CyberSec Research

Continuous-time deep learning models, such as neural ordinary differential equations (ODEs), offer a promising framework for surrogate modeling of complex physical systems. A central challenge in training these models lies in learning expressive yet stable time-varying weights, particularly under computational constraints. This work investigates weight parameterization strategies that constrain the temporal evolution of weights to a low-dimensional subspace spanned by polynomial basis functions. We evaluate both monomial and Legendre polynomial bases within neural ODE and residual network (ResNet) architectures under discretize-then-optimize and optimize-then-discretize training paradigms. Experimental results across three high-dimensional benchmark problems show that Legendre parameterizations yield more stable training dynamics, reduce computational cost, and achieve accuracy comparable to or better than both monomial parameterizations and unconstrained weight models. These findings elucidate the role of basis choice in time-dependent weight parameterization and demonstrate that using orthogonal polynomial bases offers a favorable tradeoff between model expressivity and training efficiency.

Model predictive control (MPC) combined with reduced-order template models has emerged as a powerful tool for trajectory optimization in dynamic legged locomotion. However, loco-manipulation tasks performed by legged robots introduce additional complexity, necessitating computationally efficient MPC algorithms capable of handling high-degree-of-freedom (DoF) models. This letter presents a computationally efficient nonlinear MPC (NMPC) framework tailored for loco-manipulation tasks of quadrupedal robots equipped with robotic manipulators whose dynamics are non-negligible relative to those of the quadruped. The proposed framework adopts a decomposition strategy that couples locomotion template models -- such as the single rigid body (SRB) model -- with a full-order dynamic model of the robotic manipulator for torque-level control. This decomposition enables efficient real-time solution of the NMPC problem in a receding horizon fashion at 60 Hz. The optimal state and input trajectories generated by the NMPC for locomotion are tracked by a low-level nonlinear whole-body controller (WBC) running at 500 Hz, while the optimal torque commands for the manipulator are directly applied. The layered control architecture is validated through extensive numerical simulations and hardware experiments on a 15-kg Unitree Go2 quadrupedal robot augmented with a 4.4-kg 4-DoF Kinova arm. Given that the Kinova arm dynamics are non-negligible relative to the Go2 base, the proposed NMPC framework demonstrates robust stability in performing diverse loco-manipulation tasks, effectively handling external disturbances, payload variations, and uneven terrain.

This paper investigates the application of Deep Reinforcement Learning (DRL) to classical inventory management problems, with a focus on practical implementation considerations. We apply a DRL algorithm based on DirectBackprop to several fundamental inventory management scenarios including multi-period systems with lost sales (with and without lead times), perishable inventory management, dual sourcing, and joint inventory procurement and removal. The DRL approach learns policies across products using only historical information that would be available in practice, avoiding unrealistic assumptions about demand distributions or access to distribution parameters. We demonstrate that our generic DRL implementation performs competitively against or outperforms established benchmarks and heuristics across these diverse settings, while requiring minimal parameter tuning. Through examination of the learned policies, we show that the DRL approach naturally captures many known structural properties of optimal policies derived from traditional operations research methods. To further improve policy performance and interpretability, we propose a Structure-Informed Policy Network technique that explicitly incorporates analytically-derived characteristics of optimal policies into the learning process. This approach can help interpretability and add robustness to the policy in out-of-sample performance, as we demonstrate in an example with realistic demand data. Finally, we provide an illustrative application of DRL in a non-stationary setting. Our work bridges the gap between data-driven learning and analytical insights in inventory management while maintaining practical applicability.

In the Simple Plant Location Problem with Order (SPLPO), the aim is to open a subset of plants to assign every customer taking into account their preferences. Customers rank the plants in strict order and are assigned to their favorite open plant, and the objective is to minimize the location plus allocation costs. Here, we study a generalization of the SPLPO named the Capacitated Facility Location Problem with Customer Preferences (CFLCP) where a limited number of customers can be allocated to each facility. We consider the global preference maximization setting, where the customers preferences are globally maximized. For this setting, we define three new types of stable allocations, namely customer stable, pairwise stable and cyclic-coalition stable allocations, and we provide two mixed-integer linear formulations for each setting. In particular, our cyclic-coalition stable formulations are Pareto optimal in a global-preference maximization setting, in the sense that no customer can improve their allocation without making another one worse off. We provide extensive computational experiments and compare the quality of our allocations with previous ones defined in the literature. As an additional result, we present a novel formulation that provides Pareto optimal matchings in the Capacitated House Allocation problem of maximum cardinality.

