The rapid growth of the ride-hailing industry has revolutionized urban transportation worldwide. Despite its benefits, equity concerns arise as underserved communities face limited accessibility to affordable ride-hailing services. A key issue in this context is the vehicle rebalancing problem, where idle vehicles are moved to areas with anticipated demand. Without equitable approaches in demand forecasting and rebalancing strategies, these practices can further deepen existing inequities. In the realm of ride-hailing, three main facets of fairness are recognized: algorithmic fairness, fairness to drivers, and fairness to riders. This paper focuses on enhancing both algorithmic and rider fairness through a novel vehicle rebalancing method. We introduce an approach that combines a Socio-Aware Spatial-Temporal Graph Convolutional Network (SA-STGCN) for refined demand prediction and a fairness-integrated Matching-Integrated Vehicle Rebalancing (MIVR) model for subsequent vehicle rebalancing. Our methodology is designed to reduce prediction discrepancies and ensure equitable service provision across diverse regions. The effectiveness of our system is evaluated using simulations based on real-world ride-hailing data. The results suggest that our proposed method enhances both accuracy and fairness in forecasting ride-hailing demand, ultimately resulting in more equitable vehicle rebalancing in subsequent operations. Specifically, the algorithm developed in this study effectively reduces the standard deviation and average customer wait times by 6.48% and 0.49%, respectively. This achievement signifies a beneficial outcome for ride-hailing platforms, striking a balance between operational efficiency and fairness.

The tasks of designing messenger RNAs and non-coding RNAs are discrete optimization problems, and several versions of these problems are NP-hard. As an alternative to commonly used local search methods, we formulate these problems as continuous optimization and develop a general framework for this optimization based on a new concept of "expected partition function". The basic idea is to start with a distribution over all possible candidate sequences, and extend the objective function from a sequence to a distribution. We then use gradient descent-based optimization methods to improve the extended objective function, and the distribution will gradually shrink towards a one-hot sequence (i.e., a single sequence). We consider two important case studies within this framework, the mRNA design problem optimizing for partition function (i.e., ensemble free energy) and the non-coding RNA design problem optimizing for conditional (i.e., Boltzmann) probability. In both cases, our approach demonstrate promising preliminary results.

Design patterns provide a systematic way to convey solutions to recurring modeling challenges. This paper introduces design patterns for hybrid modeling, an approach that combines modeling based on first principles with data-driven modeling techniques. While both approaches have complementary advantages there are often multiple ways to combine them into a hybrid model, and the appropriate solution will depend on the problem at hand. In this paper, we provide four base patterns that can serve as blueprints for combining data-driven components with domain knowledge into a hybrid approach. In addition, we also present two composition patterns that govern the combination of the base patterns into more complex hybrid models. Each design pattern is illustrated by typical use cases from application areas such as climate modeling, engineering, and physics.

Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions produced by this so-called \emph{predict-then-optimize} procedure can be highly sensitive to uncertain parameters. In this work, we contribute to recent efforts in producing \emph{decision-focused} predictions, i.e., to build predictive models that are constructed with the goal of minimizing a \emph{regret} measure on the decisions taken with them. We formulate the exact expected regret minimization as a pessimistic bilevel optimization model. Then, using duality arguments, we reformulate it as a non-convex quadratic optimization problem. Finally, we show various computational techniques to achieve tractability. We report extensive computational results on shortest-path instances with uncertain cost vectors. Our results indicate that our approach can improve training performance over the approach of Elmachtoub and Grigas (2022), a state-of-the-art method for decision-focused learning.

There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the proposed stochastic method exhibits a linear convergence rate for solving sharp instances with a high probability. In addition, we propose an efficient coordinate-based stochastic oracle for unconstrained bilinear problems, which has $\mathcal O(1)$ per iteration cost and improves the complexity of the existing deterministic and stochastic algorithms. Finally, we show that the obtained linear convergence rate is nearly optimal (upto $\log$ terms) for a wide class of stochastic primal dual methods.

