Oleg Arenz

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.

Bang You, Oleg Arenz, Youping Chen et al.

Recent methods for reinforcement learning from images use auxiliary tasks to learn image features that are used by the agent's policy or Q-function. In particular, methods based on contrastive learning that induce linearity of the latent dynamics or invariance to data augmentation have been shown to greatly improve the sample efficiency of the reinforcement learning algorithm and the generalizability of the learned embedding. We further argue, that explicitly improving Markovianity of the learned embedding is desirable and propose a self-supervised representation learning method which integrates contrastive learning with dynamic models to synergistically combine these three objectives: (1) We maximize the InfoNCE bound on the mutual information between the state- and action-embedding and the embedding of the next state to induce a linearly predictive embedding without explicitly learning a linear transition model, (2) we further improve Markovianity of the learned embedding by explicitly learning a non-linear transition model using regression, and (3) we maximize the mutual information between the two nonlinear predictions of the next embeddings based on the current action and two independent augmentations of the current state, which naturally induces transformation invariance not only for the state embedding, but also for the nonlinear transition model. Experimental evaluation on the Deepmind control suite shows that our proposed method achieves higher sample efficiency and better generalization than state-of-art methods based on contrastive learning or reconstruction.

Oleg Arenz, Philipp Dahlinger, Zihan Ye et al.

Variational inference with Gaussian mixture models (GMMs) enables learning of highly tractable yet multi-modal approximations of intractable target distributions with up to a few hundred dimensions. The two currently most effective methods for GMM-based variational inference, VIPS and iBayes-GMM, both employ independent natural gradient updates for the individual components and their weights. We show for the first time, that their derived updates are equivalent, although their practical implementations and theoretical guarantees differ. We identify several design choices that distinguish both approaches, namely with respect to sample selection, natural gradient estimation, stepsize adaptation, and whether trust regions are enforced or the number of components adapted. We argue that for both approaches, the quality of the learned approximations can heavily suffer from the respective design choices: By updating the individual components using samples from the mixture model, iBayes-GMM often fails to produce meaningful updates to low-weight components, and by using a zero-order method for estimating the natural gradient, VIPS scales badly to higher-dimensional problems. Furthermore, we show that information-geometric trust-regions (used by VIPS) are effective even when using first-order natural gradient estimates, and often outperform the improved Bayesian learning rule (iBLR) update used by iBayes-GMM. We systematically evaluate the effects of design choices and show that a hybrid approach significantly outperforms both prior works. Along with this work, we publish our highly modular and efficient implementation for natural gradient variational inference with Gaussian mixture models, which supports 432 different combinations of design choices, facilitates the reproduction of all our experiments, and may prove valuable for the practitioner.

Firas Al-Hafez, Davide Tateo, Oleg Arenz et al.

Recent methods for imitation learning directly learn a $Q$-function using an implicit reward formulation rather than an explicit reward function. However, these methods generally require implicit reward regularization to improve stability and often mistreat absorbing states. Previous works show that a squared norm regularization on the implicit reward function is effective, but do not provide a theoretical analysis of the resulting properties of the algorithms. In this work, we show that using this regularizer under a mixture distribution of the policy and the expert provides a particularly illuminating perspective: the original objective can be understood as squared Bellman error minimization, and the corresponding optimization problem minimizes a bounded $χ^2$-Divergence between the expert and the mixture distribution. This perspective allows us to address instabilities and properly treat absorbing states. We show that our method, Least Squares Inverse Q-Learning (LS-IQ), outperforms state-of-the-art algorithms, particularly in environments with absorbing states. Finally, we propose to use an inverse dynamics model to learn from observations only. Using this approach, we retain performance in settings where no expert actions are available.

Bang You, Jingming Xie, Youping Chen et al.

