arXiv subjects

Sebastian Trimpe

Publications and source records attributed to Sebastian Trimpe.

At least 19 recordsLinked to original sources

arXiv2026

Gibbs Variational Last Layers for Long-Horizon Dynamics Learning

Accurate long-horizon probabilistic predictions of dynamical systems are a prerequisite for model-based decision-making. Variational Bayesian last layers (VBLLs) are an attractive model class for this setting, offering tractable uncertainty at near-deterministic cost, yet they are trained exclusively with single-step likelihood objectives that may be insufficient for reliable multi-step rollouts. We revisit VBLLs through the lens of Gibbs variational inference, which decouples posterior inference from the choice of training loss. Building on this perspective, we introduce a family of multi-step training losses that progressively incorporate long-horizon structure, robustness via continuous ranked probability scores (CRPS), and training on full autoregressive rollouts. Our approach retains the simplicity of VBLLs while directly optimizing for multi-step predictive quality. Across illustrative synthetic environments, a diverse suite of chaotic dynamical systems, and real-world data, we show that multi-step, CRPS-based objectives substantially improve long-horizon accuracy and distributional fit, consistently outperforming single-step likelihood training.

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arXiv2026

A Decade of Learning-Based Control: From Theoretic Foundations to Practical Deployment

Motivated by ten years of Learning-Based Control Invited Sessions at the IEEE Conference on Decision and Control (CDC), this tutorial paper reviews key advances at the intersection of machine learning and control. We focus on methods that combine the flexibility of machine learning techniques with the structure and theoretical foundations of control to design autonomous systems that are capable, reliable, and safe. We first introduce core notions for establishing stability and safety guarantees, then review approaches that learn dynamics models to improve control under uncertainty, and finally discuss data-driven methods that directly synthesize or learn policies, including reinforcement learning, imitation learning, and Bayesian optimization. We further discuss representative applications and open challenges. The goal is to provide an accessible entry point to the field and to support continued progress toward reliable learning-based control in real-world systems. To support learning and practical exploration, we share implementations and illustrative examples along with our discussion, together with additional resources on our website: https://learning-based-control.github.io/tutorial/.

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arXiv2026

Efficiently Approximating Attention Is Hard

Softmax attention is ubiquitous in modern machine learning, but its quadratic scaling with sequence length makes it costly. To reduce this cost, attention is often approximated with fast algorithms, which incur error but can still perform well in practice and on some inputs. At the same time, the growing diversity of attention applications makes approximation guarantees that do not depend on particular input structure a compelling target. For such uniform guarantees over all inputs, known runtime lower bounds rule out fast algorithms for near-exact attention, but leave open the practically important regime: is there an efficient algorithm with even a modest uniform approximation guarantee? We answer this question negatively. Under standard complexity-theoretic assumptions, no truly subquadratic algorithm can approximate attention with any nontrivial additive or relative guarantee uniformly over all inputs. This impossibility holds in the mildest parameter regime for which known algorithms do not already achieve strong approximation guarantees in near-linear time, and extends to practically relevant relaxations: even after polynomial preprocessing of the KV cache, no efficient algorithm can obtain a nontrivial uniform approximation guarantee, or identify a small set of keys receiving substantial attention under sparsity. Overall, our results settle the computational limits of uniform attention approximation.

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arXiv2026

RLLBC-Lib: An Educational Code Library for Reinforcement Learning and Learning-Based Control

Reinforcement learning (RL) is an exciting concept as well as a remarkable success story worth sharing. However, RL builds on rather complex interactions between different objects that play out over several cycles. Such dynamics are often best explained with an easily accessible implementation. We present RLLBC-Lib, a carefully crafted code library with the goal of lowering the entry barrier for students and other learners of RL in the context of learning-based control. At its heart, RLLBC-Lib comprises a comprehensive library of tabular RL approaches to enforce a clear understanding of the theoretical foundations. A deep RL library follows the same design principles, underscoring the parallels between simple tabular and state-of-the-art deep RL approaches. Additionally, RLLBC-Lib provides a collection of implementations illustrating core RL principles and contrasting RL to other learning-based control approaches. Finally, RLLBC-Lib provides an ideal basis for creating programming assignments with automated grading.

