With a computationally efficient approximation of the second-order information, natural gradient methods have been successful in solving large-scale structured optimization problems. We study the natural gradient methods for the large-scale decentralized optimization problems on Riemannian manifolds, where the local objective function defined by the local dataset is of a log-probability type. By utilizing the structure of the Riemannian Fisher information matrix (RFIM), we present an efficient decentralized Riemannian natural gradient descent (DRNGD) method. To overcome the communication issue of the high-dimension RFIM, we consider a class of structured problems for which the RFIM can be approximated by a Kronecker product of two low-dimension matrices. By performing the communications over the Kronecker factors, a high-quality approximation of the RFIM can be obtained in a low cost. We prove that DRNGD converges to a stationary point with the best-known rate of $\mathcal{O}(1/K)$. Numerical experiments demonstrate the efficiency of our proposed method compared with the state-of-the-art ones. To the best of our knowledge, this is the first Riemannian second-order method for solving decentralized manifold optimization problems.

This paper considers enforcing safety and stability of dynamical systems in the presence of model uncertainty. Safety and stability constraints may be specified using a control barrier function (CBF) and a control Lyapunov function (CLF), respectively. To take model uncertainty into account, robust and chance formulations of the constraints are commonly considered. However, this requires known error bounds or a known distribution for the model uncertainty, and the resulting formulations may suffer from over-conservatism or over-confidence. In this paper, we assume that only a finite set of model parametric uncertainty samples is available and formulate a distributionally robust chance-constrained program (DRCCP) for control synthesis with CBF safety and CLF stability guarantees. To facilitate efficient computation of control inputs during online execution, we present a reformulation of the DRCCP as a second-order cone program (SOCP). Our formulation is evaluated in an adaptive cruise control example in comparison to 1) a baseline CLF-CBF quadratic programming approach, 2) a robust approach that assumes known error bounds of the system uncertainty, and 3) a chance-constrained approach that assumes a known Gaussian Process distribution of the uncertainty.

Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local minima, limiting their applicability to complex or large-scale problems. Learning-based approaches have been developed to accelerate the topology optimization process, but these methods can generate designs with floating material and low performance when challenged with out-of-distribution constraint configurations. Recently, deep generative models, such as Generative Adversarial Networks and Diffusion Models, conditioned on constraints and physics fields have shown promise, but they require extensive pre-processing and surrogate models for improving performance. To address these issues, we propose a Generative Optimization method that integrates classic optimization like SIMP as a refining mechanism for the topology generated by a deep generative model. We also remove the need for conditioning on physical fields using a computationally inexpensive approximation inspired by classic ODE solutions and reduce the number of steps needed to generate a feasible and performant topology. Our method allows us to efficiently generate good topologies and explicitly guide them to regions with high manufacturability and high performance, without the need for external auxiliary models or additional labeled data. We believe that our method can lead to significant advancements in the design and optimization of structures in engineering applications, and can be applied to a broader spectrum of performance-aware engineering design problems.

Mirror descent, introduced by Nemirovski and Yudin in the 1970s, is a primal-dual convex optimization method that can be tailored to the geometry of the optimization problem at hand through the choice of a strongly convex potential function. It arises as a basic primitive in a variety of applications, including large-scale optimization, machine learning, and control. This paper proposes a variational formulation of mirror descent and of its stochastic variant, mirror Langevin dynamics. The main idea, inspired by the classic work of Brezis and Ekeland on variational principles for gradient flows, is to show that mirror descent emerges as a closed-loop solution for a certain optimal control problem, and the Bellman value function is given by the Bregman divergence between the initial condition and the global minimizer of the objective function.

We consider the problem of minimizing a non-convex function over a smooth manifold $\mathcal{M}$. We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method (ODCGM) which only requires computing a projection onto a vector space. ODCGM is infeasible but the iterates are constantly pulled towards the manifold, ensuring the convergence of ODCGM towards $\mathcal{M}$. ODCGM is much simpler to implement than the classical methods which require the computation of a retraction. Moreover, we show that ODCGM exhibits the near-optimal oracle complexities $\mathcal{O}(1/\varepsilon^2)$ and $\mathcal{O}(1/\varepsilon^4)$ in the deterministic and stochastic cases, respectively. Furthermore, we establish that, under an appropriate choice of the projection metric, our method recovers the landing algorithm of Ablin and Peyr\'e (2022), a recently introduced algorithm for optimization over the Stiefel manifold. As a result, we significantly extend the analysis of Ablin and Peyr\'e (2022), establishing near-optimal rates both in deterministic and stochastic frameworks. Finally, we perform numerical experiments which shows the efficiency of ODCGM in a high-dimensional setting.