Effective exploration is critical for reinforcement learning agents in environments with sparse rewards or high-dimensional state-action spaces. Recent works based on state-visitation counts, curiosity and entropy-maximization generate intrinsic reward signals to motivate the agent to visit novel states for exploration. However, the agent can get distracted by perturbations to sensor inputs that contain novel but task-irrelevant information, e.g. due to sensor noise or changing background. In this work, we introduce the sequential information bottleneck objective for learning compressed and temporally coherent representations by modelling and compressing sequential predictive information in time-series observations. For efficient exploration in noisy environments, we further construct intrinsic rewards that capture task-relevant state novelty based on the learned representations. We derive a variational upper bound of our sequential information bottleneck objective for practical optimization and provide an information-theoretic interpretation of the derived upper bound. Our experiments on a set of challenging image-based simulated control tasks show that our method achieves better sample efficiency, and robustness to both white noise and natural video backgrounds compared to state-of-art methods based on curiosity, entropy maximization and information-gain.

Siwei Ju, Jan Tauberschmidt, Oleg Arenz et al.

Learning high-performance control policies that remain consistent with expert behavior is a fundamental challenge in robotics. Reinforcement learning can discover high-performing strategies but often departs from desirable human behavior, whereas imitation learning is limited by demonstration quality and struggles to improve beyond expert data. We propose a behavior-constrained reinforcement learning framework that improves beyond demonstrations while explicitly controlling deviation from expert behavior. Because expert-consistent behavior in dynamic control is inherently trajectory-level, we introduce a receding-horizon predictive mechanism that models short-term future trajectories and provides look-ahead rewards during training. To account for the natural variability of human behavior under disturbances and changing conditions, we further condition the policy on reference trajectories, allowing it to represent a distribution of expert-consistent behaviors rather than a single deterministic target. Empirically, we evaluate the approach in high-fidelity race car simulation using data from professional drivers, a domain characterized by extreme dynamics and narrow performance margins. The learned policies achieve competitive lap times while maintaining close alignment with expert driving behavior, outperforming baseline methods in both performance and imitation quality. Beyond standard benchmarks, we conduct human-grounded evaluation in a driver-in-the-loop simulator and show that the learned policies reproduce setup-dependent driving characteristics consistent with the feedback of top-class professional race drivers. These results demonstrate that our method enables learning high-performance control policies that are both optimal and behavior-consistent, and can serve as reliable surrogates for human decision-making in complex control systems.

Anish Diwan, Davide Tateo, Christopher E. Mower et al.

Inverse reinforcement learning (IRL) is typically formulated as maximizing entropy subject to matching the distribution of expert trajectories. Classical (dual-ascent) IRL guarantees monotonic performance improvement but requires fully solving an RL problem each iteration to compute dual gradients. More recent adversarial methods avoid this cost at the expense of stability and monotonic dual improvement, by directly optimizing the primal problem and using a discriminator to provide rewards. In this work, we bridge the gap between these approaches by enabling monotonic improvement of the reward function and policy without having to fully solve an RL problem at every iteration. Our key theoretical insight is that a trust-region-optimal policy for a reward function update can be globally optimal for a smaller update in the same direction. This smaller update allows us to explicitly optimize the dual objective while only relying on a local search around the current policy. In doing so, our approach avoids the training instabilities of adversarial methods, offers monotonic performance improvement, and learns a reward function in the traditional sense of IRL--one that can be globally optimized to match expert demonstrations. Our proposed algorithm, Trust Region Inverse Reinforcement Learning (TRIRL), outperforms state-of-the-art imitation learning methods across multiple challenging tasks by a factor of 2.4x in terms of aggregate inter-quartile mean, while recovering reward functions that generalize to system dynamics shifts.