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arXiv2026

A Decade of Bayesian Optimization for Controller Tuning and Robot Learning: Tutorial, Review, and Future Prospects

In the past decade, Bayesian optimization (BO) has emerged as a powerful and adaptable framework for automatic controller tuning and robot learning. This article offers a comprehensive overview of the state-of-the-art in BO, designed to support both researchers and practitioners in understanding recent advancements, practical applications, and future research directions. We begin by adopting a practitioner's perspective, illustrating how to effectively set up BO through a representative controller tuning example. We position BO within the broader context of learning paradigms, ranging from deep reinforcement learning to data-driven control, and highlight scenarios where BO is most advantageous. Next, we discuss the diverse range of BO methods that have been developed to tackle complex problems and specific applications. This article provides a unified perspective on the current landscape of BO, emphasizing its relevance to control systems and robotics, and it highlights future prospects by identifying key research challenges and promising avenues for advancing BO in the field. This includes addressing a significant gap in the BO landscape: the lack of standardized benchmark problems specifically for control-related applications. To foster future research and ensure rigorous evaluation, we start an effort towards a lightweight benchmark suite for control engineering and robotics. We also present metrics and best practices to facilitate direct comparisons between new BO algorithms and established state-of-the-art methods.

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arXiv2026

Scalable Gaussian Process Regression via Deterministic Trigonometric Features: Uniform Bounds for Safe Model Predictive Control

Learning-based Model Predictive Control (MPC) using Gaussian processes (GPs) is an effective approach for safe control in the presence of model mismatch. High-probability safety guarantees typically require uncertainty bounds that hold uniformly over the entire state--input domain, but existing bounds are available only for full GP regression. Since exact GP inference scales poorly with the number of data points, its deployment is impractical in large-data regimes. We close this gap by developing a scalable GP framework that admits the derivation of uniform uncertainty bounds. We formalize a deterministic trigonometric feature Gaussian process (DTF-GP), a finite-dimensional kernel approximation based on discretized trigonometric features that reduces GP regression to Bayesian linear regression in feature space. We derive a high-probability uniform uncertainty bound for the proposed DTF-GP and provide its closed-form solution for the squared-exponential kernel case. Finally, we integrate the DTF-GP into a learning-based MPC scheme and demonstrate that it provides high-probability safety guarantees and exploration performance comparable to a full GP while improving computational efficiency in large-data regimes.

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arXiv2026

Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics

Predictive safety filters (PSFs) leverage model predictive control to enforce constraint satisfaction during deep reinforcement learning (RL) exploration, yet their reliance on first-principles models or Gaussian processes limits scalability and broader applicability. Meanwhile, model-based RL (MBRL) methods routinely employ probabilistic ensemble (PE) neural networks to capture complex, high-dimensional dynamics from data with minimal prior knowledge. However, existing attempts to integrate PEs into PSFs lack rigorous uncertainty quantification. We introduce the Uncertainty-Aware Predictive Safety Filter (UPSi), a PSF that provides rigorous safety verification using PE dynamics models by formulating future outcomes as reachable sets. UPSi introduces an explicit certainty constraint that prevents model exploitation and integrates seamlessly into common MBRL frameworks. We evaluate UPSi under practical simplifications within Dyna-style MBRL on standard safe RL benchmarks and report substantial improvements in exploration safety over prior neural network PSFs while maintaining performance on par with standard MBRL. UPSi bridges the gap between the scalability and generality of modern MBRL and the safety guarantees of predictive safety filters.

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arXiv2026

CENDRe: Concept Extraction with Natural Domain Representations

Convolutional neural networks (CNNs) are widely used for time-series classification, but their deployment in critical domains requires understanding the temporal and spectral patterns that drive their predictions. Concept extraction (CE) methods identify such patterns by analyzing representations within the models' latent space. However, existing time-series CE methods have three limitations: they operate only in the time domain and overlook frequency features, predefine the number of concepts, and produce localizations misaligned with the regions the model uses. We address these limitations by proposing CENDRe, a concept extraction method for CNNs. It first discovers concepts by clustering per-timestep latent representations in two stages, where silhouette-guided aggregation selects the number of concepts automatically. Then, it localizes each concept through gradients of a presence score that contrasts the latent representations with their prototypes, producing masks that concentrate on the regions driving the concept. These gradients, propagated through a differentiable invertible mapping of the input such as a Fourier transform, yield localizations for the same concepts in the frequency domain. Finally, each concept receives a relevance score that quantifies its contribution to each class. On synthetic benchmarks, CENDRe achieves representation correctness comparable to state-of-the-art CE methods and significantly higher importance correctness. On real bearing-fault data, CENDRe extracts the frequency bands driving the model's predictions, located in regions commonly inspected for fault diagnosis, producing evidence to assess the model that time-domain CE methods cannot.