Aruba AirMatch is designed to optimize network performance by quickly adapting to system-wide RF conditions. It goes beyond Aruba's Adaptive Radio Management technology by utilizing AI machine learning principles to automate RF optimization across the entire network.

The toolchain reduces the engineering complexity of NMPC implementations by providing the user with an easy-to-use application programming interface, and with the flexibility of using multiple state-of-the-art tools and numerical optimization solvers for rapid prototyping of NMPC solutions. IMPACT is written in Python, users can call it from Python and MATLAB, and the generated NMPC solvers can be directly executed from C, Python, MATLAB and Simulink. An application example is presented involving problem specification and deployment on embedded hardware using Simulink, showing the effectiveness and applicability of IMPACT for NMPC-based solutions.

The open-radio access network (O-RAN) embraces cloudification and network function virtualization for base-band function processing by dis-aggregated radio units (RUs), distributed units (DUs), and centralized units (CUs). These enable the cloud-RAN vision in full, where multiple mobile network operators (MNOs) can install their proprietary or open RUs, but lease on-demand computational resources for DU-CU functions from commonly available open-clouds via open x-haul interfaces. In this paper, we propose and compare the performances of min-max fairness and Vickrey-Clarke-Groves (VCG) auction-based x-haul and DU-CU resource allocation mechanisms to create a multi-tenant O-RAN ecosystem that is sustainable for small, medium, and large MNOs. The min-max fair approach minimizes the maximum OPEX of RUs through cost-sharing proportional to their demands, whereas the VCG auction-based approach minimizes the total OPEX for all resources utilized while extracting truthful demands from RUs. We consider time-wavelength division multiplexed (TWDM) passive optical network (PON)-based x-haul interfaces where PON virtualization technique is used to flexibly provide optical connections among RUs and edge-clouds at macro-cell RU locations as well as open-clouds at the central office locations. Moreover, we design efficient heuristics that yield significantly better economic efficiency and network resource utilization than conventional greedy resource allocation algorithms and reinforcement learning-based algorithms.

In this paper, we approach the problem of optimizing blackbox functions over large hybrid search spaces consisting of both combinatorial and continuous parameters. We demonstrate that previous evolutionary algorithms which rely on mutation-based approaches, while flexible over combinatorial spaces, suffer from a curse of dimensionality in high dimensional continuous spaces both theoretically and empirically, which thus limits their scope over hybrid search spaces as well. In order to combat this curse, we propose ES-ENAS, a simple and modular joint optimization procedure combining the class of sample-efficient smoothed gradient techniques, commonly known as Evolutionary Strategies (ES), with combinatorial optimizers in a highly scalable and intuitive way, inspired by the one-shot or supernet paradigm introduced in Efficient Neural Architecture Search (ENAS). By doing so, we achieve significantly more sample efficiency, which we empirically demonstrate over synthetic benchmarks, and are further able to apply ES-ENAS for architecture search over popular RL benchmarks.

In Autonomous Underwater Vehicles (AUVs) design, hull resistance is an important factor in determining the power requirements and range of vehicle and consequently affect battery size, weight, and volume requirement of the design. In this paper, we leverage on AI-based optimization algorithm along with Computational Fluid Dynamics (CFD) simulation to study the optimal hull design that minimizing the resistance. By running the CFD-based optimization at different operating velocities and turbulence intensity, we want to study/search the possibility of a universal design that will provide least resistance/near-optimal design across all operating conditions (operating velocity) and environmental conditions (turbulence intensity). Early result demonstrated that the optimal design found at low velocity and low turbulence condition performs very poor at high velocity and high turbulence conditions. However, a design that is optimal at high velocity and high turbulence conditions performs near-optimal across many considered velocity and turbulence conditions.