Lucas Schulze, Jan Peters, Oleg Arenz

Controlling a robot based on physics-consistent dynamic models, such as Deep Lagrangian Networks (DeLaN), can improve the generalizability and interpretability of the resulting behavior. However, in complex environments, the number of objects to potentially interact with is vast, and their physical properties are often uncertain. This complexity makes it infeasible to employ a single global model. Therefore, we need to resort to online system identification of context-aware models that capture only the currently relevant aspects of the environment. While physical principles such as the conservation of energy may not hold across varying contexts, ensuring physical plausibility for any individual context-aware model can still be highly desirable, particularly when using it for receding horizon control methods such as model predictive control (MPC). Hence, in this work, we extend DeLaN to make it context-aware, combine it with a recurrent network for online system identification, and integrate it with an MPC for adaptive, physics-consistent control. We also combine DeLaN with a residual dynamics model to leverage the fact that a nominal model of the robot is typically available. We evaluate our method on a 7-DOF robot arm for trajectory tracking under varying loads. Our method reduces the end-effector tracking error by 39%, compared to a 21% improvement achieved by a baseline that uses an extended Kalman filter.

Bang You, Puze Liu, Huaping Liu et al.

Simplicity is a powerful inductive bias. In reinforcement learning, regularization is used for simpler policies, data augmentation for simpler representations, and sparse reward functions for simpler objectives, all that, with the underlying motivation to increase generalizability and robustness by focusing on the essentials. Supplementary to these techniques, we investigate how to promote simple behavior throughout the episode. To that end, we introduce a modification of the reinforcement learning problem that additionally maximizes the total correlation within the induced trajectories. We propose a practical algorithm that optimizes all models, including policy and state representation, based on a lower-bound approximation. In simulated robot environments, our method naturally generates policies that induce periodic and compressible trajectories, and that exhibit superior robustness to noise and changes in dynamics compared to baseline methods, while also improving performance in the original tasks.

Levin Maier, Lucas Schulze, Robert Lilow et al.

Extract-Transform-Load (ETL) processes are core components of modern data processing infrastructures. The throughput of processed data records can be adjusted by changing the amount of allocated resources, i.e.~the number of parallel processing threads for each of the three ETL phases, but also depends on stochastic variations in the per-record processing times. In chains of multiple consecutive ETL processes, the relation between allocated resources and overall throughput is further complicated, for example by the occurrence of bottlenecks affecting all subsequent ETL processes. We develop a mathematical model of ETL process chains that is accurate at the level of time-aggregated throughput and suitable for efficient simulation. The process chain is represented as a controlled discrete-time Markov process on a directed acyclic graph whose edges are individual ETL processes. We model the mean throughput as a bounded, monotone function of the number of parallel threads, to capture the diminishing benefit of allocating more threads. We furthermore introduce a Flow Balance postulate linking number of threads, mean throughput, and mean processing time. The stochastic processing times are then modeled by non-negative heavy-tailed distributions around the mean processing time. This framework provides a principled simulator for ETL networks and a foundation for learning- and control-based resource allocation.

Zihan Ye, Phil Chau, Raban Emunds et al.

Deep reinforcement learning agents are often misaligned, as they over-exploit early reward signals. Recently, several symbolic approaches have addressed these challenges by encoding sparse objectives along with aligned plans. However, purely symbolic architectures are complex to scale and difficult to apply to continuous settings. Hence, we propose a hybrid approach, inspired by humans' ability to acquire new skills. We use a two-stage framework that injects symbolic structure into neural-based reinforcement learning agents without sacrificing the expressivity of deep policies. Our method, called Hybrid Hierarchical RL (H^2RL), introduces a logical option-based pretraining strategy to steer the learning policy away from short-term reward loops and toward goal-directed behavior while allowing the final policy to be refined via standard environment interaction. Empirically, we show that this approach consistently improves long-horizon decision-making and yields agents that outperform strong neural, symbolic, and neuro-symbolic baselines.

Michael Drolet, Firas Al-Hafez, Aditya Bhatt et al.