The performance of modern machine learning algorithms depends upon the selection of a set of hyperparameters. Common examples of hyperparameters are learning rate and the number of layers in a dense neural network. Auto-ML is a branch of optimization that has produced important contributions in this area. Within Auto-ML, hyperband-based approaches, which eliminate poorly-performing configurations after evaluating them at low budgets, are among the most effective. However, the performance of these algorithms strongly depends on how effectively they allocate the computational budget to various hyperparameter configurations. We present the new Parameter Optimization with Conscious Allocation (POCA), a hyperband-based algorithm that adaptively allocates the inputted budget to the hyperparameter configurations it generates following a Bayesian sampling scheme. We compare POCA to its nearest competitor at optimizing the hyperparameters of an artificial toy function and a deep neural network and find that POCA finds strong configurations faster in both settings.

Neural networks (NNs), both living and artificial, work due to being complex systems of neurons, each having its own specialization. Revealing these specializations is important for understanding NNs inner working mechanisms. The only way to do this for a living system, the neural response of which to a stimulus is not a known (let alone differentiable) function is to build a feedback loop of exposing it to stimuli, the properties of which can be iteratively varied aiming in the direction of maximal response. To test such a loop on a living network, one should first learn how to run it quickly and efficiently, reaching most effective stimuli (ones that maximize certain neurons activation) in least possible number of iterations. We present a framework with an effective design of such a loop, successfully testing it on an artificial spiking neural network (SNN, a model that mimics the behaviour of NNs in living brains). Our optimization method used for activation maximization (AM) was based on low-rank tensor decomposition (Tensor Train, TT) of the activation function's discretization over its domain the latent parameter space of stimuli (CIFAR10-size color images, generated by either VQ-VAE or SN-GAN from their latent description vectors, fed to the SNN). To our knowledge, the present work is the first attempt to perform effective AM for SNNs. The source code of our framework, MANGO (for Maximization of neural Activation via Non-Gradient Optimization) is available on GitHub.

This study proposes a unified optimization-based planning framework that addresses the precise and efficient navigation of a controlled object within a constrained region, while contending with obstacles. We focus on handling two collision avoidance problems, i.e., the object not colliding with obstacles and not colliding with boundaries of the constrained region. The object or obstacle is denoted as a union of convex polytopes and ellipsoids, and the constrained region is denoted as an intersection of such convex sets. Using these representations, collision avoidance can be approached by formulating explicit constraints that separate two convex sets, or ensure that a convex set is contained in another convex set, referred to as separating constraints and containing constraints, respectively. We propose to use the hyperplane separation theorem to formulate differentiable separating constraints, and utilize the S-procedure and geometrical methods to formulate smooth containing constraints. We state that compared to the state of the art, the proposed formulations allow a considerable reduction in nonlinear program size and geometry-based initialization in auxiliary variables used to formulate collision avoidance constraints. Finally, the efficacy of the proposed unified planning framework is evaluated in two contexts, autonomous parking in tractor-trailer vehicles and overtaking on curved lanes. The results in both cases exhibit an improved computational performance compared to existing methods.

The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the entire chain of operations executed by an iterative optimization solver. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is asymptotically equivalent to the solution of a linear system by a particular iterative method. Several practical pitfalls of unrolling are demonstrated in light of these insights, and a system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations. Experiments over various end-to-end optimization and learning tasks demonstrate the advantages of this system both computationally, and in terms of flexibility over various optimization problem forms.

Adaptive optimization methods are widely recognized as among the most popular approaches for training Deep Neural Networks (DNNs). Techniques such as Adam, AdaGrad, and AdaHessian utilize a preconditioner that modifies the search direction by incorporating information about the curvature of the objective function. However, despite their adaptive characteristics, these methods still require manual fine-tuning of the step-size. This, in turn, impacts the time required to solve a particular problem. This paper presents an optimization framework named SANIA to tackle these challenges. Beyond eliminating the need for manual step-size hyperparameter settings, SANIA incorporates techniques to address poorly scaled or ill-conditioned problems. We also explore several preconditioning methods, including Hutchinson's method, which approximates the Hessian diagonal of the loss function. We conclude with an extensive empirical examination of the proposed techniques across classification tasks, covering both convex and non-convex contexts.