Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification

The fields of MPC and RL consider two successful control techniques for Markov decision processes. Both approaches are derived from similar fundamental principles, and both are widely used in practical applications, including robotics, process control, energy systems, and autonomous driving. Despite their similarities, MPC and RL follow distinct paradigms that emerged from diverse communities and different requirements. Various technical discrepancies, particularly the role of an environment model as part of the algorithm, lead to methodologies with nearly complementary advantages. Due to their orthogonal benefits, research interest in combination methods has recently increased significantly, leading to a large and growing set of complex ideas leveraging MPC and RL. This work illuminates the differences, similarities, and fundamentals that allow for different combination algorithms and categorizes existing work accordingly. Particularly, we focus on the versatile actor-critic RL approach as a basis for our categorization and examine how the online optimization approach of MPC can be used to improve the overall closed-loop performance of a policy.

Solving Inverse Problem for Multi-armed Bandits via Convex Optimization

We consider the inverse problem of multi-armed bandits (IMAB) that are widely used in neuroscience and psychology research for behavior modelling. We first show that the IMAB problem is not convex in general, but can be relaxed to a convex problem via variable transformation. Based on this result, we propose a two-step sequential heuristic for (approximately) solving the IMAB problem. We discuss a condition where our method provides global solution to the IMAB problem with certificate, as well as approximations to further save computing time. Numerical experiments indicate that our heuristic method is more robust than directly solving the IMAB problem via repeated local optimization, and can achieve the performance of Monte Carlo methods within a significantly decreased running time. We provide the implementation of our method based on CVXPY, which allows straightforward application by users not well versed in convex optimization.

Inverse Reinforcement Learning via Convex Optimization

We consider the inverse reinforcement learning (IRL) problem, where an unknown reward function of some Markov decision process is estimated based on observed expert demonstrations. In most existing approaches, IRL is formulated and solved as a nonconvex optimization problem, posing challenges in scenarios where robustness and reproducibility are critical. We discuss a convex formulation of the IRL problem (CIRL) initially proposed by Ng and Russel, and reformulate the problem such that the domain-specific language CVXPY can be applied directly to specify and solve the convex problem. We also extend the CIRL problem to scenarios where the expert policy is not given analytically but by trajectory as state-action pairs, which can be strongly inconsistent with optimality, by augmenting some of the constraints. Theoretical analysis and practical implementation for hyperparameter auto-selection are introduced. This note helps the users to easily apply CIRL for their problems, without background knowledge on convex optimization.

SR-Reward: Taking The Path More Traveled

In this paper, we propose a novel method for learning reward functions directly from offline demonstrations. Unlike traditional inverse reinforcement learning (IRL), our approach decouples the reward function from the learner's policy, eliminating the adversarial interaction typically required between the two. This results in a more stable and efficient training process. Our reward function, called \textit{SR-Reward}, leverages successor representation (SR) to encode a state based on expected future states' visitation under the demonstration policy and transition dynamics. By utilizing the Bellman equation, SR-Reward can be learned concurrently with most reinforcement learning (RL) algorithms without altering the existing training pipeline. We also introduce a negative sampling strategy to mitigate overestimation errors by reducing rewards for out-of-distribution data, thereby enhancing robustness. This strategy inherently introduces a conservative bias into RL algorithms that employ the learned reward. We evaluate our method on the D4RL benchmark, achieving competitive results compared to offline RL algorithms with access to true rewards and imitation learning (IL) techniques like behavioral cloning. Moreover, our ablation studies on data size and quality reveal the advantages and limitations of SR-Reward as a proxy for true rewards.

The Surprising Ineffectiveness of Pre-Trained Visual Representations for Model-Based Reinforcement Learning

Visual Reinforcement Learning (RL) methods often require extensive amounts of data. As opposed to model-free RL, model-based RL (MBRL) offers a potential solution with efficient data utilization through planning. Additionally, RL lacks generalization capabilities for real-world tasks. Prior work has shown that incorporating pre-trained visual representations (PVRs) enhances sample efficiency and generalization. While PVRs have been extensively studied in the context of model-free RL, their potential in MBRL remains largely unexplored. In this paper, we benchmark a set of PVRs on challenging control tasks in a model-based RL setting. We investigate the data efficiency, generalization capabilities, and the impact of different properties of PVRs on the performance of model-based agents. Our results, perhaps surprisingly, reveal that for MBRL current PVRs are not more sample efficient than learning representations from scratch, and that they do not generalize better to out-of-distribution (OOD) settings. To explain this, we analyze the quality of the trained dynamics model. Furthermore, we show that data diversity and network architecture are the most important contributors to OOD generalization performance.

