Michael Lutter

Daniel Palenicek, Michael Lutter, João Carvalho et al.

Model-based reinforcement learning aims to increase sample efficiency, but the accuracy of dynamics models and the resulting compounding errors are often seen as key limitations. This paper empirically investigates potential sample efficiency gains from improved dynamics models in model-based value expansion methods. Our study reveals two key findings when using oracle dynamics models to eliminate compounding errors. First, longer rollout horizons enhance sample efficiency, but the improvements quickly diminish with each additional expansion step. Second, increased model accuracy only marginally improves sample efficiency compared to learned models with identical horizons. These diminishing returns in sample efficiency are particularly noteworthy when compared to model-free value expansion methods. These model-free algorithms achieve comparable performance without the computational overhead. Our results suggest that the limitation of model-based value expansion methods cannot be attributed to model accuracy. Although higher accuracy is beneficial, even perfect models do not provide unrivaled sample efficiency. Therefore, the bottleneck exists elsewhere. These results challenge the common assumption that model accuracy is the primary constraint in model-based reinforcement learning.

Michael Lutter, Leonard Hasenclever, Arunkumar Byravan et al.

Model-Based Reinforcement Learning involves learning a \textit{dynamics model} from data, and then using this model to optimise behaviour, most often with an online \textit{planner}. Much of the recent research along these lines presents a particular set of design choices, involving problem definition, model learning and planning. Given the multiple contributions, it is difficult to evaluate the effects of each. This paper sets out to disambiguate the role of different design choices for learning dynamics models, by comparing their performance to planning with a ground-truth model -- the simulator. First, we collect a rich dataset from the training sequence of a model-free agent on 5 domains of the DeepMind Control Suite. Second, we train feed-forward dynamics models in a supervised fashion, and evaluate planner performance while varying and analysing different model design choices, including ensembling, stochasticity, multi-step training and timestep size. Besides the quantitative analysis, we describe a set of qualitative findings, rules of thumb, and future research directions for planning with learned dynamics models. Videos of the results are available at https://sites.google.com/view/learning-better-models.

Michael Lutter, Shie Mannor, Jan Peters et al.

When transferring a control policy from simulation to a physical system, the policy needs to be robust to variations in the dynamics to perform well. Commonly, the optimal policy overfits to the approximate model and the corresponding state-distribution, often resulting in failure to trasnfer underlying distributional shifts. In this paper, we present Robust Fitted Value Iteration, which uses dynamic programming to compute the optimal value function on the compact state domain and incorporates adversarial perturbations of the system dynamics. The adversarial perturbations encourage a optimal policy that is robust to changes in the dynamics. Utilizing the continuous-time perspective of reinforcement learning, we derive the optimal perturbations for the states, actions, observations and model parameters in closed-form. Notably, the resulting algorithm does not require discretization of states or actions. Therefore, the optimal adversarial perturbations can be efficiently incorporated in the min-max value function update. We apply the resulting algorithm to the physical Furuta pendulum and cartpole. By changing the masses of the systems we evaluate the quantitative and qualitative performance across different model parameters. We show that robust value iteration is more robust compared to deep reinforcement learning algorithm and the non-robust version of the algorithm. Videos of the experiments are shown at https://sites.google.com/view/rfvi

Michael Lutter, Shie Mannor, Jan Peters et al.

Classical value iteration approaches are not applicable to environments with continuous states and actions. For such environments, the states and actions are usually discretized, which leads to an exponential increase in computational complexity. In this paper, we propose continuous fitted value iteration (cFVI). This algorithm enables dynamic programming for continuous states and actions with a known dynamics model. Leveraging the continuous-time formulation, the optimal policy can be derived for non-linear control-affine dynamics. This closed-form solution enables the efficient extension of value iteration to continuous environments. We show in non-linear control experiments that the dynamic programming solution obtains the same quantitative performance as deep reinforcement learning methods in simulation but excels when transferred to the physical system. The policy obtained by cFVI is more robust to changes in the dynamics despite using only a deterministic model and without explicitly incorporating robustness in the optimization. Videos of the physical system are available at \url{https://sites.google.com/view/value-iteration}.

Kai Ploeger, Michael Lutter, Jan Peters

Robots that can learn in the physical world will be important to en-able robots to escape their stiff and pre-programmed movements. For dynamic high-acceleration tasks, such as juggling, learning in the real-world is particularly challenging as one must push the limits of the robot and its actuation without harming the system, amplifying the necessity of sample efficiency and safety for robot learning algorithms. In contrast to prior work which mainly focuses on the learning algorithm, we propose a learning system, that directly incorporates these requirements in the design of the policy representation, initialization, and optimization. We demonstrate that this system enables the high-speed Barrett WAM manipulator to learn juggling two balls from 56 minutes of experience with a binary reward signal. The final policy juggles continuously for up to 33 minutes or about 4500 repeated catches. The videos documenting the learning process and the evaluation can be found at https://sites.google.com/view/jugglingbot

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.

Michael Lutter, Boris Belousov, Kim Listmann et al.

Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement learning is sample inefficient, optimal control only plans an optimal trajectory from a specific starting configuration. In this paper we propose deep optimal feedback control to learn an optimal feedback policy rather than a single trajectory. By exploiting the inherent structure of the robot dynamics and strictly convex action cost, we can derive principled cost functions such that the optimal policy naturally obeys the action limits, is globally optimal and stable on the training domain given the optimal value function. The corresponding optimal value function is learned end-to-end by embedding a deep differential network in the Hamilton-Jacobi-Bellmann differential equation and minimizing the error of this equality while simultaneously decreasing the discounting from short- to far-sighted to enable the learning. Our proposed approach enables us to learn an optimal feedback control law in continuous time, that in contrast to existing approaches generates an optimal trajectory from any point in state-space without the need of replanning. The resulting approach is evaluated on non-linear systems and achieves optimal feedback control, where standard optimal control methods require frequent replanning.

Michael Lutter, Christian Ritter, Jan Peters

Deep learning has achieved astonishing results on many tasks with large amounts of data and generalization within the proximity of training data. For many important real-world applications, these requirements are unfeasible and additional prior knowledge on the task domain is required to overcome the resulting problems. In particular, learning physics models for model-based control requires robust extrapolation from fewer samples - often collected online in real-time - and model errors may lead to drastic damages of the system. Directly incorporating physical insight has enabled us to obtain a novel deep model learning approach that extrapolates well while requiring fewer samples. As a first example, we propose Deep Lagrangian Networks (DeLaN) as a deep network structure upon which Lagrangian Mechanics have been imposed. DeLaN can learn the equations of motion of a mechanical system (i.e., system dynamics) with a deep network efficiently while ensuring physical plausibility. The resulting DeLaN network performs very well at robot tracking control. The proposed method did not only outperform previous model learning approaches at learning speed but exhibits substantially improved and more robust extrapolation to novel trajectories and learns online in real-time