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arXiv2026

Biased Dreams: Limitations to Epistemic Uncertainty Quantification in Latent Dynamics Models

Model-based reinforcement learning distinguishes between dynamics models operating on proprioceptive states and latent dynamics models typically operating on high-dimensional image observations. Among the latter, Dreamer's Recurrent State Space Model (RSSM) has emerged as a dominant architecture. While ensemble-based epistemic uncertainty has proven effective in proprioceptive dynamics for mitigating model exploitation, guiding exploration, or promoting caution, its behavior in latent dynamics remains largely unexplored. Our experiments reveal that although ensemble disagreement captures local epistemic uncertainty, it does not reliably reflect global compounding model error accumulated over prolonged RSSM latent rollouts. We provide evidence for an attractor behavior that draws rollouts toward well-supported latent regions, where uncertainty diminishes despite increasing discrepancies from the true environment dynamics. This can cause the model to overestimate returns when attractor regions correspond to high-reward behaviors. Our findings reveal a structural limitation of epistemic uncertainty estimation in RSSMs and challenge the assumption that epistemic uncertainty estimation transfers directly from proprioceptive to latent dynamics.

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arXiv2026

WarpMPC: Large-Batch MPC on GPU via ADMM with Unrolled $LDL^\top$ Factorization

This paper introduces numerical optimizations for maximizing throughput on GPU when solving large batches (10,000 to over 100,000) of sequential quadratic programming (SQP) iterations, where all problems have the same structure. The optimizations are implemented in a toolbox WarpMPC for model-predictive control (MPC) in JAX and Warp. Based on the insight that all MPC problem instances in a batch share the same sparsity in time, cost, and constraints, we propose unrolling sparse linear factorizations and solves, which dominate alternating direction method of multipliers (ADMM) solver runtime. We avoid memory access bottlenecks and wasting computations via optimized memory layout, padding-reducing segmentation of the unrolled factorization, and dependency level scheduled backsolves, additionally accelerating sensitivity computation. We achieve throughputs of 8,000 to 250,000 SQP iterations per second on nonlinear cartpole, quadrotor, and humanoid robot benchmarks, outperforming baselines by 3$\times$ to 25$\times$. We illustrate practical usefulness by synthesizing a dataset and training a neural network approximation of an MPC in under 4 minutes that stabilizes a nano quadrotor in hardware experiments.

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arXiv2026

The risk of KV cache compression

Transformer inference on long sequences is expensive because softmax attention repeatedly reads from a large KV cache. The prevalent approach to this bottleneck is KV cache compression, which replaces the full cache with a compact summary. Despite its practical importance, the design of such summaries is largely driven by empirical experimentation. On the theoretical side, existing results show that KV cache compression can be impossible in the worst case, but offer little systematic guidance for designing algorithms in regimes where accurate compression is possible. We bridge this gap by characterizing the minimax risk of KV cache compression in terms of the intrinsic compressibility of a cache, revealing when and how accurate compression is possible. These results yield novel design principles for KV cache compression under causal masking that map efficiently to prefill and autoregressive decoding while achieving minimax-optimal risk. We instantiate these principles in a practical algorithm and report promising performance on LongBench in targeted experiments. Overall, our results provide a principled avenue for practical KV cache compression with theoretical guarantees.

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arXiv2026

Generative AI for Safe and Photorealistic Drone Light Shows

Drone light shows are redefining aerial entertainment, yet their widespread adoption is bottlenecked by labor-intensive, manual animation. While generative AI promises an automated alternative, current frameworks fail to provide photorealism with fluid, dynamic motion. To address this limitation, we introduce SWAN, an end-to-end pipeline that synthesizes photorealistic, large-scale, and collision-free drone choreographies directly from text prompts. SWAN converts text into realistic reference videos and translates these pixel-space dynamics into physical swarm kinematics using a novel, adaptive point-tracking algorithm. Unlike existing trackers, this method maintains spatial coherence through severe occlusions and rapid topological shifts. A dedicated planner then allocates these trajectories to individual drones, while a subsequent safety filter ensures collision-free execution. We demonstrate scalability by safely orchestrating simulated 2,000-drone formations and validate physical feasibility on a dense real-world swarm of 49 quadcopters, operating everything entirely on standard consumer hardware. Combined, this work demonstrates how generative AI can be leveraged to automate multi-robot choreography design, providing an accessible new framework for drone light shows.

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arXiv2026

Local Preferential Bayesian Optimization

Bayesian optimization (BO) is a popular and effective approach for tuning expensive, noisy experiments, but requires the formulation of an explicit objective function. Preferential BO (PBO) removes this requirement by learning from pairwise human feedback, yet existing methods struggle to efficiently optimize beyond low- and medium-dimensional problems due to their global search approaches. We address this limitation by developing a family of local PBO methods that transfer key ideas from high-dimensional BO to the preferential setting. In particular, we introduce local PBO methods which adapt trust-region and derivative-informed local search to pairwise preference feedback, where the latter exploits first- and second-order derivatives of the Laplace-approximated GP posterior. Our benchmark on GP sample paths, standard optimization benchmark functions, and policy-search tasks shows that local PBO methods are especially effective in high-dimensional and complex landscapes with steep optima. Compared with global preference-based baselines, they can substantially reduce cumulative regret, making them particularly useful for real-world preference-based optimization tasks such as policy search.

