Related papers: A Constrained Optimisation Framework for Parameter…
This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given a first-order method, a function class, and a noise model…
A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
We address the problem of parameter identification for the standard pharmacokinetic/pharmacodynamic (PK/PD) model for anesthetic drugs. Our main contribution is the development of a global optimization method that guarantees finding the…
The Robust Satisficing (RS) model is an emerging approach to robust optimization, offering streamlined procedures and robust generalization across various applications. However, the statistical theory of RS remains unexplored in the…
Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…
Some of the most used sampling mechanisms that implicitly leverage a social network depend on tuning parameters; for instance, Respondent-Driven Sampling (RDS) is specified by the number of seeds and maximum number of referrals. We are…
A novel framework is introduced to formalize identifiability in well-specified but ill-posed linear regression models. The framework is distribution-free and accommodates highly correlated features that may or may not relate to the…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
In this paper, we introduce a new optimization algorithm that is well suited for solving parameter estimation problems. We call our new method cubic regularized Newton with affine scaling (CRNAS). In contrast to so-called first-order…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
Data-driven decision-making has drawn scrutiny from policy makers due to fears of potential discrimination, and a growing literature has begun to develop fair statistical techniques. However, these techniques are often specialized to one…
This paper studies lower bounds for fundamental optimization problems in the CONGEST model. We show that solving problems exactly in this model can be a hard task, by providing $\tilde{\Omega}(n^2)$ lower bounds for cornerstone problems,…
We consider an identification problem, where the state $u$ is governed by a fractional elliptic equation and the unknown variable corresponds to the order $s \in (0,1)$ of the underlying operator. We study the existence of an optimal pair…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
This is a technical report that extends and clarifies the results presented in [1]. The model identification problem for asymptotically stable linear time invariant systems is considered. The system output is affected by an additive noise…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
This paper introduces Tempered Fractional Gradient Descent (TFGD), a novel optimization framework that synergizes fractional calculus with exponential tempering to enhance gradient-based learning. Traditional gradient descent methods often…