We explore how warm-starting strategies can be integrated into scalarization-based approaches for multi-objective optimization in (mixed) integer linear programming. Scalarization methods remain widely used classical techniques to compute Pareto-optimal solutions in applied settings. They are favored due to their algorithmic simplicity and broad applicability across continuous and integer programs with an arbitrary number of objectives. While warm-starting has been applied in this context before, a systematic methodology and analysis remain lacking. We address this gap by providing a theoretical characterization of warm-starting within scalarization methods, focusing on the sequencing of subproblems. However, optimizing the order of subproblems to maximize warm-start efficiency may conflict with alternative criteria, such as early identification of infeasible regions. We quantify these trade-offs through an extensive computational study.

As renewable energy integration, sector coupling, and spatiotemporal detail increase, energy system optimization models grow in size and complexity, often pushing solvers to their performance limits. This systematic review explores parallelization strategies that can address these challenges. We first propose a classification scheme for linear energy system optimization models, covering their analytical focus, mathematical structure, and scope. We then review parallel decomposition methods, finding that while many offer performance benefits, no single approach is universally superior. The lack of standardized benchmark suites further complicates comparison. To address this, we recommend essential criteria for future benchmarks and minimum reporting standards. We also survey available software tools for parallel decomposition, including modular frameworks and algorithmic abstractions. Though centered on energy system models, our insights extend to the broader operations research field.

We study stochastic nonconvex Polyak-{\L}ojasiewicz minimax problems and propose algorithms that are both communication- and sample-efficient. The proposed methods are developed under three setups: decentralized/distributed, federated/centralized, and single-agent. By exploiting second-order Lipschitz continuity and integrating communication-efficient strategies, we develop a new decentralized normalized accelerated momentum method with local updates and establish its convergence to an $\varepsilon$-game stationary point. Compared to existing decentralized minimax algorithms, our proposed algorithm is the first to achieve a state-of-the-art communication complexity of order $\mathcal{O}\Big( \frac{ \kappa^3\varepsilon^{-3}}{NK(1-\lambda)^{3/2}}\Big)$, demonstrating linear speedup with respect to both the number of agents $K$ and the number of local updates $N$, as well as the best known dependence on the level of accuracy of the solution $\varepsilon$. In addition to improved complexity, our algorithm offers several practical advantages: it relaxes the strict two-time-scale step size ratio required by many existing algorithms, simplifies the stability conditions for step size selection, and eliminates the need for large batch sizes to attain the optimal sample complexity. Moreover, we propose more efficient variants tailored to federated/centralized and single-agent setups, and show that all variants achieve best-known results while effectively addressing some key issues. Experiments on robust logistic regression and fair neural network classifier using real-world datasets demonstrate the superior performance of the proposed methods over existing baselines.

Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop efficient first- and second-order optimization algorithms that exploit the intrinsic quotient structure of TTNs. Additionally, we devise a backpropagation algorithm for training TTNs in a kernel learning setting. We validate our methods through numerical experiments on a representative machine learning task.

This study evaluates the performance of a quantum-classical metaheuristic and a traditional classical mathematical programming solver, applied to two mathematical optimization models for an industry-relevant scheduling problem with autonomous guided vehicles (AGVs). The two models are: (1) a time-indexed mixed-integer linear program, and (2) a novel binary optimization problem with linear and quadratic constraints and a linear objective. Our experiments indicate that optimization methods are very susceptible to modeling techniques and different solvers require dedicated methods. We show in this work that quantum-classical metaheuristics can benefit from a new way of modeling mathematical optimization problems. Additionally, we present a detailed performance comparison of the two solution methods for each optimization model.

