X-ray computed tomography (CT) plays a key role in digitizing three-dimensional structures for a wide range of medical and industrial applications. Traditional CT systems often rely on standard circular and helical scan trajectories, which may not be optimal for challenging scenarios involving large objects, complex structures, or resource constraints. In response to these challenges, we are exploring the potential of twin robotic CT systems, which offer the flexibility to acquire projections from arbitrary views around the object of interest. Ensuring complete and mathematically sound reconstructions becomes critical in such systems. In this work, we present an integer programming-based CT trajectory optimization method. Utilizing discrete data completeness conditions, we formulate an optimization problem to select an optimized set of projections. This approach enforces data completeness and considers absorption-based metrics for reliability evaluation. We compare our method with an equidistant circular CT trajectory and a greedy approach. While greedy already performs well in some cases, we provide a way to improve greedy-based projection selection using an integer optimization approach. Our approach improves CT trajectories and quantifies the optimality of the solution in terms of an optimality gap.

This paper addresses the resolution of the 3-SAT problem using a QAOA-like approach. The chosen principle involves modeling the solution ranks of the 3-SAT problem, which, in this particular case, directly represent a solution. This results in a highly compact circuit with few gates, enabling the modeling of large-sized 3-SAT problems. Numerical experimentation demonstrates that the approach can solve instances composed of 91 clauses and 20 variables with an implementation based on Qiskit.

This paper proposes a novel, more computationally efficient method for optimizing robot excitation trajectories for dynamic parameter identification, emphasizing self-collision avoidance. This addresses the system identification challenges for getting high-quality training data associated with co-manipulated robotic arms that can be equipped with a variety of tools, a common scenario in industrial but also clinical and research contexts. Utilizing the Unified Robotics Description Format (URDF) to implement a symbolic Python implementation of the Recursive Newton-Euler Algorithm (RNEA), the approach aids in dynamically estimating parameters such as inertia using regression analyses on data from real robots. The excitation trajectory was evaluated and achieved on par criteria when compared to state-of-the-art reported results which didn't consider self-collision and tool calibrations. Furthermore, physical Human-Robot Interaction (pHRI) admittance control experiments were conducted in a surgical context to evaluate the derived inverse dynamics model showing a 30.1\% workload reduction by the NASA TLX questionnaire.

Creating and maximizing influence among the customers is one of the central goals of an advertiser, and hence, remains an active area of research in recent times. In this advertisement technique, the advertisers approach an influence provider for a specific number of views of their content on a payment basis. Now, if the influence provider can provide the required number of views or more, he will receive the full, else a partial payment. In the context of an influence provider, it is a loss for him if he offers more or less views. This is formalized as 'Regret', and naturally, in the context of the influence provider, the goal will be to minimize this quantity. In this paper, we solve this problem in the context of billboard advertisement and pose it as a discrete optimization problem. We propose four efficient solution approaches for this problem and analyze them to understand their time and space complexity. We implement all the solution methodologies with real-life datasets and compare the obtained results with the existing solution approaches from the literature. We observe that the proposed solutions lead to less regret while taking less computational time.

Federated Learning (FL) is an emerging paradigm in machine learning without exposing clients' raw data. In practical scenarios with numerous clients, encouraging fair and efficient client participation in federated learning is of utmost importance, which is also challenging given the heterogeneity in data distribution and device properties. Existing works have proposed different client-selection methods that consider fairness; however, they fail to select clients with high utilities while simultaneously achieving fair accuracy levels. In this paper, we propose a fair client-selection approach that unlocks threefold fairness in federated learning. In addition to having a fair client-selection strategy, we enforce an equitable number of rounds for client participation and ensure a fair accuracy distribution over the clients. The experimental results demonstrate that FedFair^3, in comparison to the state-of-the-art baselines, achieves 18.15% less accuracy variance on the IID data and 54.78% on the non-IID data, without decreasing the global accuracy. Furthermore, it shows 24.36% less wall-clock training time on average.

This paper presents a new approach and algorithm for solving a class of constrained Bi-Level Optimization (BLO) problems in which the lower-level problem involves constraints coupling both upper-level and lower-level variables. Such problems have recently gained significant attention due to their broad applicability in machine learning. However, conventional gradient-based methods unavoidably rely on computationally intensive calculations related to the Hessian matrix. To address this challenge, we begin by devising a smooth proximal Lagrangian value function to handle the constrained lower-level problem. Utilizing this construct, we introduce a single-level reformulation for constrained BLOs that transforms the original BLO problem into an equivalent optimization problem with smooth constraints. Enabled by this reformulation, we develop a Hessian-free gradient-based algorithm-termed proximal Lagrangian Value function-based Hessian-free Bi-level Algorithm (LV-HBA)-that is straightforward to implement in a single loop manner. Consequently, LV-HBA is especially well-suited for machine learning applications. Furthermore, we offer non-asymptotic convergence analysis for LV-HBA, eliminating the need for traditional strong convexity assumptions for the lower-level problem while also being capable of accommodating non-singleton scenarios. Empirical results substantiate the algorithm's superior practical performance.

