Optimization over Riemannian manifolds has drawn a lot of attention due to its applications in machine learning and related disciplines, including low-rank matrix completion [6, 49], phase retrieval [3, 45], blind deconvolution [21] and dictionary learning [11, 43]. Riemannian optimization aims at minimizing an objective function over a Riemannian manifold. When the objective function is smooth, people have proposed to solve them using Riemannian gradient method, Riemannian quasi-Newton method, Riemannian trust-region method, etc. Work along this line has been summarized in the monographs [1, 5] as well as some other references. Recently, due to increasing demand from application areas such as machine learning, statistics, signal processing and so on, there is a line of work designing efficient and scalable algorithms for solving Riemannian optimization problems with nonsmooth objectives. For example, people have studied Riemannian subgradient method [33], Riemannian proximal gradient method [10, 23], Riemannian proximal point algorithm [9], Riemannian proximal-linear algorithm [51], zeroth-order Riemannian algorithms [32], and so on. One thing that has not been widely considered is how to design alternating direction method of multipliers (ADMM) on manifolds.

We present a novel approach for black-box VI that bypasses the difficulties of stochastic gradient ascent, including the task of selecting step-sizes. Our approach involves using a sequence of sample average approximation (SAA) problems. SAA approximates the solution of stochastic optimization problems by transforming them into deterministic ones. We use quasi-Newton methods and line search to solve each deterministic optimization problem and present a heuristic policy to automate hyperparameter selection. Our experiments show that our method simplifies the VI problem and achieves faster performance than existing methods.

Robots often rely on a repertoire of previously-learned motion policies for performing tasks of diverse complexities. When facing unseen task conditions or when new task requirements arise, robots must adapt their motion policies accordingly. In this context, policy optimization is the \emph{de facto} paradigm to adapt robot policies as a function of task-specific objectives. Most commonly-used motion policies carry particular structures that are often overlooked in policy optimization algorithms. We instead propose to leverage the structure of probabilistic policies by casting the policy optimization as an optimal transport problem. Specifically, we focus on robot motion policies that build on Gaussian mixture models (GMMs) and formulate the policy optimization as a Wassertein gradient flow over the GMMs space. This naturally allows us to constrain the policy updates via the $L^2$-Wasserstein distance between GMMs to enhance the stability of the policy optimization process. Furthermore, we leverage the geometry of the Bures-Wasserstein manifold to optimize the Gaussian distributions of the GMM policy via Riemannian optimization. We evaluate our approach on common robotic settings: Reaching motions, collision-avoidance behaviors, and multi-goal tasks. Our results show that our method outperforms common policy optimization baselines in terms of task success rate and low-variance solutions.

Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem, subjected to a set of dynamics constraints characterized by a nonlinear dynamics model, is solved at each time step. Despite its versatility, the performance of nonlinear MPC often depends on the accuracy of the dynamics model. In this work, we leverage deep learning tools, namely knowledge-based neural ordinary differential equations (KNODE) and deep ensembles, to improve the prediction accuracy of this model. In particular, we learn an ensemble of KNODE models, which we refer to as the KNODE ensemble, to obtain an accurate prediction of the true system dynamics. This learned model is then integrated into a novel learning-enhanced nonlinear MPC framework. We provide sufficient conditions that guarantees asymptotic stability of the closed-loop system and show that these conditions can be implemented in practice. We show that the KNODE ensemble provides more accurate predictions and illustrate the efficacy and closed-loop performance of the proposed nonlinear MPC framework using two case studies.

By enabling vehicles to communicate with each other and with the traffic environment using cellular networks, we redefine transportation, improving road safety and transportation services, increasing efficiency of traffic flows, and reducing environmental impact. This paper proposes a decentralized approach for provisioning Cellular Vehicular-to-Network (C-V2N) services, addressing the coupled problems of service task placement and scaling of edge resources. We formalize the joint problem and prove its complexity. We propose an approach to tackle it, linking the two problems, employing decentralized decision-making using (i) a greedy approach for task placement and (ii) a Deep Deterministic Policy Gradient (DDPG) based approach for scaling. We benchmark the performance of our approach, focusing on the scaling agent, against several State-of-the-Art (SoA) scaling approaches via simulations using a real C-V2N traffic data set. The results show that DDPG-based solutions outperform SoA solutions, keeping the latency experienced by the C-V2N service below the target delay while optimizing the use of computing resources. By conducting a complexity analysis, we prove that DDPG-based solutions achieve runtimes in the range of sub-milliseconds, meeting the strict latency requirements of C-V2N services. Index Terms--cellular vehicle to network, task placement, edge resource scaling, deep deterministic policy gradient.

