Related papers: A Probabilistic Baby-Step Giant-Step Algorithm

We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…

In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…

We propose a new algorithm for numerical path tracking in polynomial homotopy continuation. The algorithm is `robust' in the sense that it is designed to prevent path jumping and in many cases, it can be used in (only) double precision…

We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019)…

We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…

This paper aims at developing two versions of the generalized Newton method to compute not merely arbitrary local minimizers of nonsmooth optimization problems but just those, which possess an important stability property known as tilt…

Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…

Densest subgraph detection is a fundamental graph mining problem, with a large number of applications. There has been a lot of work on efficient algorithms for finding the densest subgraph in massive networks. However, in many domains, the…

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…

Probabilistic programming languages (PPLs) are expressive means for creating and reasoning about probabilistic models. Unfortunately hybrid probabilistic programs, involving both continuous and discrete structures, are not well supported by…

In stochastic optimization, the population risk is generally approximated by the empirical risk. However, in the large-scale setting, minimization of the empirical risk may be computationally restrictive. In this paper, we design an…

Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…

A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

Gradient-based iterative optimization methods are the workhorse of modern machine learning. They crucially rely on careful tuning of parameters like learning rate and momentum. However, one typically sets them using heuristic approaches…

In cryptanalysis, solving the discrete logarithm problem (DLP) is key to assessing the security of many public-key cryptosystems. The index-calculus methods, that attack the DLP in multiplicative subgroups of finite fields, require solving…

We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our…

Stochastic optimisation problems minimise expectations of random cost functions. We use 'optimise then discretise' method to solve stochastic optimisation. In our approach, accurate quadrature methods are required to calculate the…

Let $p$ be a odd prime such that 2 is a primitive element of finite field $F_p*$. In this short note we propose a new algorithm for the computation of discrete logarithm in $F_p*$. This algorithm is based on elementary properties of finite…

The problem of steering a particular class of $n$-dimensional continuous-time dynamical systems towards the minima of a function without gradient information is considered. We propose an hybrid controller, implementing a discrete-time…