Answering complex logical queries on incomplete knowledge graphs (KGs) is a fundamental and challenging task in multi-hop reasoning. Recent work defines this task as an end-to-end optimization problem, which significantly reduces the training cost and enhances the generalization of the model by a pretrained link predictors for query answering. However, most existing proposals ignore the critical semantic knowledge inherently available in KGs, such as type information, which could help answer complex logical queries. To this end, we propose TypE-based Neural Link Prediction Adapter (TENLPA), a novel model that constructs type-based entity-relation graphs to discover the latent relationships between entities and relations by leveraging type information in KGs. Meanwhile, in order to effectively combine type information with complex logical queries, an adaptive learning mechanism is introduced, which is trained by back-propagating during the complex query answering process to achieve adaptive adjustment of neural link predictors. Experiments on 3 standard datasets show that TENLPA model achieves state-of-the-art performance on complex query answering with good generalization and robustness.

PPO (Proximal Policy Optimization) algorithm has demonstrated excellent performance in many fields, and it is considered as a simple version of TRPO (Trust Region Policy Optimization) algorithm. However, the ratio clipping operation in PPO may not always effectively enforce the trust region constraints, this can be a potential factor affecting the stability of the algorithm. In this paper, we propose SPO (Simple Policy Optimization) algorithm, which introduces a novel clipping method for KL divergence between the old and current policies. SPO can effectively enforce the trust region constraints in almost all environments, while still maintaining the simplicity of a first-order algorithm. Comparative experiments in Atari 2600 environments show that SPO sometimes provides stronger performance than PPO. Code is available at https://github.com/MyRepositories-hub/Simple-Policy-Optimization.

Deep Generative Models (DGMs) are versatile tools for learning data representations while adequately incorporating domain knowledge such as the specification of conditional probability distributions. Recently proposed DGMs tackle the important task of comparing data sets from different sources. One such example is the setting of contrastive analysis that focuses on describing patterns that are enriched in a target data set compared to a background data set. The practical deployment of those models often assumes that DGMs naturally infer interpretable and modular latent representations, which is known to be an issue in practice. Consequently, existing methods often rely on ad-hoc regularization schemes, although without any theoretical grounding. Here, we propose a theory of identifiability for comparative DGMs by extending recent advances in the field of non-linear independent component analysis. We show that, while these models lack identifiability across a general class of mixing functions, they surprisingly become identifiable when the mixing function is piece-wise affine (e.g., parameterized by a ReLU neural network). We also investigate the impact of model misspecification, and empirically show that previously proposed regularization techniques for fitting comparative DGMs help with identifiability when the number of latent variables is not known in advance. Finally, we introduce a novel methodology for fitting comparative DGMs that improves the treatment of multiple data sources via multi-objective optimization and that helps adjust the hyperparameter for the regularization in an interpretable manner, using constrained optimization. We empirically validate our theory and new methodology using simulated data as well as a recent data set of genetic perturbations in cells profiled via single-cell RNA sequencing.

Federated learning (FL) enables multiple clients to collaboratively learn a shared model without sharing their individual data. Concerns about utility, privacy, and training efficiency in FL have garnered significant research attention. Differential privacy has emerged as a prevalent technique in FL, safeguarding the privacy of individual user data while impacting utility and training efficiency. Within Differential Privacy Federated Learning (DPFL), previous studies have primarily focused on the utility-privacy trade-off, neglecting training efficiency, which is crucial for timely completion. Moreover, differential privacy achieves privacy by introducing controlled randomness (noise) on selected clients in each communication round. Previous work has mainly examined the impact of noise level ($\sigma$) and communication rounds ($T$) on the privacy-utility dynamic, overlooking other influential factors like the sample ratio ($q$, the proportion of selected clients). This paper systematically formulates an efficiency-constrained utility-privacy bi-objective optimization problem in DPFL, focusing on $\sigma$, $T$, and $q$. We provide a comprehensive theoretical analysis, yielding analytical solutions for the Pareto front. Extensive empirical experiments verify the validity and efficacy of our analysis, offering valuable guidance for low-cost parameter design in DPFL.