This study considers the control problem with signal temporal logic (STL) specifications. Prior works have adopted smoothing techniques to address this problem within a feasible time frame and solve the problem by applying sequential quadratic programming (SQP) methods naively. However, one of the drawbacks of this approach is that solutions can easily become trapped in local minima that do not satisfy the specification. In this study, we propose a new optimization method, termed CCP-based SQP, based on the convex-concave procedure (CCP). Our framework includes a new robustness decomposition method that decomposes the robustness function into a set of constraints, resulting in a form of difference of convex (DC) program that can be solved efficiently. We solve this DC program sequentially as a quadratic program by only approximating the disjunctive parts of the specifications. Our experimental results demonstrate that our method has a superior performance compared to the state-of-the-art SQP methods in terms of both robustness and computational time.

Signal Temporal Logic (STL) is capable of expressing a broad range of temporal properties that controlled dynamical systems must satisfy. In the literature, both mixed-integer programming (MIP) and nonlinear programming (NLP) methods have been applied to solve optimal control problems with STL specifications. However, neither approach has succeeded in solving problems with complex long-horizon STL specifications within a realistic timeframe. This study proposes a new optimization framework, called \textit{STLCCP}, which explicitly incorporates several structures of STL to mitigate this issue. The core of our framework is a structure-aware decomposition of STL formulas, which converts the original program into a difference of convex (DC) programs. This program is then solved as a convex quadratic program sequentially, based on the convex-concave procedure (CCP). Our numerical experiments on several commonly used benchmarks demonstrate that this framework can effectively handle complex scenarios over long horizons, which have been challenging to address even using state-of-the-art optimization methods.

It has been commonly observed that a teacher model with superior performance does not necessarily result in a stronger student, highlighting a discrepancy between current teacher training practices and effective knowledge transfer. In order to enhance the guidance of the teacher training process, we introduce the concept of distillation influence to determine the impact of distillation from each training sample on the student's generalization ability. In this paper, we propose Learning Good Teacher Matters (LGTM), an efficient training technique for incorporating distillation influence into the teacher's learning process. By prioritizing samples that are likely to enhance the student's generalization ability, our LGTM outperforms 10 common knowledge distillation baselines on 6 text classification tasks in the GLUE benchmark.

Machine learning has recently made significant strides in reducing design cycle time for complex products. Ship design, which currently involves years long cycles and small batch production, could greatly benefit from these advancements. By developing a machine learning tool for ship design that learns from the design of many different types of ships, tradeoffs in ship design could be identified and optimized. However, the lack of publicly available ship design datasets currently limits the potential for leveraging machine learning in generalized ship design. To address this gap, this paper presents a large dataset of thirty thousand ship hulls, each with design and functional performance information, including parameterization, mesh, point cloud, and image representations, as well as thirty two hydrodynamic drag measures under different operating conditions. The dataset is structured to allow human input and is also designed for computational methods. Additionally, the paper introduces a set of twelve ship hulls from publicly available CAD repositories to showcase the proposed parameterizations ability to accurately reconstruct existing hulls. A surrogate model was developed to predict the thirty two wave drag coefficients, which was then implemented in a genetic algorithm case study to reduce the total drag of a hull by sixty percent while maintaining the shape of the hulls cross section and the length of the parallel midbody. Our work provides a comprehensive dataset and application examples for other researchers to use in advancing data driven ship design.

In this paper, we consider the problem of inferring the sign of a link based on limited sign data in signed networks. Regarding this link sign prediction problem, SDGNN (Signed Directed Graph Neural Networks) provides the best prediction performance currently to the best of our knowledge. In this paper, we propose a different link sign prediction architecture call SELO (Subgraph Encoding via Linear Optimization), which obtains overall leading prediction performances compared the state-of-the-art algorithm SDGNN. The proposed model utilizes a subgraph encoding approach to learn edge embeddings for signed directed networks. In particular, a signed subgraph encoding approach is introduced to embed each subgraph into a likelihood matrix instead of the adjacency matrix through a linear optimization method. Comprehensive experiments are conducted on six real-world signed networks with AUC, F1, micro-F1, and Macro-F1 as the evaluation metrics. The experiment results show that the proposed SELO model outperforms existing baseline feature-based methods and embedding-based methods on all the six real-world networks and in all the four evaluation metrics.