Related papers: Greedy Quasi-Newton Methods with Explicit Superlin…

Recent Newton-type federated learning algorithms have demonstrated linear convergence with respect to the communication rounds. However, communicating Hessian matrices is often unfeasible due to their quadratic communication complexity. In…

This paper addresses the challenge of developing efficient algorithms for large-scale nonconvex multiobjective optimization problems (MOPs). While quasi-Newton methods are effective, their traditional application to MOPs is computationally…

We consider Broyden's method and some accelerated schemes for nonlinear equations having a strongly regular singularity of first order with a one-dimensional nullspace. Our two main results are as follows. First, we show that the use of a…

The purpose of this paper is to introduce $\omega$-Chebyshev-greedy and $\omega$-partially greedy approximation classes and to study their relation with $\omega$-approximation spaces, where the latter are a generalization of the classical…

Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta…

We derive a sound positive semi-definite approximation of the Hessian of deep models for which Hessian-vector products are easily computable. This enables us to provide an adaptive SGD learning rate strategy based on the minimization of the…

It is known that a basis is almost greedy if and only if the thresholding greedy algorithm gives essentially the smallest error term compared to errors from projections onto intervals or in other words, consecutive terms of $\mathbb{N}$. In…

In this paper we study a new class of bases, weaker than quasi-greedy bases, which retain their unconditionality properties and can provide the same optimality for the thresholding greedy algorithm. We measure how far these bases are from…

Greedy-GQ is an off-policy two timescale algorithm for optimal control in reinforcement learning. This paper develops the first finite-sample analysis for the Greedy-GQ algorithm with linear function approximation under Markovian noise. Our…

Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…

It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…

In this paper we develop a procedure to deal with a family of parameter-dependent ill-posed problems, for which the exact solution in general does not exist. The original problems are relaxed by considering corresponding approximate ones,…

Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…

We consider the class of optimization problems arising from computationally intensive L1-regularized M-estimators, where the function or gradient values are very expensive to compute. A particular instance of interest is the L1-regularized…

We propose a quasi-Newton-type method for nonconvex optimization with Lipschitz continuous gradients and Hessians. The algorithm finds an $\varepsilon$-stationary point within $\tilde{\mathrm{O}}(d^{1/4} \varepsilon^{-13/8})$ gradient…

In this paper, we study the application of quasi-Newton methods for solving empirical risk minimization (ERM) problems defined over a large dataset. Traditional deterministic and stochastic quasi-Newton methods can be executed to solve such…

We propose a novel limited-memory stochastic block BFGS update for incorporating enriched curvature information in stochastic approximation methods. In our method, the estimate of the inverse Hessian matrix that is maintained by it, is…

A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…

In their standard form Gaussian processes (GPs) provide a powerful non-parametric framework for regression and classificaton tasks. Their one limiting property is their $\mathcal{O}(N^{3})$ scaling where $N$ is the number of training data…

For quasi-Newton methods in unconstrained minimization, it is valuable to develop methods that are robust, i.e., methods that converge on a large number of problems. Trust-region algorithms are often regarded to be more robust than…