Related papers: Complexity of Classical Acceleration for $\ell_1$-…
The convergence behavior of gradient methods for minimizing convex differentiable functions is one of the core questions in convex optimization. This paper shows that their well-known complexities can be achieved under conditions weaker…
We analyze two classical algorithms for solving additively composite convex optimization problems where the objective is the sum of a smooth term and a nonsmooth regularizer: proximal stochastic gradient method for a single regularizer; and…
This paper investigates the fundamental performance limits of gradient-based algorithms for time-varying optimization. Leveraging the internal model principle and root locus techniques, we show that temporal variabilities impose intrinsic…
Streaming Linear Discriminant Analysis (LDA) while proven in Class-incremental Learning deployments at the edge with limited classes (upto 1000), has not been proven for deployment in extreme classification scenarios. In this paper, we…
Stochastic optimization of engineering systems is often infeasible due to repeated evaluations of a computationally expensive, high-fidelity simulation. Bi-fidelity methods mitigate this challenge by leveraging a cheaper, approximate model…
This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating $\ell_{0}$ and $\ell_{2,0}$ regularization is minimized over a box constraint. Although such problems arise frequently in…
Motivated by industrial computed tomography, we propose a memory efficient strategy to estimate the regularization hyperparameter of a non-smooth variational model. The approach is based on a combination of FISTA and Condat-Vu algorithms…
In unconstrained optimisation on an Euclidean space, to prove convergence in Gradient Descent processes (GD) $x_{n+1}=x_n-\delta _n \nabla f(x_n)$ it usually is required that the learning rates $\delta _n$'s are bounded: $\delta _n\leq…
A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…
We deal with the problem, initiated in [8], of finding randomized and quantum complexity of initial-value problems. We showed in [8] that a speed-up in both settings over the worst-case deterministic complexity is possible. In the present…
Feature subset selection arises in many high-dimensional applications of statistics, such as compressed sensing and genomics. The $\ell_0$ penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of…
Sparse principal component analysis (PCA), an important variant of PCA, attempts to find sparse loading vectors when conducting dimension reduction. This paper considers the nonsmooth Riemannian optimization problem associated with the…
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…
Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
This paper takes an initial step to systematically investigate the generalization bounds of algorithms for solving nonconvex-(strongly)-concave (NC-SC/NC-C) stochastic minimax optimization measured by the stationarity of primal functions.…
Robust Principal Component Analysis (RPCA) aims to recover a low-rank structure from noisy, partially observed data that is also corrupted by sparse, potentially large-magnitude outliers. Traditional RPCA models rely on convex relaxations,…
We consider a numerical framework tailored to identifying optimal parameters in the context of modelling disease propagation. Our focus is on understanding the behaviour of optimisation algorithms for such problems, where the dynamics are…
Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…