Advancements in high-frequency communication technologies using millimeter waves (mmWave), Tera- Hertz (THz), and optical wireless frequency bands are key for extending wireless connectivity beyond 5G. These technologies offer a broader spectrum than the one available on low- and mid-bands, enabling ultra-high-speed data rates, higher device density, enhanced security, and improved positioning accuracy. However, their performance relies heavily on clear Line-of-Sight (LoS) conditions, as Non-LoS components are significantly weaker, making blockages a major challenge to ensure suitable received signal power. This paper addresses this limitation by identifying the minimum number and optimal placement of access points (APs) needed to ensure LoS connectivity in stochastic/dynamic environments with random obstacle locations. To achieve this, the stochastic environment is carefully modeled as a graph, where the nodes represent sub-polygons of layout realizations, and the edges capture the visibility overlaps between them. By employing maximal clique clustering and maximum clique packing methods over this graph, the proposed approach determines the AP placement locations that guarantee either full LoS coverage or controlled LoS gaps, while seamlessly adapting to the stochastic variability in obstacle locations. Simulations results in a representative stochastic environment demonstrate a 25% reduction in the required number of APs, achieving a tolerable 5% coverage gap compared to AP deployment optimized for full LoS coverage.

This paper proposes an algorithm to efficiently solve multistage stochastic programs with block separable recourse where each recourse problem is a multistage stochastic program with stage-wise independent uncertainty. The algorithm first decomposes the full problem into a reduced master problem and subproblems using Adaptive Benders decomposition. The subproblems are then solved by an enhanced SDDP. The enhancement includes (1) valid bounds at each iteration, (2) a path exploration rule, (3) cut sharing among subproblems, and (4) guaranteed {\delta}-optimal convergence. The cuts for the subproblems are then shared by calling adaptive oracles. The key contribution of the paper is the first algorithm for solving this class of problems. The algorithm is demonstrated on a power system investment planning problem with multi-timescale uncertainty. The case study results show that (1) the proposed algorithm can efficiently solve this type of problem, (2) deterministic wind modelling underestimate the objective function, and (3) stochastic modelling of wind leads to different investment decisions.

Uncertainty in demand and supply conditions poses critical challenges to effective inventory management, especially in collaborative environments. Traditional inventory models, such as those based on the Economic Order Quantity (EOQ), often rely on fixed parameters and deterministic assumptions, limiting their ability to capture the complexity of real-world scenarios. This paper focuses on interval inventory situations, an extension of classical models in which demand is represented as intervals to account for uncertainty. This framework allows for a more flexible and realistic analysis of inventory decisions and cost-sharing among cooperating agents. We examine two interval-based allocation rules, the interval SOC-rule and the interval Shapley rule, designed to distribute joint ordering costs fairly and efficiently under uncertain demand. Their theoretical properties are analyzed, and their practical applicability is demonstrated through a case study involving the coordination of perfume inventories across seven Spanish airports, based on 2023 passenger traffic data provided by AENA. The findings highlight the potential of interval-based models to enable a robust and equitable allocation of inventory costs in the face of operational uncertainty.

This paper investigates a new class of homogeneous stochastic control problems with cone control constraints, extending the classical homogeneous stochastic linear-quadratic (LQ) framework to encompass nonlinear system dynamics and non-quadratic cost functionals. We demonstrate that, analogous to the LQ case, the optimal controls and value functions for these generalized problems are intimately connected to a novel class of highly nonlinear backward stochastic differential equations (BSDEs). We establish the existence and uniqueness of solutions to these BSDEs under three distinct sets of conditions, employing techniques such as truncation functions and logarithmic transformations. Furthermore, we derive explicit feedback representations for the optimal controls and value functions in terms of the solutions to these BSDEs, supported by rigorous verification arguments. Our general solvability conditions allow us to recover many known results for homogeneous LQ problems, including both standard and singular cases, as special instances of our framework.

This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the cost function of the design to be minimized depend on uncertain parameters. The probability distribution of the latter is itself known imperfectly, through a nominal law, reconstructed from a few observed samples. The distributionally robust optimal design problem is an intricate bilevel program which consists in minimizing the worst value of a statistical quantity of the cost function (typically, its expectation) when the law of the uncertain parameters belongs to a certain ``ambiguity set''. We address three classes of such problems: firstly, this ambiguity set is made of the probability laws whose Wasserstein distance to the nominal law is less than a given threshold; secondly, the ambiguity set is based on the first- and second-order moments of the actual and nominal probability laws. Eventually, a statistical quantity of the cost other than its expectation is made robust with respect to the law of the parameters, namely its conditional value at risk. Using techniques from convex duality, we derive tractable, single-level reformulations of these problems, framed over augmented sets of variables. Our methods are essentially agnostic of the optimal design framework; they are described in a unifying abstract framework, before being applied to multiple situations in density-based topology optimization and in geometric shape optimization. Several numerical examples are discussed in two and three space dimensions to appraise the features of the proposed techniques.

