285 citations · 499 across the 55 of their papers we have counts for
44 papers · 1 filter
Stochastic Nonconvex Bilevel Optimization: Improved Rates Without Rare-Visit Assumption
Daniel Cortild, Mathias Staudigl, Juan Peypouquet +1
We investigate stochastic simple bilevel optimization with smooth and possibly nonconvex upper- and lower-level objectives. Existing stochastic extensions of dynamic barrier gradie…
A note on the complexity of random subspace model-based methods for derivative-free optimization
Coralia Cartis, Lindon Roberts
We demonstrate that, with a suitable rescaling, using Johnson-Lindenstrauss transforms (JLTs) in the random subspace model-based derivative-free optimization (DFO) algorithm from […
Stochastic Krasnoselskii-Mann Iterations: Convergence without Uniformly Bounded Variance
Daniel Cortild, Coralia Cartis, Juan Peypouquet
We investigate the Stochastic Krasnoselskii-Mann iterations for expected nonexpansive fixed-point problems in a real separable Hilbert space. We establish convergence guarantees un…
A Parameter-Free First-Order Algorithm for Non-Convex Optimization with Global Rate
Sichao Xiong, Sadok Jerad, Coralia Cartis
We introduce PF-AGD, the first parameter-free, deterministic, accelerated first-order method to achieve oracle complexity bound when minimizing sufficiently…
A Globally Convergent Third-Order Newton Method via Unified Semidefinite Programming Subproblems
Yubo Cai, Wenqi Zhu, Coralia Cartis +1
We propose the Adaptive Levenberg-Marquardt Third-Order Newton Method (ALM-TON) method for unconstrained nonconvex optimization; to our knowledge, the framework provides the first…
Sufficiently Regularized Nonnegative Quartic Polynomials are Sum-of-Squares
Wenqi Zhu, Coralia Cartis
A polynomial that is nonnegative need not be a sum of squares of polynomials. This classical gap, identified by Hilbert in 1888, lies at the heart of why the global optimization of…
Local Convergence of Adaptively Regularized Tensor Methods
Karl Welzel, Yang Liu, Raphael A. Hauser +1
Optimization methods that make use of derivatives of the objective function up to order are called tensor methods. Among them, ones that minimize a regularized th-order…
Nonlinear Dimensionality Reduction Techniques for Bayesian Optimization
Luo Long, Coralia Cartis, Paz Fink Shustin
Bayesian optimisation (BO) enables sample-efficient global optimisation of expensive black-box functions but remains challenging in high dimensions. We investigate nonlinear dimens…
On Global Rates for Regularization Methods based on Secant Derivative Approximations
Coralia Cartis, Sadok Jerad, Karl Welzel
An inexact and globally convergent framework for high-order adaptive regularization methods is presented, in which approximations may be used for the th-order tensor, based on l…
Global Optimality Characterizations and Algorithms for Minimizing Quartically-Regularized Third-Order Taylor Polynomials
Wenqi Zhu, Coralia Cartis
High-order methods for convex and nonconvex optimization, particularly th-order Adaptive Regularization Methods (AR), have attracted significant research interest by naturall…
Random Subspace Cubic-Regularization Methods, with Applications to Low-Rank Functions
Coralia Cartis, Zhen Shao, Edward Tansley
We propose and analyze random subspace variants of the second-order Adaptive Regularization using Cubics (ARC) algorithm. These methods iteratively restrict the search space to som…
Scalable Second-Order Optimization Algorithms for Minimizing Low-rank Functions
Edward Tansley, Coralia Cartis
We present a random-subspace variant of cubic regularization algorithm that chooses the size of the subspace adaptively, based on the rank of the projected second derivative matrix…
Efficient Implementation of Third-Order Tensor Methods with Adaptive Regularization for Unconstrained Optimization
Coralia Cartis, Raphael Hauser, Yang Liu +2
High-order tensor methods that employ local Taylor models of degree within adaptive regularization frameworks (AR) have recently received significant attention, due to their…
Randomized Subspace Derivative-Free Optimization with Quadratic Models and Second-Order Convergence
Coralia Cartis, Lindon Roberts
We consider model-based derivative-free optimization (DFO) for large-scale problems, based on iterative minimization in random subspaces. We provide the first worst-case complexity…
Dimensionality Reduction Techniques for Global Bayesian Optimisation
Luo Long, Coralia Cartis, Paz Fink Shustin
Bayesian Optimisation (BO) is a state-of-the-art global optimisation technique for black-box problems where derivative information is unavailable, and sample efficiency is crucial.…
Global Convergence of High-Order Regularization Methods with Sums-of-Squares Taylor Models
Wenqi Zhu, Coralia Cartis
High-order tensor methods that employ Taylor-based local models (of degree ) within adaptive regularization frameworks have been recently proposed for both convex and nonco…
Learning the subspace of variation for global optimization of functions with low effective dimension
Coralia Cartis, Xinzhu Liang, Estelle Massart +1
We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-ra…
Registration of algebraic varieties using Riemannian optimization
Florentin Goyens, Coralia Cartis, Stéphane Chrétien
We consider the point cloud registration problem, the task of finding a transformation between two point clouds that represent the same object but are expressed in different coordi…
Cubic-quartic regularization models for solving polynomial subproblems in third-order tensor methods
Wenqi Zhu, Coralia Cartis
High-order tensor methods for solving both convex and nonconvex optimization problems have generated significant research interest, leading to algorithms with optimal global rates…
Second-order methods for quartically-regularised cubic polynomials, with applications to high-order tensor methods
Coralia Cartis, Wenqi Zhu
There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexi…
Randomised subspace methods for non-convex optimization, with applications to nonlinear least-squares
Coralia Cartis, Jaroslav Fowkes, Zhen Shao
We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we sh…
A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares
Coralia Cartis, Jaroslav Fowkes, Zhen Shao
We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the vari…
Convergent least-squares optimisation methods for variational data assimilation
Coralia Cartis, Maha H. Kaouri, Amos S. Lawless +1
Data assimilation combines prior (or background) information with observations to estimate the initial state of a dynamical system over a given time-window. A common application is…
Global optimization using random embeddings
Coralia Cartis, Estelle Massart, Adilet Otemissov
We propose a random-subspace algorithmic framework for global optimization of Lipschitz-continuous objectives, and analyse its convergence using novel tools from conic integral geo…