Hyperparameter optimization (HPO) is a key component of machine learning models for achieving peak predictive performance. While numerous methods and algorithms for HPO have been proposed over the last years, little progress has been made in illuminating and examining the actual structure of these black-box optimization problems. Exploratory landscape analysis (ELA) subsumes a set of techniques that can be used to gain knowledge about properties of unknown optimization problems. In this paper, we evaluate the performance of five different black-box optimizers on 30 HPO problems, which consist of two-, three- and five-dimensional continuous search spaces of the XGBoost learner trained on 10 different data sets. This is contrasted with the performance of the same optimizers evaluated on 360 problem instances from the black-box optimization benchmark (BBOB). We then compute ELA features on the HPO and BBOB problems and examine similarities and differences. A cluster analysis of the HPO and BBOB problems in ELA feature space allows us to identify how the HPO problems compare to the BBOB problems on a structural meta-level. We identify a subset of BBOB problems that are close to the HPO problems in ELA feature space and show that optimizer performance is comparably similar on these two sets of benchmark problems. We highlight open challenges of ELA for HPO and discuss potential directions of future research and applications.

Neural architecture search (NAS) has been studied extensively and has grown to become a research field with substantial impact. While classical single-objective NAS searches for the architecture with the best performance, multi-objective NAS considers multiple objectives that should be optimized simultaneously, e.g., minimizing resource usage along the validation error. Although considerable progress has been made in the field of multi-objective NAS, we argue that there is some discrepancy between the actual optimization problem of practical interest and the optimization problem that multi-objective NAS tries to solve. We resolve this discrepancy by formulating the multi-objective NAS problem as a quality diversity optimization (QDO) problem and introduce three quality diversity NAS optimizers (two of them belonging to the group of multifidelity optimizers), which search for high-performing yet diverse architectures that are optimal for application-specific niches, e.g., hardware constraints. By comparing these optimizers to their multi-objective counterparts, we demonstrate that quality diversity NAS in general outperforms multi-objective NAS with respect to quality of solutions and efficiency. We further show how applications and future NAS research can thrive on QDO.

This work presents a computationally lightweight motion planner for over-actuated platforms. For this purpose, a general state-space model for mobile platforms with several kinematic chains is defined, which considers non-linearities and constraints. The proposed motion planner is based on a sequential multi-stage approach that takes advantage of the warm start on each step. Firstly, a globally optimal and smooth 2D/3D trajectory is generated using the Fast Marching Method. This trajectory is fed as a warm start to a sequential linear quadratic regulator that is able to generate an optimal motion plan without constraints for all the platform actuators. Finally, a feasible motion plan is generated considering the constraints defined in the model. In this respect, the sequential linear quadratic regulator is employed again, taking the previously generated unconstrained motion plan as a warm start. This novel approach has been deployed into the Exomars Testing Rover of the European Space Agency. This rover is an Ackermann-capable planetary exploration testbed that is equipped with a robotic arm. Several experiments were carried out demonstrating that the proposed approach speeds up the computation time, increasing the success ratio for a martian sample retrieval mission, which can be considered as a representative use case of an over-actuated mobile platform.

Vehicle Routing Problems (VRPs) in real-world applications often come with various constraints, therefore bring additional computational challenges to exact solution methods or heuristic search approaches. The recent idea to learn heuristic move patterns from sample data has become increasingly promising to reduce solution developing costs. However, using learning-based approaches to address more types of constrained VRP remains a challenge. The difficulty lies in controlling for constraint violations while searching for optimal solutions. To overcome this challenge, we propose a Reinforcement Learning based method to solve soft-constrained VRPs by incorporating the Lagrangian relaxation technique and using constrained policy optimization. We apply the method on three common types of VRPs, the Travelling Salesman Problem with Time Windows (TSPTW), the Capacitated VRP (CVRP) and the Capacitated VRP with Time Windows (CVRPTW), to show the generalizability of the proposed method. After comparing to existing RL-based methods and open-source heuristic solvers, we demonstrate its competitive performance in finding solutions with a good balance in travel distance, constraint violations and inference speed.

We consider online imitation learning (OIL), where the task is to find a policy that imitates the behavior of an expert via active interaction with the environment. We aim to bridge the gap between the theory and practice of policy optimization algorithms for OIL by analyzing one of the most popular OIL algorithms, DAGGER. Specifically, if the class of policies is sufficiently expressive to contain the expert policy, we prove that DAGGER achieves constant regret. Unlike previous bounds that require the losses to be strongly-convex, our result only requires the weaker assumption that the losses be strongly-convex with respect to the policy's sufficient statistics (not its parameterization). In order to ensure convergence for a wider class of policies and losses, we augment DAGGER with an additional regularization term. In particular, we propose a variant of Follow-the-Regularized-Leader (FTRL) and its adaptive variant for OIL and develop a memory-efficient implementation, which matches the memory requirements of FTL. Assuming that the loss functions are smooth and convex with respect to the parameters of the policy, we also prove that FTRL achieves constant regret for any sufficiently expressive policy class, while retaining $O(\sqrt{T})$ regret in the worst-case. We demonstrate the effectiveness of these algorithms with experiments on synthetic and high-dimensional control tasks.

