Joe Watson

Joe Watson, Chen Song, Oliver Weeger et al. · cambridge

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.

Joe Watson, Jan Peters

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/.

Christian Scherer, Joe Watson, Theo Gruner et al.

Distilling expert demonstration data into large generative models using behavioral cloning is a scalable approach to learning capable policies for robotic control, particularly for dexterous manipulation. Reinforcement learning (RL) can be used as a means to finetune these policies further using additional experience. An open question is whether RL is more sample-efficient than collecting more human demonstrations. Prior work has finetuned large pretrained policies in a scalable fashion by applying RL to a smaller residual policy that corrects the pretrained model. However, for the typical sparse reward tasks, RL algorithms can struggle to optimize the behavior in a sample-efficient manner. We explore inverse reinforcement learning, where a dense reward function is learned from expert demonstrations, potentially reducing the challenge of RL finetuning. We specifically consider coherent imitation learning, an IRL method that facilitates improvement of the BC policy through using a specific reward formulation with theoretical guarantees. We show that our IRL method maintains or improves the performance of pi-0.5 on all six sparse manipulation tasks and achieves a $\geq 90\%$ success rate on five out of six complex manipulation tasks, outperforming RL-based baselines using sparse rewards. By ensuring our initial pretrained finetuning policy is optimal for our initial reward and critic, our method circumvents the initial drop commonly seen in RL finetuning and enables faster improvement.

Jihao Andreas Lin, Joe Watson, Pascal Klink et al.

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.

Markus W. Baumgartner, Anson Lei, Joe Watson et al.

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.

Daniel Palenicek, Florian Vogt, Joe Watson et al.

For reinforcement learning in the real world online exploration is expensive A common practice in robotic reinforcement learning is to incorporate additional data to improve sample efficiency Expert demonstration data is often crucial for solving hard exploration tasks with sparse rewards While prior data is used to augment experience and pretrain models we show that the design of existing algorithms fails to achieve the sample efficiency that is possible in this setting due to a failure to use pretrained policies effectively We propose XQCfD which extends the sample-efficient XQC actor-critic to learn from demonstrations using augmented replay buffers pretrained policies and stationary policy architectures designed to avoid rapidly unlearning the strong initial policy like prior works We show our stationary network architecture enables policy improvement out-of-distribution better than standard network architectures due to its higher entropy predictions XQCfD achieves state of the art performance across a range of complex manipulation tasks with sparse rewards from the popular Adroit Robomimic and MimicGen benchmarks -- notably with a low update-to-data ratio and no ensemble networks

Joe Watson, Sandy H. Huang, Nicolas Heess

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 facilitates 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. For the open-source implementation and simulation results, see https://joemwatson.github.io/csil/.

Niklas Funk, Charles Schaff, Rishabh Madan et al.

Dexterous manipulation is a challenging and important problem in robotics. While data-driven methods are a promising approach, current benchmarks require simulation or extensive engineering support due to the sample inefficiency of popular methods. We present benchmarks for the TriFinger system, an open-source robotic platform for dexterous manipulation and the focus of the 2020 Real Robot Challenge. The benchmarked methods, which were successful in the challenge, can be generally described as structured policies, as they combine elements of classical robotics and modern policy optimization. This inclusion of inductive biases facilitates sample efficiency, interpretability, reliability and high performance. The key aspects of this benchmarking is validation of the baselines across both simulation and the real system, thorough ablation study over the core features of each solution, and a retrospective analysis of the challenge as a manipulation benchmark. The code and demo videos for this work can be found on our website (https://sites.google.com/view/benchmark-rrc).

Daniel Palenicek, Florian Vogt, Joe Watson et al.

Reinforcement learning has achieved significant milestones, but sample efficiency remains a bottleneck for real-world applications. Recently, CrossQ has demonstrated state-of-the-art sample efficiency with a low update-to-data (UTD) ratio of 1. In this work, we explore CrossQ's scaling behavior with higher UTD ratios. We identify challenges in the training dynamics, which are emphasized by higher UTD ratios. To address these, we integrate weight normalization into the CrossQ framework, a solution that stabilizes training, has been shown to prevent potential loss of plasticity and keeps the effective learning rate constant. Our proposed approach reliably scales with increasing UTD ratios, achieving competitive performance across 25 challenging continuous control tasks on the DeepMind Control Suite and Myosuite benchmarks, notably the complex dog and humanoid environments. This work eliminates the need for drastic interventions, such as network resets, and offers a simple yet robust pathway for improving sample efficiency and scalability in model-free reinforcement learning.

An T. Le, Kay Hansel, João Carvalho et al.