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arXiv2026

All Models are Wrong, Knowing Where is Useful: On Model Uncertainty in Reinforcement Learning

Model-based reinforcement learning (MBRL) infers information about the environment from a learned dynamics model and bears the potential to address open problems such as data efficient and safe learning in robotics. However, inaccuracies of the learned dynamics model are typically exploited by the agent, substantially hampering the capabilities of MBRL methods. We present a framework for dealing with inaccuracies of probabilistic models through targeted handling of uncertainty that effectively mitigates model exploitation. We present recent successes in learning directly on hardware and safe exploration, and discuss future directions for uncertainty-aware MBRL.

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arXiv2026

Going Beyond the Edge: Distributed Inference of Transformer Models on Ultra-Low-Power Wireless Devices

Transformer models are rapidly becoming a cornerstone of modern Internet of Things (IoT) applications, yet their computational and memory demands far exceed the capabilities of a single typical ultra-low-power IoT device. We present CATS, a framework for distributed transformer inference on ultra-low-power wireless devices, enabling multiple devices to collaboratively execute models far larger than what a single device can sustain. At its core, CATS is a communication-aware distributed transformer inference scheme co-designed across transformer partitioning, wireless communication and training. It employs SomeGather, a new pruned communication primitive that selectively broadcasts activation columns to reduce communication bandwidth and RAM usage without sacrificing model accuracy. Building on SomeGather, we design a partitioning method that exploits this primitive for efficient model parallelism. To cope with unreliable wireless communication, CATS employs message-dropout during training, which mimics packet losses and yields models that are robust to message loss during inference. In real-world experiments, we show that CATS brings distributed transformer inference to ultra-low-power wireless devices for the first time, with deployments on up to 16 devices that collaboratively execute transformer models up to 14 times larger than what a single device can run.

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arXiv2026

Learning to Race in Minutes: Infoprop Dyna on the Mini Wheelbot

Reinforcement Learning (RL) has the potential to enable robots with fast, nonlinear, and unstable dynamics to reach the limits of their performance. However, most recent advances rely on carefully designed physics-based simulators and domain randomization to achieve successful sim-to-real transfer within reasonable wall-clock time. In this work, we bypass the need for such simulators and demonstrate that Infoprop Dyna, a state-of-the-art uncertainty-aware model-based reinforcement learning (MBRL) framework, can enable robots to learn directly from real-world interactions. Using Infoprop Dyna, the Mini Wheelbot, an underactuated unicycle robot, learns to race around a track within 11 minutes of real-world experience.

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arXiv2026

Dyna-Style Safety Augmented Reinforcement Learning: Staying Safe in the Face of Uncertainty

Safety remains an open problem in reinforcement learning (RL), especially during training. While safety filters are promising to address safe exploration, they are generally poorly suited for high-dimensional systems with unknown dynamics. We propose Dyna-style Safety Augmented Reinforcement Learning (Dyna-SAuR), a novel algorithm that learns both a scalable safety filter and a control policy using a learned uncertainty-aware dynamics model, while requiring minimal domain knowledge. The filter avoids failures and high uncertainty regions. Thus, better models expand the set of safe and certain states, reducing filter conservatism. We present the effectiveness of Dyna-SAuR on goal-reaching CartPole as well as MuJoCo Walker, reducing failures compared to state-of-the-art methods by 2 orders of magnitude.

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arXiv2026

Preferential Bayesian Optimization with Crash Feedback

Bayesian optimization is a popular black-box optimization method for parameter learning in control and robotics. It typically requires an objective function that reflects the user's optimization goal. However, in practical applications, this objective function is often inaccessible due to complex or unmeasurable performance metrics. Preferential Bayesian optimization (PBO) overcomes this limitation by leveraging human feedback through pairwise comparisons, eliminating the need for explicit performance quantification. When applying PBO to hardware systems, such as in quadcopter control, crashes can cause time-consuming experimental resets, wear and tear, or otherwise undesired outcomes. Standard PBO methods cannot incorporate feedback from such crashed experiments, resulting in the exploration of parameters that frequently lead to experimental crashes. We thus introduce CrashPBO, a user-friendly mechanism that enables users to both express preferences and report crashes during the optimization process. Benchmarking on synthetic functions shows that this mechanism reduces crashes by 63% and increases data efficiency. Through experiments on three robotics platforms, we demonstrate the wide applicability and transferability of CrashPBO, highlighting that it provides a flexible, user-friendly framework for parameter learning with human feedback on preferences and crashes.

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