arXiv research

Flexible algorithms for maximizing rewards in structured bandits.

A generalized optimistic method for saddle point problems with improved complexity.

In this paper we study the smooth convex-concave saddle point problem. Specifically, we analyze the last iterate convergence properties of the Extragradient (EG) algorithm. It is well known that the ergodic (averaged) iterates of EG converge at a rate of $O(1/T)$ (Nemirovski, 2004). In this paper, we show that the last…

New ODE models show saddle-point optimization methods converge differently, with last-iterate convergence for OGDA.

We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained smooth convex-concave saddle point (SP) problems. Remarkably, the method only requires access to linear minimization oracles. Leveraging recent advances in FW optimization, we provide the first proof of convergence of a FW-type saddle point solv…

Nonconvex optimization algorithms with random initialization have attracted increasing attention recently. It has been showed that many first-order methods always avoid saddle points with random starting points. In this paper, we answer a question: can the nonconvex heavy-ball algorithms with random initialization avoi…

Simple gradient descent algorithm escapes saddle points efficiently.

OKRidge solves sparse ridge regression problems for nonlinear systems.

We study robust distributed learning that involves minimizing a non-convex loss function with saddle points. We consider the Byzantine setting where some worker machines have abnormal or even arbitrary and adversarial behavior. In this setting, the Byzantine machines may create fake local minima near a saddle point tha…

A new method solves sparse regularization problems efficiently and robustly.

New method stabilizes saddle-point optimization with unbounded gradients.

This paper extends Newton's method to distributed learning, avoiding saddle points and handling Byzantine workers.

New algorithm solves saddle point problems in Banach spaces.

Improved convergence rates for saddle-point optimization algorithms.

The paper speeds up hyperparameter optimisation in Gaussian processes.

New method solves saddle-point problems faster than existing methods.

Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most first-order methods only guarantee an ergodic convergence rate, that is, the uniform…

A new method combines classical and machine learning PDE solvers efficiently.

Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.

In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for non-convex optimization problems. All proposed algorithms can escape from saddle poi…

New framework for probabilistic linear solvers reduces manual effort.

A new algorithm trains deep neural networks by adding neurons greedily.

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be sub-optimal for specific classes of problems. In contrast to existing hand-craft…

We consider the convex-concave saddle point problem $\min_{x}\max_{y} f(x)+y^\top A x-g(y)$ where $f$ is smooth and convex and $g$ is smooth and strongly convex. We prove that if the coupling matrix $A$ has full column rank, the vanilla primal-dual gradient method can achieve linear convergence even if $f$ is not stron…

We consider saddle point problems which objective functions are the average of $n$ strongly convex-concave individual components. Recently, researchers exploit variance reduction methods to solve such problems and achieve linear-convergence guarantees. However, these methods have a slow convergence when the condition n…

Developing stable and scalable probabilistic ODE solvers for stiff and high-dimensional problems.

skscope simplifies sparsity-constrained optimization in Python.

RL accelerates portfolio optimization and option pricing by dynamically adjusting preconditioner sizes.

Leveraging on the convexity of the Lasso problem , screening rules help in accelerating solvers by discarding irrelevant variables, during the optimization process. However, because they provide better theoretical guarantees in identifying relevant variables, several non-convex regularizers for the Lasso have been prop…

This paper shows that a perturbed form of gradient descent converges to a second-order stationary point in a number iterations which depends only poly-logarithmically on dimension (i.e., it is almost "dimension-free"). The convergence rate of this procedure matches the well-known convergence rate of gradient descent to…

Exact solver speeds up Weston-Watkins SVM subproblem significantly.

This work introduces a new loss function to improve the efficiency of optimization-based PDE solvers.

Neural networks that are based on unfolding of an iterative solver, such as LISTA (learned iterative soft threshold algorithm), are widely used due to their accelerated performance. Nevertheless, as opposed to non-learned solvers, these networks are trained on a certain dictionary, and therefore they are inapplicable f…

New method solves constrained optimization problems efficiently.

New methods solve saddle point problems without line search.

We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates of the primal and dual solutions to update. The linear convergence of our method…

In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al. We prove convergence of OMD with exact gradients for coherent saddle point problems, and show that monotone convergence on…

This paper speeds up iterative GP inference with warm starting.

We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation operations per iteration, which has a computational cost comparable to two standard for…

A new approach RA improves stochastic optimization by executing multiple steps between subsample updates.

In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent…

New method solves constrained stochastic optimization problems efficiently.

GeONet learns the Wasserstein geodesic without mesh discretization.

New CAGP-GS framework improves Gaussian process uncertainty quantification.

AI-driven framework optimizes MCMC-based preconditioners for faster linear system solving.

Paper proposes a working set algorithm for non-convex sparse regression with provable convergence.

We analyze stochastic gradient descent for optimizing non-convex functions. In many cases for non-convex functions the goal is to find a reasonable local minimum, and the main concern is that gradient updates are trapped in saddle points. In this paper we identify strict saddle property for non-convex problem that allo…

We study the iteration complexity of the optimistic gradient descent-ascent (OGDA) method and the extra-gradient (EG) method for finding a saddle point of a convex-concave unconstrained min-max problem. To do so, we first show that both OGDA and EG can be interpreted as approximate variants of the proximal point method…