Disentangling Dynamical Systems: Causal Representation Learning Meets Local Sparse Attention

Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of candidate functions chosen via available domain knowledge. In contrast, deep learning can demonstrably model systems of broad complexity with high fidelity, but black-box function approximation typically fails to yield explicit descriptive or disentangled representations revealing the structure of a system. We develop a novel identifiability theorem, leveraging causal representation learning, to uncover disentangled representations of system parameters without structural assumptions. We derive a graphical criterion specifying when system parameters can be uniquely disentangled from raw trajectory data, up to permutation and diffeomorphism. Crucially, our analysis demonstrates that global causal structures provide a lower bound on the disentanglement guarantees achievable when considering local state-dependent causal structures. We instantiate system parameter identification as a variational inference problem, leveraging a sparsity-regularised transformer to uncover state-dependent causal structures. We empirically validate our approach across four synthetic domains, demonstrating its ability to recover highly disentangled representations that baselines fail to recover. Corroborating our theoretical analysis, our results confirm that enforcing local causal structure is often necessary for full identifiability.

Posterior Sampling Reinforcement Learning with Gaussian Processes for Continuous Control: Sublinear Regret Bounds for Unbounded State Spaces

We analyze the Bayesian regret of the Gaussian process posterior sampling reinforcement learning (GP-PSRL) algorithm. Posterior sampling is an effective heuristic for decision-making under uncertainty that has been used to develop successful algorithms for a variety of continuous control problems. However, theoretical work on GP-PSRL is limited. All known regret bounds either fail to achieve a tight dependence on a kernel-dependent quantity called the maximum information gain or fail to properly account for the fact that the set of possible system states is unbounded. Through a recursive application of the Borell-Tsirelson-Ibragimov-Sudakov inequality, we show that, with high probability, the states actually visited by the algorithm are contained within a ball of near-constant radius. To obtain tight dependence on the maximum information gain, we use the chaining method to control the regret suffered by GP-PSRL. Our main result is a Bayesian regret bound of the order $\widetilde{\mathcal{O}}(H^{3/2}\sqrt{γ_{T/H} T})$, where $H$ is the horizon, $T$ is the number of time steps and $γ_{T/H}$ is the maximum information gain. With this result, we resolve the limitations with prior theoretical work on PSRL, and provide the theoretical foundation and tools for analyzing PSRL in complex settings.

Building Gradient by Gradient: Decentralised Energy Functions for Bimanual Robot Assembly

There are many challenges in bimanual assembly, including high-level sequencing, multi-robot coordination, and low-level, contact-rich operations such as component mating. Task and motion planning (TAMP) methods, while effective in this domain, may be prohibitively slow to converge when adapting to disturbances that require new task sequencing and optimisation. These events are common during tight-tolerance assembly, where difficult-to-model dynamics such as friction or deformation require rapid replanning and reattempts. Moreover, defining explicit task sequences for assembly can be cumbersome, limiting flexibility when task replanning is required. To simplify this planning, we introduce a decentralised gradient-based framework that uses a piecewise continuous energy function through the automatic composition of adaptive potential functions. This approach generates sub-goals using only myopic optimisation, rather than long-horizon planning. It demonstrates effectiveness at solving long-horizon tasks due to the structure and adaptivity of the energy function. We show that our approach scales to physical bimanual assembly tasks for constructing tight-tolerance assemblies. In these experiments, we discover that our gradient-based rapid replanning framework generates automatic retries, coordinated motions and autonomous handovers in an emergent fashion.

Towards Safe Robot Foundation Models Using Inductive Biases

Safety is a critical requirement for the real-world deployment of robotic systems. Unfortunately, while current robot foundation models show promising generalization capabilities across a wide variety of tasks, they fail to address safety, an important aspect for ensuring long-term operation. Current robot foundation models assume that safe behavior should emerge by learning from a sufficiently large dataset of demonstrations. However, this approach has two clear major drawbacks. Firstly, there are no formal safety guarantees for a behavior cloning policy trained using supervised learning. Secondly, without explicit knowledge of any safety constraints, the policy may require an unreasonable number of additional demonstrations to even approximate the desired constrained behavior. To solve these key issues, we show how we can instead combine robot foundation models with geometric inductive biases using ATACOM, a safety layer placed after the foundation policy that ensures safe state transitions by enforcing action constraints. With this approach, we can ensure formal safety guarantees for generalist policies without providing extensive demonstrations of safe behavior, and without requiring any specific fine-tuning for safety. Our experiments show that our approach can be beneficial both for classical manipulation tasks, where we avoid unwanted collisions with irrelevant objects, and for dynamic tasks, such as the robot air hockey environment, where we can generate fast trajectories respecting complex tasks and joint space constraints.

