Optimizing an unknown function under safety constraints is a central task in robotics, biomedical engineering, and many other disciplines, and increasingly safe Bayesian Optimization (BO) is used for this. Due to the safety critical nature of these applications, it is of utmost importance that theoretical safety guarantees for these algorithms translate into the real world. In this work, we investigate three safety-related issues of the popular class of SafeOpt-type algorithms. First, these algorithms critically rely on frequentist uncertainty bounds for Gaussian Process (GP) regression, but concrete implementations typically utilize heuristics that invalidate all safety guarantees. We provide a detailed analysis of this problem and introduce Real-\b{eta}-SafeOpt, a variant of the SafeOpt algorithm that leverages recent GP bounds and thus retains all theoretical guarantees. Second, we identify assuming an upper bound on the reproducing kernel Hilbert space (RKHS) norm of the target function, a key technical assumption in SafeOpt-like algorithms, as a central obstacle to real-world usage. To overcome this challenge, we introduce the Lipschitz-only Safe Bayesian Optimization (LoSBO) algorithm, which guarantees safety without an assumption on the RKHS bound, and empirically show that this algorithm is not only safe, but also exhibits superior performance compared to the state-of-the-art on several function classes. Third, SafeOpt and derived algorithms rely on a discrete search space, making them difficult to apply to higher-dimensional problems. To widen the applicability of these algorithms, we introduce Lipschitz-only GP-UCB (LoS-GP-UCB), a variant of LoSBO applicable to moderately high-dimensional problems, while retaining safety.

Constrained variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due to their simplicity and scalability. However, they typically rely on projection or linear minimization oracles to navigate the feasible set, which becomes computationally expensive in practical scenarios featuring multiple functional constraints. Existing efforts to tackle such functional constrained variational inequality problems have centered on primal-dual algorithms grounded in the Lagrangian function. These algorithms along with their theoretical analysis often require the existence and prior knowledge of the optimal Lagrange multipliers. In this work, we propose a simple primal method, termed Constrained Gradient Method (CGM), for addressing functional constrained variational inequality problems, without necessitating any information on the optimal Lagrange multipliers. We establish a non-asymptotic convergence analysis of the algorithm for variational inequality problems with monotone operators under smooth constraints. Remarkably, our algorithms match the complexity of projection-based methods in terms of operator queries for both monotone and strongly monotone settings, while utilizing significantly cheaper oracles based on quadratic programming. Furthermore, we provide several numerical examples to evaluate the efficacy of our algorithms.

With the increasing demand for dynamic behaviors in automotive use cases, Software Defined Vehicles (SDVs) have emerged as a promising solution by bringing dynamic onboard service management capabilities. While users may request a wide range of services during vehicle operation, background tasks such as cooperative Vehicle-to-Everything (V2X) services can activate on-the-fly in response to real-time road conditions. In this dynamic environment, the efficient allocation of onboard resources becomes a complex challenge, in order to meet mixed-criticality onboard Quality-of-Service (QoS) network requirements while ensuring an optimal user experience. Additionally, the ever-evolving real-time network connectivity and computational availability conditions further complicate the process. In this context, we present a dynamic resource-based onboard service orchestration algorithm that considers real-time in-vehicle and V2X network health, along with onboard resource constraints, to select degraded modes for onboard applications and maximize user experience. To enable dynamic orchestration, we introduce the concept of Automotive eXperience Integrity Level (AXIL) which expresses a runtime priority for non-safety-critical applications. This algorithm produces near-optimal solutions while significantly reducing execution time compared to straightforward methods as demonstrated by simulation results. With this approach, we aim to enable efficient onboard execution for a user experience-focused service orchestration.

Autonomous racing in robotics combines high-speed dynamics with the necessity for reliability and real-time decision-making. While such racing pushes software and hardware to their limits, many existing full-system solutions necessitate complex, custom hardware and software, and usually focus on Time-Trials rather than full unrestricted Head-to-Head racing, due to financial and safety constraints. This limits their reproducibility, making advancements and replication feasible mostly for well-resourced laboratories with comprehensive expertise in mechanical, electrical, and robotics fields. Researchers interested in the autonomy domain but with only partial experience in one of these fields, need to spend significant time with familiarization and integration. The ForzaETH Race Stack addresses this gap by providing an autonomous racing software platform designed for F1TENTH, a 1:10 scaled Head-to-Head autonomous racing competition, which simplifies replication by using commercial off-the-shelf hardware. This approach enhances the competitive aspect of autonomous racing and provides an accessible platform for research and development in the field. The ForzaETH Race Stack is designed with modularity and operational ease of use in mind, allowing customization and adaptability to various environmental conditions, such as track friction and layout. Capable of handling both Time-Trials and Head-to-Head racing, the stack has demonstrated its effectiveness, robustness, and adaptability in the field by winning the official F1TENTH international competition multiple times.

