Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping

We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas laid out in [H. Attouch and G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima, preprint, arXiv:1506.02823, 201]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order $O(t^{-2})$ for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.Comment: 25 pages, 3 Figure

A multiobjective continuation method to compute the regularization path of deep neural networks

Sparsity is a highly desired feature in deep neural networks (DNNs) since it ensures numerical efficiency, improves the interpretability of models (due to the smaller number of relevant features), and robustness. In machine learning approaches based on linear models, it is well known that there exists a connecting path between the sparsest solution in terms of the $\ell^1$ norm (i.e., zero weights) and the non-regularized solution, which is called the regularization path. Very recently, there was a first attempt to extend the concept of regularization paths to DNNs by means of treating the empirical loss and sparsity ($\ell^1$ norm) as two conflicting criteria and solving the resulting multiobjective optimization problem. However, due to the non-smoothness of the $\ell^1$ norm and the high number of parameters, this approach is not very efficient from a computational perspective. To overcome this limitation, we present an algorithm that allows for the approximation of the entire Pareto front for the above-mentioned objectives in a very efficient manner. We present numerical examples using both deterministic and stochastic gradients. We furthermore demonstrate that knowledge of the regularization path allows for a well-generalizing network parametrization.Comment: 7 pages, 6 figure

Multiobjective Optimization of Non-Smooth PDE-Constrained Problems

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization"

The Crowdsourced Replication Initiative: Investigating Immigration and Social Policy Preferences. Executive Report.

In an era of mass migration, social scientists, populist parties and social movements raise concerns over the future of immigration-destination societies. What impacts does this have on policy and social solidarity? Comparative cross-national research, relying mostly on secondary data, has findings in different directions. There is a threat of selective model reporting and lack of replicability. The heterogeneity of countries obscures attempts to clearly define data-generating models. P-hacking and HARKing lurk among standard research practices in this area.This project employs crowdsourcing to address these issues. It draws on replication, deliberation, meta-analysis and harnessing the power of many minds at once. The Crowdsourced Replication Initiative carries two main goals, (a) to better investigate the linkage between immigration and social policy preferences across countries, and (b) to develop crowdsourcing as a social science method. The Executive Report provides short reviews of the area of social policy preferences and immigration, and the methods and impetus behind crowdsourcing plus a description of the entire project. Three main areas of findings will appear in three papers, that are registered as PAPs or in process

A unified design allows fine-tuning of biosensor parameters and application across bacterial species

In recent years, transcriptional biosensors have become valuable tools in metabolic engineering as they allow semiquantitative determination of metabolites in single cells. Although being perfectly suitable tools for high-throughput screenings, application of transcriptional biosensors is often limited by the intrinsic characteristics of the individual sensor components and their interplay. In addition, biosensors often fail to work properly in heterologous host systems due to signal saturation at low intracellular metabolite concentrations, which typically limits their use in high-level producer strains at advanced engineering stages.We here introduce a biosensor design, which allows fine-tuning of important sensor parameters and restores the sensor response in a heterologous expression host. As a key feature of our design, the regulator activity is controlled through the expression level of the respective gene by different (synthetic) constitutive promoters selected for the used expression host. In this context, we constructed biosensors responding to basic amino acids or ring-hydroxylated phenylpropanoids for applications in Corynebacterium glutamicum and Escherichia coli. Detailed characterization of these biosensors in liquid cultures and during single-cell analysis using flow cytometry showed that the presented sensor design enables customization of important biosensor parameters as well as application of these sensors in relevant heterologous hosts

The Crowdsourced Replication Initiative: Investigating Immigration and Social Policy Preferences. Executive Report

Breznau N, Rinke EM, Wuttke A, et al. The Crowdsourced Replication Initiative: Investigating Immigration and Social Policy Preferences. Executive Report. 2019

Observing many researchers using the same data and hypothesis reveals a hidden universe of uncertainty.

This study explores how researchers' analytical choices affect the reliability of scientific findings. Most discussions of reliability problems in science focus on systematic biases. We broaden the lens to emphasize the idiosyncrasy of conscious and unconscious decisions that researchers make during data analysis. We coordinated 161 researchers in 73 research teams and observed their research decisions as they used the same data to independently test the same prominent social science hypothesis: that greater immigration reduces support for social policies among the public. In this typical case of social science research, research teams reported both widely diverging numerical findings and substantive conclusions despite identical start conditions. Researchers' expertise, prior beliefs, and expectations barely predict the wide variation in research outcomes. More than 95% of the total variance in numerical results remains unexplained even after qualitative coding of all identifiable decisions in each team's workflow. This reveals a universe of uncertainty that remains hidden when considering a single study in isolation. The idiosyncratic nature of how researchers' results and conclusions varied is a previously underappreciated explanation for why many scientific hypotheses remain contested. These results call for greater epistemic humility and clarity in reporting scientific findings

The Crowdsourced Replication Initiative

Crowdsourced Research on Immigration and Social Policy Preference

Observing Many Researchers Using the Same Data and Hypothesis Reveals a Hidden Universe of Uncertainty

Breznau N, Rinke EM, Wuttke A, et al. Observing Many Researchers Using the Same Data and Hypothesis Reveals a Hidden Universe of Uncertainty. 2021.This study explores how researchers’ analytical choices affect the reliability of scientific findings. Most discussions of reliability problems in science focus on systematic biases. We broaden the lens to include conscious and unconscious decisions that researchers make during data analysis and that may lead to diverging results. We coordinated 161 researchers in 73 research teams and observed their research decisions as they used the same data to independently test the same prominent social science hypothesis: that greater immigration reduces support for social policies among the public. In this typical case of research based on secondary data, we find that research teams reported widely diverging numerical findings and substantive conclusions despite identical start conditions. Researchers’ expertise, prior beliefs, and expectations barely predicted the wide variation in research outcomes. More than 90% of the total variance in numerical results remained unexplained even after accounting for research decisions identified via qualitative coding of each team’s workflow. This reveals a universe of uncertainty that is hidden when considering a single study in isolation. The idiosyncratic nature of how researchers’ results and conclusions varied is a new explanation for why many scientific hypotheses remain contested. It calls for greater humility and clarity in reporting scientific findings