Batch planning is increasingly necessary to quickly produce diverse and quality motion plans for downstream learning applications, such as distillation and imitation learning. 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 a 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.

Joe Watson, Ivan O'Conner, Chia-Wen Chen et al. · cambridge

Psychological assessments typically rely on structured rating scales, which cannot incorporate the rich nuance of a respondent's natural language. This study leverages recent LLM advances to harness qualitative data within a novel conceptual framework, combining LLM-scored text and traditional rating-scale items to create an augmented test. We demonstrate this approach using depression as a case study, developing and assessing the framework on a real-world sample of upper secondary students (n=693) and corresponding synthetic dataset (n=3,000). On held-out test sets, augmented tests achieved statistically significant improvements in measurement precision and accuracy. The information gain from the LLM items was equivalent to adding between 6.3 (real data) and 16.0 (synthetic data) items to the original 19-item test. Our approach marks a conceptual shift in automated scoring that bypasses its typical bottlenecks: instead of relying on pre-labelled data or complex expert-created rubrics, we empirically select the most informative LLM scoring instructions based on calculations of item information. This framework provides a scalable approach for leveraging the growing stream of transcribed text to enhance traditional psychometric measures, and we discuss its potential utility in clinical health and beyond.

Daniel Palenicek, Florian Vogt, Joe Watson et al.

Sample efficiency is a central property of effective deep reinforcement learning algorithms. Recent work has improved this through added complexity, such as larger models, exotic network architectures, and more complex algorithms, which are typically motivated purely by empirical performance. We take a more principled approach by focusing on the optimization landscape of the critic network. Using the eigenspectrum and condition number of the critic's Hessian, we systematically investigate the impact of common architectural design decisions on training dynamics. Our analysis reveals that a novel combination of batch normalization (BN), weight normalization (WN), and a distributional cross-entropy (CE) loss produces condition numbers orders of magnitude smaller than baselines. This combination also naturally bounds gradient norms, a property critical for maintaining a stable effective learning rate under non-stationary targets and bootstrapping. Based on these insights, we introduce XQC: a well-motivated, sample-efficient deep actor-critic algorithm built upon soft actor-critic that embodies these optimization-aware principles. We achieve state-of-the-art sample efficiency across 55 proprioception and 15 vision-based continuous control tasks, all while using significantly fewer parameters than competing methods.

Michael Lutter, Johannes Silberbauer, Joe Watson et al.

Obtaining dynamics models is essential for robotics to achieve accurate model-based controllers and simulators for planning. The dynamics models are typically obtained using model specification of the manufacturer or simple numerical methods such as linear regression. However, this approach does not guarantee physically plausible parameters and can only be applied to kinematic chains consisting of rigid bodies. In this article, we describe a differentiable simulator that can be used to identify the system parameters of real-world mechanical systems with complex friction models, holonomic as well as non-holonomic constraints. To guarantee physically consistent parameters, we utilize virtual parameters and gradient-based optimization. The described Differentiable Newton-Euler Algorithm (DiffNEA) can be applied to a class of dynamical systems and guarantees physically plausible predictions. The extensive experimental evaluation shows, that the proposed model learning approach learns accurate dynamics models of systems with complex friction and non-holonomic constraints. Especially in the offline reinforcement learning experiments, the identified DiffNEA models excel. For the challenging ball in a cup task, these models solve the task using model-based offline reinforcement learning on the physical system. The black-box baselines fail on this task in simulation and on the physical system despite using more data for learning the model.

Stefan Bauer, Felix Widmaier, Manuel Wüthrich et al.

Dexterous manipulation remains an open problem in robotics. To coordinate efforts of the research community towards tackling this problem, we propose a shared benchmark. We designed and built robotic platforms that are hosted at MPI for Intelligent Systems and can be accessed remotely. Each platform consists of three robotic fingers that are capable of dexterous object manipulation. Users are able to control the platforms remotely by submitting code that is executed automatically, akin to a computational cluster. Using this setup, i) we host robotics competitions, where teams from anywhere in the world access our platforms to tackle challenging tasks ii) we publish the datasets collected during these competitions (consisting of hundreds of robot hours), and iii) we give researchers access to these platforms for their own projects.

Joe Watson, Hany Abdulsamad, Rolf Findeisen et al.

Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate inference techniques can be used to handle the statistical approximations principled and practically by framing the control problem as a problem of input estimation. Analyzing the Gaussian setting, we present an inference-based solver that is effective in stochastic and deterministic settings and was found to be superior to popular baselines on nonlinear simulated tasks. We draw connections that relate this inference formulation to previous approaches for stochastic optimal control and outline several advantages that this inference view brings due to its statistical nature.