Towards Safe Robot Foundation Models

Robot foundation models hold the potential for deployment across diverse environments, from industrial applications to household tasks. While current research focuses primarily on the policies' generalization capabilities across a variety of tasks, it fails to address safety, a critical requirement for deployment on real-world systems. In this paper, we introduce a safety layer designed to constrain the action space of any generalist policy appropriately. Our approach uses ATACOM, a safe reinforcement learning algorithm that creates a safe action space and, therefore, ensures safe state transitions. By extending ATACOM to generalist policies, our method facilitates their deployment in safety-critical scenarios without requiring any specific safety fine-tuning. We demonstrate the effectiveness of this safety layer in an air hockey environment, where it prevents a puck-hitting agent from colliding with its surroundings, a failure observed in generalist policies.

Global Tensor Motion Planning

Batch planning is increasingly crucial for the scalability of robotics tasks and dataset generation diversity. This paper presents Global Tensor Motion Planning (GTMP) -- a sampling-based motion planning algorithm comprising only tensor operations. We introduce a novel discretization structure represented as a random multipartite graph, enabling efficient vectorized sampling, collision checking, and search. We provide an early theoretical investigation showing that GTMP exhibits probabilistic completeness while supporting modern GPU/TPU. Additionally, by incorporating smooth structures into the multipartite graph, GTMP directly plans smooth splines without requiring gradient-based optimization. Experiments on lidar-scanned occupancy maps and the MotionBenchMarker dataset demonstrate GTMP's computation efficiency in batch planning compared to baselines, underscoring GTMP's potential as a robust, scalable planner for diverse applications and large-scale robot learning tasks.

Machine Learning with Physics Knowledge for Prediction: A Survey

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.

Function-Space Regularization for Deep Bayesian Classification

Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However, weight-space priors are model-specific, can be difficult to interpret and are hard to specify. Instead, we apply a Dirichlet prior in predictive space and perform approximate function-space variational inference. To this end, we interpret conventional categorical predictions from stochastic neural network classifiers as samples from an implicit Dirichlet distribution. By adapting the inference, the same function-space prior can be combined with different models without affecting model architecture or size. We illustrate the flexibility and efficacy of such a prior with toy experiments and demonstrate scalability, improved uncertainty quantification and adversarial robustness with large-scale image classification experiments.

Coherent Soft Imitation Learning

Imitation learning methods seek to learn from an expert either through behavioral cloning (BC) of the policy or inverse reinforcement learning (IRL) of the reward. Such methods enable agents to learn complex tasks from humans that are difficult to capture with hand-designed reward functions. Choosing BC or IRL for imitation depends on the quality and state-action coverage of the demonstrations, as well as additional access to the Markov decision process. Hybrid strategies that combine BC and IRL are not common, as initial policy optimization against inaccurate rewards diminishes the benefit of pretraining the policy with BC. This work derives an imitation method that captures the strengths of both BC and IRL. In the entropy-regularized ('soft') reinforcement learning setting, we show that the behaviour-cloned policy can be used as both a shaped reward and a critic hypothesis space by inverting the regularized policy update. This coherency facilities fine-tuning cloned policies using the reward estimate and additional interactions with the environment. This approach conveniently achieves imitation learning through initial behaviour cloning, followed by refinement via RL with online or offline data sources. The simplicity of the approach enables graceful scaling to high-dimensional and vision-based tasks, with stable learning and minimal hyperparameter tuning, in contrast to adversarial approaches.

Inferring Smooth Control: Monte Carlo Posterior Policy Iteration with Gaussian Processes

Monte Carlo methods have become increasingly relevant for control of non-differentiable systems, approximate dynamics models and learning from data. These methods scale to high-dimensional spaces and are effective at the non-convex optimizations often seen in robot learning. We look at sample-based methods from the perspective of inference-based control, specifically posterior policy iteration. From this perspective, we highlight how Gaussian noise priors produce rough control actions that are unsuitable for physical robot deployment. Considering smoother Gaussian process priors, as used in episodic reinforcement learning and motion planning, we demonstrate how smoother model predictive control can be achieved using online sequential inference. This inference is realized through an efficient factorization of the action distribution and a novel means of optimizing the likelihood temperature to improve importance sampling accuracy. We evaluate this approach on several high-dimensional robot control tasks, matching the sample efficiency of prior heuristic methods while also ensuring smoothness. Simulation results can be seen at https://monte-carlo-ppi.github.io/.