Discrete latent bottlenecks in variational autoencoders (VAEs) offer high bit efficiency and can be modeled with autoregressive discrete distributions, enabling parameter-efficient multimodal search with transformers. However, discrete random variables do not allow for exact differentiable parameterization; therefore, discrete VAEs typically rely on approximations, such as Gumbel-Softmax reparameterization or straight-through gradient estimates, or employ high-variance gradient-free methods such as REINFORCE that have had limited success on high-dimensional tasks such as image reconstruction. Inspired by popular techniques in policy search, we propose a training framework for discrete VAEs that leverages the natural gradient of a non-parametric encoder to update the parametric encoder without requiring reparameterization. Our method, combined with automatic step size adaptation and a transformer-based encoder, scales to challenging datasets such as ImageNet and outperforms both approximate reparameterization methods and quantization-based discrete autoencoders in reconstructing high-dimensional data from compact latent spaces, achieving a 20% improvement on FID Score for ImageNet 256.

Claudius Kienle, Benjamin Alt, Oleg Arenz et al.

Domain models enable autonomous agents to solve long-horizon tasks by producing interpretable plans. However, in open-world environments, a single general domain model cannot capture the variety of tasks, so agents must generate suitable task-specific models on the fly. Large Language Models (LLMs), with their implicit common knowledge, can generate such domains, but suffer from high error rates that limit their applicability. Hence, related work relies on extensive human feed-back or prior knowledge, which undermines autonomous, open-world deployment. In this work, we propose LODGE, a framework for autonomous domain learning from LLMs and environment grounding. LODGE builds on hierarchical abstractions and automated simulations to identify and correct inconsistencies between abstraction layers and between the model and environment. Our framework is task-agnostic, as it generates predicates, operators, and their preconditions and effects, while only assuming access to a simulator and a set of generic, executable low-level skills. Experiments on two International Planning Competition ( IPC) domains and a robotic assembly domain show that LODGE yields more accurate domain models and higher task success than existing methods, requiring remarkably few environment interactions and no human feedback or demonstrations.

Marco Ewerton, Oleg Arenz, Jan Peters

Haptic guidance is a powerful technique to combine the strengths of humans and autonomous systems for teleoperation. The autonomous system can provide haptic cues to enable the operator to perform precise movements; the operator can interfere with the plan of the autonomous system leveraging his/her superior cognitive capabilities. However, providing haptic cues such that the individual strengths are not impaired is challenging because low forces provide little guidance, whereas strong forces can hinder the operator in realizing his/her plan. Based on variational inference, we learn a Gaussian mixture model (GMM) over trajectories to accomplish a given task. The learned GMM is used to construct a potential field which determines the haptic cues. The potential field smoothly changes during teleoperation based on our updated belief over the plans and their respective phases. Furthermore, new plans are learned online when the operator does not follow any of the proposed plans, or after changes in the environment. User studies confirm that our framework helps users perform teleoperation tasks more accurately than without haptic cues and, in some cases, faster. Moreover, we demonstrate the use of our framework to help a subject teleoperate a 7 DoF manipulator in a pick-and-place task.

Oleg Arenz, Gerhard Neumann

Many modern methods for imitation learning and inverse reinforcement learning, such as GAIL or AIRL, are based on an adversarial formulation. These methods apply GANs to match the expert's distribution over states and actions with the implicit state-action distribution induced by the agent's policy. However, by framing imitation learning as a saddle point problem, adversarial methods can suffer from unstable optimization, and convergence can only be shown for small policy updates. We address these problems by proposing a framework for non-adversarial imitation learning. The resulting algorithms are similar to their adversarial counterparts and, thus, provide insights for adversarial imitation learning methods. Most notably, we show that AIRL is an instance of our non-adversarial formulation, which enables us to greatly simplify its derivations and obtain stronger convergence guarantees. We also show that our non-adversarial formulation can be used to derive novel algorithms by presenting a method for offline imitation learning that is inspired by the recent ValueDice algorithm, but does not rely on small policy updates for convergence. In our simulated robot experiments, our offline method for non-adversarial imitation learning seems to perform best when using many updates for policy and discriminator at each iteration and outperforms behavioral cloning and ValueDice.

Melvin Laux, Oleg Arenz, Jan Peters et al.

