Related papers: A review of the Statistical Mechanics approach to …
In this paper, we investigate the problem of assessing statistical methods and effectively summarizing results from simulations. Specifically, we consider problems of the type where multiple methods are compared on a reasonably large test…
We analyze to what extent the random SAT and Max-SAT problems differ in their properties. Our findings suggest that for random $k$-CNF with ratio in a certain range, Max-SAT can be solved by any SAT algorithm with subexponential slowdown,…
Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…
In the foreseeable future, toolchains for quantum computing should offer automatic means of transforming a high level problem formulation down to a hardware executable form. Thereby, it is crucial to find (multiple) transformation paths…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
We study the performance of stochastic local search algorithms for random instances of the $K$-satisfiability ($K$-SAT) problem. We introduce a new stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a…
In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…
Many machine learning algorithms minimize a regularized risk, and stochastic optimization is widely used for this task. When working with massive data, it is desirable to perform stochastic optimization in parallel. Unfortunately, many…
We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the…
Let a stick be broken at random at n-1 points to form n pieces. We consider three problems on forming k-gons with k out of these n pieces, and show how a statistical approach, through a linear transformation of variables, yields simple…
We revisit random search for stochastic optimization, where only noisy function evaluations are available. We show that the method works under weaker smoothness assumptions than previously considered, and that stronger assumptions enable…
Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…
In spatial regression models, spatial heterogeneity may be considered with either continuous or discrete specifications. The latter is related to delineation of spatially connected regions with homogeneous relationships between variables…
We consider the problem of signal estimation (denoising) from a statistical mechanical perspective, using a relationship between the minimum mean square error (MMSE), of estimating a signal, and the mutual information between this signal…
Number partitioning is one of the classical NP-hard problems of combinatorial optimization. It has applications in areas like public key encryption and task scheduling. The random version of number partitioning has an "easy-hard" phase…
Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to…
We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We…
In the last decades, many efforts have focused on analyzing typical-case hardness in optimization and inference problems. Some recent work has pointed out that polynomial algorithms exist, running with a time that grows more than linearly…
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to the development of gradient-based distributed optimization…
In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. Our…