Variational inequalities (VIs) are a broad class of optimization problems encompassing machine learning problems ranging from standard convex minimization to more complex scenarios like min-max optimization and computing the equilibria of multi-player games. In convex optimization, strong convexity allows for fast statistical learning rates requiring only $\Theta(1/\epsilon)$ stochastic first-order oracle calls to find an $\epsilon$-optimal solution, rather than the standard $\Theta(1/\epsilon^2)$ calls. In this paper, we explain how one can similarly obtain fast $\Theta(1/\epsilon)$ rates for learning VIs that satisfy strong monotonicity, a generalization of strong convexity. Specifically, we demonstrate that standard stability-based generalization arguments for convex minimization extend directly to VIs when the domain admits a small covering, or when the operator is integrable and suboptimality is measured by potential functions; such as when finding equilibria in multi-player games.

Rare event sampling in dynamical systems is a fundamental problem arising in the natural sciences, which poses significant computational challenges due to an exponentially large space of trajectories. For settings where the dynamical system of interest follows a Brownian motion with known drift, the question of conditioning the process to reach a given endpoint or desired rare event is definitively answered by Doob's h-transform. However, the naive estimation of this transform is infeasible, as it requires simulating sufficiently many forward trajectories to estimate rare event probabilities. In this work, we propose a variational formulation of Doob's h-transform as an optimization problem over trajectories between a given initial point and the desired ending point. To solve this optimization, we propose a simulation-free training objective with a model parameterization that imposes the desired boundary conditions by design. Our approach significantly reduces the search space over trajectories and avoids expensive trajectory simulation and inefficient importance sampling estimators which are required in existing methods. We demonstrate the ability of our method to find feasible transition paths on real-world molecular simulation and protein folding tasks.

Bayesian optimization devolves the global optimization of a costly objective function to the global optimization of a sequence of acquisition functions. This inner-loop optimization can be catastrophically difficult if it involves posterior sample paths, especially in higher dimensions. We introduce an efficient global optimization strategy for posterior samples based on global rootfinding. It provides gradient-based optimizers with two sets of judiciously selected starting points, designed to combine exploration and exploitation. The number of starting points can be kept small without sacrificing optimization quality. Remarkably, even with just one point from each set, the global optimum is discovered most of the time. The algorithm scales practically linearly to high dimensions, breaking the curse of dimensionality. For Gaussian process Thompson sampling (GP-TS), we demonstrate remarkable improvement in both inner- and outer-loop optimization, surprisingly outperforming alternatives like EI and GP-UCB in most cases. Our approach also improves the performance of other posterior sample-based acquisition functions, such as variants of entropy search. Furthermore, we propose a sample-average formulation of GP-TS, which has a parameter to explicitly control exploitation and can be computed at the cost of one posterior sample. Our implementation is available at https://github.com/UQUH/TSRoots .

The objective of multi-view unsupervised feature and instance co-selection is to simultaneously iden-tify the most representative features and samples from multi-view unlabeled data, which aids in mit-igating the curse of dimensionality and reducing instance size to improve the performance of down-stream tasks. However, existing methods treat feature selection and instance selection as two separate processes, failing to leverage the potential interactions between the feature and instance spaces. Addi-tionally, previous co-selection methods for multi-view data require concatenating different views, which overlooks the consistent information among them. In this paper, we propose a CONsistency and DivErsity learNing-based multi-view unsupervised Feature and Instance co-selection (CONDEN-FI) to address the above-mentioned issues. Specifically, CONDEN-FI reconstructs mul-ti-view data from both the sample and feature spaces to learn representations that are consistent across views and specific to each view, enabling the simultaneous selection of the most important features and instances. Moreover, CONDEN-FI adaptively learns a view-consensus similarity graph to help select both dissimilar and similar samples in the reconstructed data space, leading to a more diverse selection of instances. An efficient algorithm is developed to solve the resultant optimization problem, and the comprehensive experimental results on real-world datasets demonstrate that CONDEN-FI is effective compared to state-of-the-art methods.

We introduce VOPy, an open-source Python library designed to address black-box vector optimization, where multiple objectives must be optimized simultaneously with respect to a partial order induced by a convex cone. VOPy extends beyond traditional multi-objective optimization (MOO) tools by enabling flexible, cone-based ordering of solutions; with an application scope that includes environments with observation noise, discrete or continuous design spaces, limited budgets, and batch observations. VOPy provides a modular architecture, facilitating the integration of existing methods and the development of novel algorithms. We detail VOPy's architecture, usage, and potential to advance research and application in the field of vector optimization. The source code for VOPy is available at https://github.com/Bilkent-CYBORG/VOPy.

