We propose a globally-accelerated, first-order method for the optimization of smooth and (strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We achieve the same convergence rates as Nesterov's accelerated gradient descent, up to a multiplicative geometric penalty and log factors. Crucially, we can enforce our method to stay within a compact set we define. Prior fully accelerated works \emph{resort to assuming} that the iterates of their algorithms stay in some pre-specified compact set, except for two previous methods of limited applicability. For our manifolds, this solves the open question in [KY22] about obtaining global general acceleration without iterates assumptively staying in the feasible set. In our solution, we design an accelerated Riemannian inexact proximal point algorithm, which is a result that was unknown even with exact access to the proximal operator, and is of independent interest. For smooth functions, we show we can implement the prox step inexactly with first-order methods in Riemannian balls of certain diameter that is enough for global accelerated optimization.

For decades, motorsport has been an incubator for innovations in the automotive sector and brought forth systems like disk brakes or rearview mirrors. Autonomous racing series such as Roborace, F1Tenth, or the Indy Autonomous Challenge (IAC) are envisioned as playing a similar role within the autonomous vehicle sector, serving as a proving ground for new technology at the limits of the autonomous systems capabilities. This paper outlines the software stack and approach of the TUM Autonomous Motorsport team for their participation in the Indy Autonomous Challenge, which holds two competitions: A single-vehicle competition on the Indianapolis Motor Speedway and a passing competition at the Las Vegas Motor Speedway. Nine university teams used an identical vehicle platform: A modified Indy Lights chassis equipped with sensors, a computing platform, and actuators. All the teams developed different algorithms for object detection, localization, planning, prediction, and control of the race cars. The team from TUM placed first in Indianapolis and secured second place in Las Vegas. During the final of the passing competition, the TUM team reached speeds and accelerations close to the limit of the vehicle, peaking at around 270 km/h and 28 ms2. This paper will present details of the vehicle hardware platform, the developed algorithms, and the workflow to test and enhance the software applied during the two-year project. We derive deep insights into the autonomous vehicle's behavior at high speed and high acceleration by providing a detailed competition analysis. Based on this, we deduce a list of lessons learned and provide insights on promising areas of future work based on the real-world evaluation of the displayed concepts.

In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty. In contrast to classical MDPs, which only account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, robust MDPs additionally account for ambiguity by optimizing in view of the most adverse transition kernel from a prescribed ambiguity set. In this paper, we develop a novel solution framework for robust MDPs with s-rectangular ambiguity sets that decomposes the problem into a sequence of robust Bellman updates and simplex projections. Exploiting the rich structure present in the simplex projections corresponding to phi-divergence ambiguity sets, we show that the associated s-rectangular robust MDPs can be solved substantially faster than with state-of-the-art commercial solvers as well as a recent first-order solution scheme, thus rendering them attractive alternatives to classical MDPs in practical applications.

This paper presents a constrained-optimization formulation for the prioritized execution of learned robot tasks. The framework lends itself to the execution of tasks encoded by value functions, such as tasks learned using the reinforcement learning paradigm. The tasks are encoded as constraints of a convex optimization program by using control Lyapunov functions. Moreover, an additional constraint is enforced in order to specify relative priorities between the tasks. The proposed approach is showcased in simulation using a team of mobile robots executing coordinated multi-robot tasks.

Resource-intensive computations are a major factor that limits the effectiveness of automated machine learning solutions. In the paper, we propose a modular approach that can be used to increase the quality of evolutionary optimization for modelling pipelines with a graph-based structure. It consists of several stages - parallelization, caching and evaluation. Heterogeneous and remote resources can be involved in the evaluation stage. The conducted experiments confirm the correctness and effectiveness of the proposed approach. The implemented algorithms are available as a part of the open-source framework FEDOT.

Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning hedging against distributional uncertainty, e.g., the uncertainty of an empirical distribution compared to the true underlying distribution. This paper investigates the connections among the three frameworks and, in particular, explores why these frameworks tend to have smaller generalization errors. Specifically, first, we suggest a quantitative definition for "distributional robustness", propose the concept of "robustness measure", and formalize several philosophical concepts in distributionally robust optimization. Second, we show that Bayesian methods are distributionally robust in the probably approximately correct (PAC) sense; In addition, by constructing a Dirichlet-process-like prior in Bayesian nonparametrics, it can be proven that any regularized empirical risk minimization method is equivalent to a Bayesian method. Third, we show that generalization errors of machine learning models can be characterized using the distributional uncertainty of the nominal distribution and the robustness measures of these machine learning models, which is a new perspective to bound generalization errors, and therefore, explain the reason why distributionally robust machine learning models, Bayesian models, and regularization models tend to have smaller generalization errors.