We present the first distributed optimization algorithm with lazy communication for collaborative geometric estimation, the backbone of modern collaborative simultaneous localization and mapping (SLAM) and structure-from-motion (SfM) applications. Our method allows agents to cooperatively reconstruct a shared geometric model on a central server by fusing individual observations, but without the need to transmit potentially sensitive information about the agents themselves (such as their locations). Furthermore, to alleviate the burden of communication during iterative optimization, we design a set of communication triggering conditions that enable agents to selectively upload a targeted subset of local information that is useful to global optimization. Our approach thus achieves significant communication reduction with minimal impact on optimization performance. As our main theoretical contribution, we prove that our method converges to first-order critical points with a global sublinear convergence rate. Numerical evaluations on bundle adjustment problems from collaborative SLAM and SfM datasets show that our method performs competitively against existing distributed techniques, while achieving up to 78% total communication reduction.

When robots operate in real-world off-road environments with unstructured terrains, the ability to adapt their navigational policy is critical for effective and safe navigation. However, off-road terrains introduce several challenges to robot navigation, including dynamic obstacles and terrain uncertainty, leading to inefficient traversal or navigation failures. To address these challenges, we introduce a novel approach for adaptation by negotiation that enables a ground robot to adjust its navigational behaviors through a negotiation process. Our approach first learns prediction models for various navigational policies to function as a terrain-aware joint local controller and planner. Then, through a new negotiation process, our approach learns from various policies' interactions with the environment to agree on the optimal combination of policies in an online fashion to adapt robot navigation to unstructured off-road terrains on the fly. Additionally, we implement a new optimization algorithm that offers the optimal solution for robot negotiation in real-time during execution. Experimental results have validated that our method for adaptation by negotiation outperforms previous methods for robot navigation, especially over unseen and uncertain dynamic terrains.

Reinforcement Learning (RL) and continuous nonlinear control have been successfully deployed in multiple domains of complicated sequential decision-making tasks. However, given the exploration nature of the learning process and the presence of model uncertainty, it is challenging to apply them to safety-critical control tasks due to the lack of safety guarantee. On the other hand, while combining control-theoretical approaches with learning algorithms has shown promise in safe RL applications, the sample efficiency of safe data collection process for control is not well addressed. In this paper, we propose a \emph{provably} sample efficient episodic safe learning framework for online control tasks that leverages safe exploration and exploitation in an unknown, nonlinear dynamical system. In particular, the framework 1) extends control barrier functions (CBFs) in a stochastic setting to achieve provable high-probability safety under uncertainty during model learning and 2) integrates an optimism-based exploration strategy to efficiently guide the safe exploration process with learned dynamics for \emph{near optimal} control performance. We provide formal analysis on the episodic regret bound against the optimal controller and probabilistic safety with theoretical guarantees. Simulation results are provided to demonstrate the effectiveness and efficiency of the proposed algorithm.

Training machine learning models on massive datasets incurs substantial computational costs. To alleviate such costs, there has been a sustained effort to develop data-efficient training methods that can carefully select subsets of the training examples that generalize on par with the full training data. However, existing methods are limited in providing theoretical guarantees for the quality of the models trained on the extracted subsets, and may perform poorly in practice. We propose AdaCore, a method that leverages the geometry of the data to extract subsets of the training examples for efficient machine learning. The key idea behind our method is to dynamically approximate the curvature of the loss function via an exponentially-averaged estimate of the Hessian to select weighted subsets (coresets) that provide a close approximation of the full gradient preconditioned with the Hessian. We prove rigorous guarantees for the convergence of various first and second-order methods applied to the subsets chosen by AdaCore. Our extensive experiments show that AdaCore extracts coresets with higher quality compared to baselines and speeds up training of convex and non-convex machine learning models, such as logistic regression and neural networks, by over 2.9x over the full data and 4.5x over random subsets.

Due to the very narrow beam used in millimeter wave communication (mmWave), beam alignment (BA) is a critical issue. In this work, we investigate the issue of mmWave BA and present a novel beam alignment scheme on the basis of a machine learning strategy, Bayesian optimization (BO). In this context, we consider the beam alignment issue to be a black box function and then use BO to find the possible optimal beam pair. During the BA procedure, this strategy exploits information from the measured beam pairs to predict the best beam pair. In addition, we suggest a novel BO algorithm based on the gradient boosting regression tree model. The simulation results demonstrate the spectral efficiency performance of our proposed schemes for BA using three different surrogate models. They also demonstrate that the proposed schemes can achieve spectral efficiency with a small overhead when compared to the orthogonal match pursuit (OMP) algorithm and the Thompson sampling-based multi-armed bandit (TS-MAB) method.