Modeling and evaluation of automated vehicles (AVs) in mixed-autonomy traffic is essential prior to their safe and efficient deployment. This is especially important at urban junctions where complex multi-agent interactions occur. Current approaches for modeling vehicular maneuvers and interactions at urban junctions have limitations in formulating non-cooperative interactions and vehicle dynamics within a unified mathematical framework. Previous studies either assume predefined paths or rely on cooperation and central controllability, limiting their realism and applicability in mixed-autonomy traffic. This paper addresses these limitations by proposing a modeling framework for trajectory planning and decentralized vehicular control at urban junctions. The framework employs a bi-level structure where the upper level generates kinematically feasible reference trajectories using an efficient graph search algorithm with a custom heuristic function, while the lower level employs a predictive controller for trajectory tracking and optimization. Unlike existing approaches, our framework does not require central controllability or knowledge sharing among vehicles. The vehicle kinematics are explicitly incorporated at both levels, and acceleration and steering angle are used as control variables. This intuitive formulation facilitates analysis of traffic efficiency, environmental impacts, and motion comfort. The framework's decentralized structure accommodates operational and stochastic elements, such as vehicles' detection range, perception uncertainties, and reaction delay, making the model suitable for safety analysis. Numerical and simulation experiments across diverse scenarios demonstrate the framework's capability in modeling accurate and realistic vehicular maneuvers and interactions at various urban junctions, including unsignalized intersections and roundabouts.

In recent years, mutual information optimal control has been proposed as an extension of maximum entropy optimal control. Both approaches introduce regularization terms to render the policy stochastic, and it is important to theoretically clarify the relationship between the temperature parameter (i.e., the coefficient of the regularization term) and the stochasticity of the policy. Unlike in maximum entropy optimal control, this relationship remains unexplored in mutual information optimal control. In this paper, we investigate this relationship for a mutual information optimal control problem (MIOCP) of discrete-time linear systems. After extending the result of a previous study of the MIOCP, we establish the existence of an optimal policy of the MIOCP, and then derive the respective conditions on the temperature parameter under which the optimal policy becomes stochastic and deterministic. Furthermore, we also derive the respective conditions on the temperature parameter under which the policy obtained by an alternating optimization algorithm becomes stochastic and deterministic. The validity of the theoretical results is demonstrated through numerical experiments.

Sequential optimality conditions play an important role in constrained optimization since they provide necessary conditions without requiring constraint qualifications (CQs). This paper introduces a second-order extension of the Approximate Karush-Kuhn-Tucker (AKKT) conditions, referred to as AKKT2, for nonlinear semidefinite optimization problems (NSDP). In particular, we provide a formal definition of AKKT2, as well as its stronger variant, called Complementary AKKT2 (CAKKT2), and prove that these conditions are necessary for local minima without any assumption. Moreover, under Robinson's CQ and the weak constant rank property, we show that AKKT2 implies the so-called weak second-order necessary condition. Finally, we propose a penalty-based algorithm that generates sequences whose accumulation points satisfy the AKKT2 and the CAKKT2 conditions.

We address the problem of steering the phase distribution of oscillators all receiving the same control input to a given target distribution. In a large population limit, the distribution of oscillators can be described by a probability density. Then, our problem can be seen as that of ensemble control with a constraint on the steady-state density. In particular, we consider the case where oscillators are subject to stochastic noise, for which the theoretical understanding is still lacking. First, we characterize the reachability of the phase distribution under periodic feedforward control via the Fourier coefficients of the target density and the phase sensitivity function of oscillators. This enables us to design a periodic input that makes the stationary distribution of oscillators closest to the target by solving a convex optimization problem. Next, we devise an ensemble control method combining periodic and feedback control, where the feedback component is designed to accelerate the convergence of the distribution of oscillators. We exhibit some convergence results for the proposed method, including a result that holds even under measurement errors in the phase distribution. The effectiveness of the proposed method is demonstrated by a numerical example.