Deep learning in combination with improved training techniques and high computational power has led to recent advances in the field of reinforcement learning (RL) and to successful robotic RL applications such as in-hand manipulation. However, most robotic RL relies on a well known initial state distribution. In real-world tasks, this information is however often not available. For example, when disentangling waste objects the actual position of the robot w.r.t.\ the objects may not match the positions the RL policy was trained for. To solve this problem, we present a novel adversarial reinforcement learning (ARL) framework. The ARL framework utilizes an adversary, which is trained to steer the original agent, the protagonist, to challenging states. We train the protagonist and the adversary jointly to allow them to adapt to the changing policy of their opponent. We show that our method can generalize from training to test scenarios by training an end-to-end system for robot control to solve a challenging object disentangling task. Experiments with a KUKA LBR+ 7-DOF robot arm show that our approach outperforms the baseline method in disentangling when starting from different initial states than provided during training.

Joni Pajarinen, Oleg Arenz, Jan Peters et al.

Physically disentangling entangled objects from each other is a problem encountered in waste segregation or in any task that requires disassembly of structures. Often there are no object models, and, especially with cluttered irregularly shaped objects, the robot can not create a model of the scene due to occlusion. One of our key insights is that based on previous sensory input we are only interested in moving an object out of the disentanglement around obstacles. That is, we only need to know where the robot can successfully move in order to plan the disentangling. Due to the uncertainty we integrate information about blocked movements into a probability map. The map defines the probability of the robot successfully moving to a specific configuration. Using as cost the failure probability of a sequence of movements we can then plan and execute disentangling iteratively. Since our approach circumvents only previously encountered obstacles, new movements will yield information about unknown obstacles that block movement until the robot has learned to circumvent all obstacles and disentangling succeeds. In the experiments, we use a special probabilistic version of the Rapidly exploring Random Tree (RRT) algorithm for planning and demonstrate successful disentanglement of objects both in 2-D and 3-D simulation, and, on a KUKA LBR 7-DOF robot. Moreover, our approach outperforms baseline methods.

Philipp Becker, Oleg Arenz, Gerhard Neumann

Modelling highly multi-modal data is a challenging problem in machine learning. Most algorithms are based on maximizing the likelihood, which corresponds to the M(oment)-projection of the data distribution to the model distribution. The M-projection forces the model to average over modes it cannot represent. In contrast, the I(information)-projection ignores such modes in the data and concentrates on the modes the model can represent. Such behavior is appealing whenever we deal with highly multi-modal data where modelling single modes correctly is more important than covering all the modes. Despite this advantage, the I-projection is rarely used in practice due to the lack of algorithms that can efficiently optimize it based on data. In this work, we present a new algorithm called Expected Information Maximization (EIM) for computing the I-projection solely based on samples for general latent variable models, where we focus on Gaussian mixtures models and Gaussian mixtures of experts. Our approach applies a variational upper bound to the I-projection objective which decomposes the original objective into single objectives for each mixture component as well as for the coefficients, allowing an efficient optimization. Similar to GANs, our approach employs discriminators but uses a more stable optimization procedure, using a tight upper bound. We show that our algorithm is much more effective in computing the I-projection than recent GAN approaches and we illustrate the effectiveness of our approach for modelling multi-modal behavior on two pedestrian and traffic prediction datasets.

Oleg Arenz, Mingjun Zhong, Gerhard Neumann

Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference. Learning sufficiently accurate approximations requires a rich model family and careful exploration of the relevant modes of the target distribution. We propose a method for learning accurate GMM approximations of intractable probability distributions based on insights from policy search by using information-geometric trust regions for principled exploration. For efficient improvement of the GMM approximation, we derive a lower bound on the corresponding optimization objective enabling us to update the components independently. Our use of the lower bound ensures convergence to a stationary point of the original objective. The number of components is adapted online by adding new components in promising regions and by deleting components with negligible weight. We demonstrate on several domains that we can learn approximations of complex, multimodal distributions with a quality that is unmet by previous variational inference methods, and that the GMM approximation can be used for drawing samples that are on par with samples created by state-of-the-art MCMC samplers while requiring up to three orders of magnitude less computational resources.