discrete optimization problem. Then a recurring task in theoretical computer science (and in approximation algorithms in…
Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A…
Achieving weighted throughput maximization (WTM) through power control has been a long standing open problem in interference-limited wireless networks. The complicated coupling between the mutual interferences of links gives rise to a…
The parallel minority game (PMG) extends the classical minority game to many choices, with each agent restricted to two predetermined alternatives. In this condition, minimizing the population variance across all choices is a complex…
The Stacker Crane Problem is NP-Hard and the best known approximation algorithm only provides a 9/5 approximation ratio. The objective of this paper is threefold. First, by embedding the problem within a stochastic framework, we present a…
The problem we consider is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust…
We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree…
In this paper, we present an efficient algorithm for solving a class of chance constrained optimization under non-parametric uncertainty. Our algorithm is built on the possibility of representing arbitrary distributions as functions in…
We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is…
Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state…
We discuss the computational complexity of random 2D Ising spin glasses, which represent an interesting class of constraint satisfaction problems for black box optimization. Two extremal cases are considered: (1) the +/- J spin glass, and…
Finding the $r\times r$ submatrix of maximum volume of a matrix $A\in\mathbb R^{n\times n}$ is an NP hard problem that arises in a variety of applications. We propose a new greedy algorithm of cost $\mathcal O(n)$, for the case $A$…
In this paper, we study the Maximum Profit Pick-up Problem with Time Windows and Capacity Constraint (MP-PPTWC). Our main results are 3 polynomial time algorithms, all having constant approximation factors. The first algorithm has an…
We explore a one-to-one correspondence between a neural network (NN) and a statistical mechanical spin model where neurons are mapped to Ising spins and weights to spin-spin couplings. The process of training an NN produces a family of spin…