While tabular classification has traditionally relied on from-scratch training, a recent breakthrough called prior-data fitted networks (PFNs) challenges this approach. Similar to large language models, PFNs make use of pretraining and in-context learning to achieve strong performance on new tasks in a single forward pass. However, current PFNs have limitations that prohibit their widespread adoption. Notably, TabPFN achieves very strong performance on small tabular datasets but is not designed to make predictions for datasets of size larger than 1000. In this work, we overcome these limitations and substantially improve the performance of PFNs by developing context optimization techniques for PFNs. Specifically, we propose TuneTables, a novel prompt-tuning strategy that compresses large datasets into a smaller learned context. TuneTables scales TabPFN to be competitive with state-of-the-art tabular classification methods on larger datasets, while having a substantially lower inference time than TabPFN. Furthermore, we show that TuneTables can be used as an interpretability tool and can even be used to mitigate biases by optimizing a fairness objective.

The stochastic proximal gradient method is a powerful generalization of the widely used stochastic gradient descent (SGD) method and has found numerous applications in Machine Learning. However, it is notoriously known that this method fails to converge in non-convex settings where the stochastic noise is significant (i.e. when only small or bounded batch sizes are used). In this paper, we focus on the stochastic proximal gradient method with Polyak momentum. We prove this method attains an optimal convergence rate for non-convex composite optimization problems, regardless of batch size. Additionally, we rigorously analyze the variance reduction effect of the Polyak momentum in the composite optimization setting and we show the method also converges when the proximal step can only be solved inexactly. Finally, we provide numerical experiments to validate our theoretical results.

For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory compact representations express the dense arrays in terms of a low rank representation and have become the state-of-the-art for software implementations on large deterministic problems. We develop new compact representations that are parameterized by a choice of vectors and that reduce to existing well known formulas for special choices. We demonstrate effectiveness of the compact representations for large eigenvalue computations, tensor factorizations and nonlinear regressions.

Inverse kinematics (IK) is a fundamental problem frequently occurred in robot control and motion planning. However, the problem is nonconvex because the kinematic map between the configuration and task spaces is generally nonlinear, which makes it challenging for fast and accurate solutions. The problem can be more complicated with the existence of different physical constraints imposed by the robot structure. In this paper, we develop an inverse kinematics solver named IKSPARK (Inverse Kinematics using Semidefinite Programming And RanK minimization) that can find solutions for robots with various structures, including open/closed kinematic chains, spherical, revolute, and/or prismatic joints. The solver works in the space of rotation matrices of the link reference frames and involves solving only convex semidefinite problems (SDPs). Specifically, the IK problem is formulated as an SDP with an additional rank-1 constraint on symmetric matrices with constant traces. The solver first solves this SDP disregarding the rank constraint to get a start point and then finds the rank-1 solution iteratively via a rank minimization algorithm with proven local convergence. Compared to other work that performs SDP relaxation for IK problems, our formulation is simpler, and uses variables with smaller sizes. We validate our approach via simulations on different robots, comparing against a standard IK method.

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

Generating receding-horizon motion trajectories for autonomous vehicles in real-time while also providing safety guarantees is challenging. This is because a future trajectory needs to be planned before the previously computed trajectory is completely executed. This becomes even more difficult if the trajectory is required to satisfy continuous-time collision-avoidance constraints while accounting for a large number of obstacles. To address these challenges, this paper proposes a novel real-time, receding-horizon motion planning algorithm named REachability-based trajectory Design via Exact Formulation of Implicit NEural signed Distance functions (REDEFINED). REDEFINED first applies offline reachability analysis to compute zonotope-based reachable sets that overapproximate the motion of the ego vehicle. During online planning, REDEFINED leverages zonotope arithmetic to construct a neural implicit representation that computes the exact signed distance between a parameterized swept volume of the ego vehicle and obstacle vehicles. REDEFINED then implements a novel, real-time optimization framework that utilizes the neural network to construct a collision avoidance constraint. REDEFINED is compared to a variety of state-of-the-art techniques and is demonstrated to successfully enable the vehicle to safely navigate through complex environments. Code, data, and video demonstrations can be found at https://roahmlab.github.io/redefined/.