Graph convolutional networks (GCNs) have been attracting widespread attentions due to their encouraging performance and powerful generalizations. However, few work provide a general view to interpret various GCNs and guide GCNs' designs. In this paper, by revisiting the original GCN, we induce an interpretable regularizer-centerd optimization framework, in which by building appropriate regularizers we can interpret most GCNs, such as APPNP, JKNet, DAGNN, and GNN-LF/HF. Further, under the proposed framework, we devise a dual-regularizer graph convolutional network (dubbed tsGCN) to capture topological and semantic structures from graph data. Since the derived learning rule for tsGCN contains an inverse of a large matrix and thus is time-consuming, we leverage the Woodbury matrix identity and low-rank approximation tricks to successfully decrease the high computational complexity of computing infinite-order graph convolutions. Extensive experiments on eight public datasets demonstrate that tsGCN achieves superior performance against quite a few state-of-the-art competitors w.r.t. classification tasks.

An enhanced framework for peak-to-average power ratio ($\mathsf{PAPR}$) reduction and waveform design for Multiple-Input-Multiple-Output ($\mathsf{MIMO}$) orthogonal frequency-division multiplexing ($\mathsf{OFDM}$) systems, based on a convolutional-autoencoder ($\mathsf{CAE}$) architecture, is presented. The end-to-end learning-based autoencoder ($\mathsf{AE}$) for communication networks represents the network by an encoder and decoder, where in between, the learned latent representation goes through a physical communication channel. We introduce a joint learning scheme based on projected gradient descent iteration to optimize the spectral mask behavior and MIMO detection under the influence of a non-linear high power amplifier ($\mathsf{HPA}$) and a multipath fading channel. The offered efficient implementation novel waveform design technique utilizes only a single $\mathsf{PAPR}$ reduction block for all antennas. It is throughput-lossless, as no side information is required at the decoder. Performance is analyzed by examining the bit error rate ($\mathsf{BER}$), the $\mathsf{PAPR}$, and the spectral response and compared with classical $\mathsf{PAPR}$ reduction $\mathsf{MIMO}$ detector methods on 5G simulated data. The suggested system exhibits competitive performance when considering all optimization criteria simultaneously. We apply gradual loss learning for multi-objective optimization and show empirically that a single trained model covers the tasks of $\mathsf{PAPR}$ reduction, spectrum design, and $\mathsf{MIMO}$ detection together over a wide range of SNR levels.

In order to achieve the dual goals of privacy and learning across distributed data, Federated Learning (FL) systems rely on frequent exchanges of large files (model updates) between a set of clients and the server. As such FL systems are exposed to, or indeed the cause of, congestion across a wide set of network resources. Lossy compression can be used to reduce the size of exchanged files and associated delays, at the cost of adding noise to model updates. By judiciously adapting clients' compression to varying network congestion, an FL application can reduce wall clock training time. To that end, we propose a Network Adaptive Compression (NAC-FL) policy, which dynamically varies the client's lossy compression choices to network congestion variations. We prove, under appropriate assumptions, that NAC-FL is asymptotically optimal in terms of directly minimizing the expected wall clock training time. Further, we show via simulation that NAC-FL achieves robust performance improvements with higher gains in settings with positively correlated delays across time.

Developments in cooperative trajectory planning of connected autonomous vehicles (CAVs) have gathered considerable momentum and research attention. Generally, such problems present strong non-linearity and non-convexity, rendering great difficulties in finding the optimal solution. Existing methods typically suffer from low computational efficiency, and this hinders the appropriate applications in large-scale scenarios involving an increasing number of vehicles. To tackle this problem, we propose a novel decentralized iterative linear quadratic regulator (iLQR) algorithm by leveraging the dual consensus alternating direction method of multipliers (ADMM). First, the original non-convex optimization problem is reformulated into a series of convex optimization problems through iterative neighbourhood approximation. Then, the dual of each convex optimization problem is shown to have a consensus structure, which facilitates the use of consensus ADMM to solve for the dual solution in a fully decentralized and parallel architecture. Finally, the primal solution corresponding to the trajectory of each vehicle is recovered by solving a linear quadratic regulator (LQR) problem iteratively, and a novel trajectory update strategy is proposed to ensure the dynamic feasibility of vehicles. With the proposed development, the computation burden is significantly alleviated such that real-time performance is attainable. Two traffic scenarios are presented to validate the proposed algorithm, and thorough comparisons between our proposed method and baseline methods (including centralized iLQR, IPOPT, and SQP) are conducted to demonstrate the scalability of the proposed approach.