Advances in Land Surface Model-based Forecasting: A comparative study of LSTM, Gradient Boosting, and Feedforward Neural Network Models as prognostic state emulators

Most useful weather prediction for the public is near the surface. The processes that are most relevant for near-surface weather prediction are also those that are most interactive and exhibit positive feedback or have key role in energy partitioning. Land surface models (LSMs) consider these processes together with surface heterogeneity and forecast water, carbon and energy fluxes, and coupled with an atmospheric model provide boundary and initial conditions. This numerical parametrization of atmospheric boundaries being computationally expensive, statistical surrogate models are increasingly used to accelerated progress in experimental research. We evaluated the efficiency of three surrogate models in speeding up experimental research by simulating land surface processes, which are integral to forecasting water, carbon, and energy fluxes in coupled atmospheric models. Specifically, we compared the performance of a Long-Short Term Memory (LSTM) encoder-decoder network, extreme gradient boosting, and a feed-forward neural network within a physics-informed multi-objective framework. This framework emulates key states of the ECMWF's Integrated Forecasting System (IFS) land surface scheme, ECLand, across continental and global scales. Our findings indicate that while all models on average demonstrate high accuracy over the forecast period, the LSTM network excels in continental long-range predictions when carefully tuned, the XGB scores consistently high across tasks and the MLP provides an excellent implementation-time-accuracy trade-off. The runtime reduction achieved by the emulators in comparison to the full numerical models are significant, offering a faster, yet reliable alternative for conducting numerical experiments on land surfaces.

The Art of Imitation: Learning Long-Horizon Manipulation Tasks from Few Demonstrations

Task Parametrized Gaussian Mixture Models (TP-GMM) are a sample-efficient method for learning object-centric robot manipulation tasks. However, there are several open challenges to applying TP-GMMs in the wild. In this work, we tackle three crucial challenges synergistically. First, end-effector velocities are non-Euclidean and thus hard to model using standard GMMs. We thus propose to factorize the robot's end-effector velocity into its direction and magnitude, and model them using Riemannian GMMs. Second, we leverage the factorized velocities to segment and sequence skills from complex demonstration trajectories. Through the segmentation, we further align skill trajectories and hence leverage time as a powerful inductive bias. Third, we present a method to automatically detect relevant task parameters per skill from visual observations. Our approach enables learning complex manipulation tasks from just five demonstrations while using only RGB-D observations. Extensive experimental evaluations on RLBench demonstrate that our approach achieves state-of-the-art performance with 20-fold improved sample efficiency. Our policies generalize across different environments, object instances, and object positions, while the learned skills are reusable.

Latent Linear Quadratic Regulator for Robotic Control Tasks

Model predictive control (MPC) has played a more crucial role in various robotic control tasks, but its high computational requirements are concerning, especially for nonlinear dynamical models. This paper presents a $\textbf{la}$tent $\textbf{l}$inear $\textbf{q}$uadratic $\textbf{r}$egulator (LaLQR) that maps the state space into a latent space, on which the dynamical model is linear and the cost function is quadratic, allowing the efficient application of LQR. We jointly learn this alternative system by imitating the original MPC. Experiments show LaLQR's superior efficiency and generalization compared to other baselines.

UDUC: An Uncertainty-driven Approach for Learning-based Robust Control

Learning-based techniques have become popular in both model predictive control (MPC) and reinforcement learning (RL). Probabilistic ensemble (PE) models offer a promising approach for modelling system dynamics, showcasing the ability to capture uncertainty and scalability in high-dimensional control scenarios. However, PE models are susceptible to mode collapse, resulting in non-robust control when faced with environments slightly different from the training set. In this paper, we introduce the $\textbf{u}$ncertainty-$\textbf{d}$riven rob$\textbf{u}$st $\textbf{c}$ontrol (UDUC) loss as an alternative objective for training PE models, drawing inspiration from contrastive learning. We analyze the robustness of UDUC loss through the lens of robust optimization and evaluate its performance on the challenging Real-world Reinforcement Learning (RWRL) benchmark, which involves significant environmental mismatches between the training and testing environments.

PlanNetX: Learning an Efficient Neural Network Planner from MPC for Longitudinal Control

Model predictive control (MPC) is a powerful, optimization-based approach for controlling dynamical systems. However, the computational complexity of online optimization can be problematic on embedded devices. Especially, when we need to guarantee fixed control frequencies. Thus, previous work proposed to reduce the computational burden using imitation learning (IL) approximating the MPC policy by a neural network. In this work, we instead learn the whole planned trajectory of the MPC. We introduce a combination of a novel neural network architecture PlanNetX and a simple loss function based on the state trajectory that leverages the parameterized optimal control structure of the MPC. We validate our approach in the context of autonomous driving by learning a longitudinal planner and benchmarking it extensively in the CommonRoad simulator using synthetic scenarios and scenarios derived from real data. Our experimental results show that we can learn the open-loop MPC trajectory with high accuracy while improving the closed-loop performance of the learned control policy over other baselines like behavior cloning.