Joe Watson, Jan Peters

Discrete-time stochastic optimal control remains a challenging problem for general, nonlinear systems under significant uncertainty, with practical solvers typically relying on the certainty equivalence assumption, replanning and/or extensive regularization. Control as inference is an approach that frames stochastic control as an equivalent inference problem, and has demonstrated desirable qualities over existing methods, namely in exploration and regularization. We look specifically at the input inference for control (i2c) algorithm, and derive three key characteristics that enable advanced trajectory optimization: An `expert' linear Gaussian controller that combines the benefits of open-loop optima and closed-loop variance reduction when optimizing for nonlinear systems, inherent adaptive risk sensitivity from the inference formulation, and covariance control functionality with only a minor algorithmic adjustment.

Michael Lutter, Johannes Silberbauer, Joe Watson et al.

A limitation of model-based reinforcement learning (MBRL) is the exploitation of errors in the learned models. Black-box models can fit complex dynamics with high fidelity, but their behavior is undefined outside of the data distribution.Physics-based models are better at extrapolating, due to the general validity of their informed structure, but underfit in the real world due to the presence of unmodeled phenomena. In this work, we demonstrate experimentally that for the offline model-based reinforcement learning setting, physics-based models can be beneficial compared to high-capacity function approximators if the mechanical structure is known. Physics-based models can learn to perform the ball in a cup (BiC) task on a physical manipulator using only 4 minutes of sampled data using offline MBRL. We find that black-box models consistently produce unviable policies for BiC as all predicted trajectories diverge to physically impossible state, despite having access to more data than the physics-based model. In addition, we generalize the approach of physics parameter identification from modeling holonomic multi-body systems to systems with nonholonomic dynamics using end-to-end automatic differentiation. Videos: https://sites.google.com/view/ball-in-a-cup-in-4-minutes/

Michael Lutter, Johannes Silberbauer, Joe Watson et al.

In this work, we examine a spectrum of hybrid model for the domain of multi-body robot dynamics. We motivate a computation graph architecture that embodies the Newton Euler equations, emphasizing the utility of the Lie Algebra form in translating the dynamical geometry into an efficient computational structure for learning. We describe the used virtual parameters that enable unconstrained physical plausible dynamics and the used actuator models. In the experiments, we define a family of 26 grey-box models and evaluate them for system identification of the simulated and physical Furuta Pendulum and Cartpole. The comparison shows that the kinematic parameters, required by previous white-box system identification methods, can be accurately inferred from data. Furthermore, we highlight that models with guaranteed bounded energy of the uncontrolled system generate non-divergent trajectories, while more general models have no such guarantee, so their performance strongly depends on the data distribution. Therefore, the main contributions of this work is the introduction of a white-box model that jointly learns dynamic and kinematics parameters and can be combined with black-box components. We then provide extensive empirical evaluation on challenging systems and different datasets that elucidates the comparative performance of our grey-box architecture with comparable white- and black-box models.

Joe Watson, Abraham Imohiosen, Jan Peters

Active inference (AI) is a persuasive theoretical framework from computational neuroscience that seeks to describe action and perception as inference-based computation. However, this framework has yet to provide practical sensorimotor control algorithms that are competitive with alternative approaches. In this work, we frame active inference through the lens of control as inference (CaI), a body of work that presents trajectory optimization as inference. From the wider view of `probabilistic numerics', CaI offers principled, numerically robust optimal control solvers that provide uncertainty quantification, and can scale to nonlinear problems with approximate inference. We show that AI may be framed as partially-observed CaI when the cost function is defined specifically in the observation states.

Joe Watson, Hany Abdulsamad, Jan Peters

Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization techniques, that heavily rely on heuristics for regularization in order to achieve stable convergence. By building upon the duality between inference and control, we develop the view of Optimal Control as Input Estimation, devising a probabilistic stochastic optimal control formulation that iteratively infers the optimal input distributions by minimizing an upper bound of the control cost. Inference is performed through Expectation Maximization and message passing on a probabilistic graphical model of the dynamical system, and time-varying linear Gaussian feedback controllers are extracted from the joint state-action distribution. This perspective incorporates uncertainty quantification, effective initialization through priors, and the principled regularization inherent to the Bayesian treatment. Moreover, it can be shown that for deterministic linearized systems, our framework derives the maximum entropy linear quadratic optimal control law. We provide a complete and detailed derivation of our probabilistic approach and highlight its advantages in comparison to other deterministic and probabilistic solvers.