In this paper, we propose FairML.jl, a Julia package providing a framework for fair classification in machine learning. In this framework, the fair learning process is divided into three stages. Each stage aims to reduce unfairness, such as disparate impact and disparate mistreatment, in the final prediction. For the preprocessing stage, we present a resampling method that addresses unfairness coming from data imbalances. The in-processing phase consist of a classification method. This can be either one coming from the MLJ.jl package, or a user defined one. For this phase, we incorporate fair ML methods that can handle unfairness to a certain degree through their optimization process. In the post-processing, we discuss the choice of the cut-off value for fair prediction. With simulations, we show the performance of the single phases and their combinations.

In modern chip design, placement aims at placing millions of circuit modules, which is an essential step that significantly influences power, performance, and area (PPA) metrics. Recently, reinforcement learning (RL) has emerged as a promising technique for improving placement quality, especially macro placement. However, current RL-based placement methods suffer from long training times, low generalization ability, and inability to guarantee PPA results. A key issue lies in the problem formulation, i.e., using RL to place from scratch, which results in limits useful information and inaccurate rewards during the training process. In this work, we propose an approach that utilizes RL for the refinement stage, which allows the RL policy to learn how to adjust existing placement layouts, thereby receiving sufficient information for the policy to act and obtain relatively dense and precise rewards. Additionally, we introduce the concept of regularity during training, which is considered an important metric in the chip design industry but is often overlooked in current RL placement methods. We evaluate our approach on the ISPD 2005 and ICCAD 2015 benchmark, comparing the global half-perimeter wirelength and regularity of our proposed method against several competitive approaches. Besides, we test the PPA performance using commercial software, showing that RL as a regulator can achieve significant PPA improvements. Our RL regulator can fine-tune placements from any method and enhance their quality. Our work opens up new possibilities for the application of RL in placement, providing a more effective and efficient approach to optimizing chip design. Our code is available at \url{https://github.com/lamda-bbo/macro-regulator}.

The rapid growth of the travel industry has increased the need for real-time optimization in reservation systems that could take care of huge data and transaction volumes. This study proposes a hybrid framework that ut folds an Artificial Intelligence and a Microservices approach for the performance optimization of the system. The AI algorithms forecast demand patterns, optimize the allocation of resources, and enhance decision-making driven by Microservices architecture, hence decentralizing system components for scalability, fault tolerance, and reduced downtime. The model provided focuses on major problems associated with the travel reservation systems such as latency of systems, load balancing and data consistency. It endows the systems with predictive models based on AI improved ability to forecast user demands. Microservices would also take care of different scales during uneven traffic patterns. Hence, both aspects ensure better handling of peak loads and spikes while minimizing delays and ensuring high service quality. A comparison was made between traditional reservation models, which are monolithic and the new model of AI-Microservices. Comparatively, the analysis results state that there is a drastic improvement in processing times where the system uptime and resource utilization proved the capability of AI and the microservices in transforming the travel industry in terms of reservation. This research work focused on AI and Microservices towards real-time optimization, providing critical insight into how to move forward with practical recommendations for upgrading travel reservation systems with this technology.

Low-rank matrix factorizations are a class of linear models widely used in various fields such as machine learning, signal processing, and data analysis. These models approximate a matrix as the product of two smaller matrices, where the left matrix captures latent features while the right matrix linearly decomposes the data based on these features. There are many ways to define what makes a component "important." Standard LRMFs, such as the truncated singular value decomposition, focus on minimizing the distance between the original matrix and its low-rank approximation. In this thesis, the notion of "importance" is closely linked to interpretability and uniqueness, which are key to obtaining reliable and meaningful results. This thesis thus focuses on volume-based constraints and regularizations designed to enhance interpretability and uniqueness. We first introduce two new volume-constrained LRMFs designed to enhance these properties. The first assumes that data points are naturally bounded (e.g., movie ratings between 1 and 5 stars) and can be explained by convex combinations of features within the same bounds, allowing them to be interpreted in the same way as the data. The second model is more general, constraining the factors to belong to convex polytopes. Then, two variants of volume-regularized LRMFs are proposed. The first minimizes the volume of the latent features, encouraging them to cluster closely together, while the second maximizes the volume of the decompositions, promoting sparse representations. Across all these models, uniqueness is achieved under the core principle that the factors must be "sufficiently scattered" within their respective feasible sets. Motivated by applications such as blind source separation and missing data imputation, this thesis also proposes efficient algorithms that make these models practical for real-world applications.

If combined to perturbations and that can be hence used in several analysis with co-design strategies, this approach allows for the simultaneous or optimization scenarios. Contact-rich loco-manipulation optimization of a robot's physical structure and problems and some dynamical systems show the property of control logic, resulting in systems that are robust and efficient deterministic chaos. Our formulation's advantage is offering in complex, dynamic environments. For instance, a legged a clearer theoretical link with the properties of their nonlinear robot could navigate uneven terrain using the same control dynamics. The Lyapunov exponents, which are at signals as on flat ground, relying on its mechanical structure the cornerstone of our method, give a powerful tool to to gracefully adapt to perturbations. Embodied intelligence characterize non-linear systems long-term behavior [14, 15].