arXiv subjects

Jona Klemenc

Publications and source records attributed to Jona Klemenc.

8 recordsLinked to original sources

arXiv2026

Trade-off invariance for weighted scalarizations in multi-objective optimization

We consider weighted-sum scalarizations for an abstract multi-objective minimization problem defined by the vector-valued map $U\ni u\mapsto ( f_1(u),\ldots, f_N(u))$, where $U$ is an arbitrary nonempty set and no topology, convexity, compactness, or lower semicontinuity assumption is imposed. Using the open simplex as parameter space for positive weights, we show that the Trade-off Invariance Principle for scalarizations yields a generic uniqueness property in the objective space. Namely, for almost every weight vector, all minimizers of the corresponding weighted-sum scalarization have the same objective vector. Moreover, excluding again a null-measure subset, all minimizing sequences determine the same limiting objective vector, independently of the chosen sequence. We also give a geometric interpretation of these results in the attainable objective set: for almost every positive weight vector, the scalarization exposes at most one nondominated point. Moreover, minimizing sequences determine at most one asymptotically exposed objective vector in the closure of the attainable set.

math.OC↗

arXiv2026

From Consensus-Based Optimization to Evolution Strategies: Proof of Global Convergence

Consensus-based optimization (CBO) is a powerful and versatile zero-order multi-particle method designed to provably solve high-dimensional global optimization problems, including those that are genuinely nonconvex or nonsmooth. The method relies on a balance between stochastic exploration and contraction toward a consensus point, which is defined via the Laplace principle as a proxy for the global minimizer. In this paper, we introduce new CBO variants that address practical and theoretical limitations of the original formulation of this novel optimization methodology. First, we propose a model called $δ$-CBO}, which incorporates nonvanishing diffusion to prevent premature collapse to suboptimal states. We also develop a numerically stable implementation, the Consensus Freezing scheme, that remains robust even for arbitrarily large time steps by freezing the consensus point over time intervals. We connect these models through appropriate asymptotic limits. Furthermore, we derive from the Consensus Freezing scheme by suitable time rescaling and asymptotics a further algorithm, the Consensus Hopping scheme, which can be interpreted as a form of $(1,λ)$-Evolution Strategy. For all these schemes, we characterize for the first time the invariant measures and establish global convergence results, including exponential convergence rates.

math.OC↗

arXiv2026

Balanced quasistatic evolutions of critical points in metric spaces

Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have been derived as vanishing viscosity and inertia limits, leading to balanced viscosity solutions. However, for nonconvex energies, these constructions have been realized in Euclidean spaces and assume non-degenerate critical points. In this paper, we take a different approach by decoupling the time scales of the energy evolution and of the transition to equilibria. Namely, starting from an equilibrium configuration, we let the energy evolve, while keeping frozen the system state; then, we update the state by freezing the energy, while letting the system transit via gradient flow or an approximation of it (e.g., minimizing movement or backward differentiation schemes). This approach has several advantages. It aligns with the physical principle that systems transit through energy-minimizing steady states. It is also fully constructive and computationally implementable, with physical and computational costs governed by appropriate action functionals. Additionally, our analysis is simpler and more general than previous formulations in the literature, as it does not require non-degenerate critical points. Finally, this approach extends to evolutions in locally compact metric path spaces, and our axiomatic presentation allows for various realizations.

math.OC↗

arXiv2025

Trade-off Invariance Principle for minimizers of regularized functionals

In this paper, we consider functionals of the form $H_α(u)=F(u)+αG(u)$ with $α\in[0,+\infty)$, where $u$ varies in a set $U\neq\emptyset$ (without further structure). We first revisit a result stating that, excluding at most countably many values of $α$, we have $\inf_{H_α^\star}G= \sup_{H_α^\star}G$, where $H_α^\star := \arg\min_UH_α$, which is assumed to be non-empty. Then, we prove a stronger result that concerns the invariance of the limiting value of the functional $G$ along minimizing sequences for $H_α$, which extends the above Principle to the case $H_α^\star= \emptyset$. Moreover, we show to what extent these findings generalize to multi-regularized functionals and -- in the presence of an underlying differentiable structure -- to critical points. Finally, the main result implies an unexpected consequence for functionals regularized with uniformly convex norms: excluding again at most countably many values of $α$, it turns out that for a minimizing sequence, convergence to a minimizer in the weak or strong sense is equivalent.

math.OC↗

arXiv2024

A-BDD: Leveraging Data Augmentations for Safe Autonomous Driving in Adverse Weather and Lighting

High-autonomy vehicle functions rely on machine learning (ML) algorithms to understand the environment. Despite displaying remarkable performance in fair weather scenarios, perception algorithms are heavily affected by adverse weather and lighting conditions. To overcome these difficulties, ML engineers mainly rely on comprehensive real-world datasets. However, the difficulties in real-world data collection for critical areas of the operational design domain (ODD) often means synthetic data is required for perception training and safety validation. Thus, we present A-BDD, a large set of over 60,000 synthetically augmented images based on BDD100K that are equipped with semantic segmentation and bounding box annotations (inherited from the BDD100K dataset). The dataset contains augmented data for rain, fog, overcast and sunglare/shadow with varying intensity levels. We further introduce novel strategies utilizing feature-based image quality metrics like FID and CMMD, which help identify useful augmented and real-world data for ML training and testing. By conducting experiments on A-BDD, we provide evidence that data augmentations can play a pivotal role in closing performance gaps in adverse weather and lighting conditions.

cs.CV↗

arXiv2023

Selecting Models based on the Risk of Damage Caused by Adversarial Attacks

Regulation, legal liabilities, and societal concerns challenge the adoption of AI in safety and security-critical applications. One of the key concerns is that adversaries can cause harm by manipulating model predictions without being detected. Regulation hence demands an assessment of the risk of damage caused by adversaries. Yet, there is no method to translate this high-level demand into actionable metrics that quantify the risk of damage. In this article, we propose a method to model and statistically estimate the probability of damage arising from adversarial attacks. We show that our proposed estimator is statistically consistent and unbiased. In experiments, we demonstrate that the estimation results of our method have a clear and actionable interpretation and outperform conventional metrics. We then show how operators can use the estimation results to reliably select the model with the lowest risk.

cs.LG↗

arXiv2022

The stable hull of an exact $\infty$-category

We construct a left adjoint $\mathcal{H}^\text{st}\colon \mathbf{Ex}_{\infty} \rightarrow \mathbf{St}_{\infty}$ to the inclusion $\mathbf{St}_{\infty} \hookrightarrow \mathbf{Ex}_{\infty}$ of the $\infty$-category of stable $\infty$-categories into the $\infty$-category of exact $\infty$-categories, which we call the stable hull. For every exact $\infty$-category $\mathcal{E}$, the unit functor $\mathcal{E} \rightarrow \mathcal{H}^\text{st}(\mathcal{E})$ is fully faithful and preserves and reflects exact sequences. This provides an $\infty$-categorical variant of the Gabriel-Quillen embedding for ordinary exact categories. If $\mathcal{E}$ is an ordinary exact category, the stable hull $\mathcal{H}^\text{st}(\mathcal{E})$ is equivalent to the bounded derived $\infty$-category of $\mathcal{E}$.

math.AT↗

arXiv2020

On angles, projections and iterations

We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean spaces the convergence of the alternating method is not determined by the principal angles between the subspaces involved. In the second part, we investigate the properties of the Oppenheim angle between two linear projections. We discuss, in particular, the question of existence and uniqueness of "consistency projections" in this context.

math.FA↗