Nicolò Botteghi

Nicolò Botteghi, Mannes Poel, Christoph Brune

This review addresses the problem of learning abstract representations of the measurement data in the context of Deep Reinforcement Learning (DRL). While the data are often ambiguous, high-dimensional, and complex to interpret, many dynamical systems can be effectively described by a low-dimensional set of state variables. Discovering these state variables from the data is a crucial aspect for (i) improving the data efficiency, robustness, and generalization of DRL methods, (ii) tackling the curse of dimensionality, and (iii) bringing interpretability and insights into black-box DRL. This review provides a comprehensive and complete overview of unsupervised representation learning in DRL by describing the main Deep Learning tools used for learning representations of the world, providing a systematic view of the method and principles, summarizing applications, benchmarks and evaluation strategies, and discussing open challenges and future directions.

Nicolò Botteghi, Mengwu Guo, Christoph Brune

This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses high-dimensional measurements into low-dimensional state variables, and a latent dynamical model for the state variables that predicts the system evolution over time. The training of the proposed model is carried out in an unsupervised manner, i.e., not relying on labeled data. Our learning method is evaluated on the motion of a pendulum -- a well studied baseline for nonlinear model identification and control with continuous states and control inputs -- measured via high-dimensional noisy RGB images. Results show that the method can effectively denoise measurements, learn compact state representations and latent dynamical models, as well as identify and quantify modeling uncertainties.

Nicolò Botteghi, Urban Fasel

This document contains an educational introduction to the problem of sparsifying parametric models with L0 regularization. We utilize this approach together with dictionary learning to learn sparse polynomial policies for deep reinforcement learning to control parametric partial differential equations. The code and a tutorial are provided here: https://github.com/nicob15/Sparsifying-Parametric-Models-with-L0.

Andreas W. M. Sauter, Nicolò Botteghi, Erman Acar et al.

Causal discovery is the challenging task of inferring causal structure from data. Motivated by Pearl's Causal Hierarchy (PCH), which tells us that passive observations alone are not enough to distinguish correlation from causation, there has been a recent push to incorporate interventions into machine learning research. Reinforcement learning provides a convenient framework for such an active approach to learning. This paper presents CORE, a deep reinforcement learning-based approach for causal discovery and intervention planning. CORE learns to sequentially reconstruct causal graphs from data while learning to perform informative interventions. Our results demonstrate that CORE generalizes to unseen graphs and efficiently uncovers causal structures. Furthermore, CORE scales to larger graphs with up to 10 variables and outperforms existing approaches in structure estimation accuracy and sample efficiency. All relevant code and supplementary material can be found at https://github.com/sa-and/CORE

Adrian Andrei Buda, Xavier Chen, Nicolò Botteghi et al.

Co-design optimisation of autonomous systems has emerged as a powerful alternative to sequential approaches by jointly optimising physical design and control strategies. However, existing frameworks often neglect the robustness required for autonomous systems navigating unstructured, real-world environments. For agile Unmanned Aerial Vehicles (UAVs) operating at the edge of the flight envelope, this lack of robustness yields designs that are sensitive to perturbations and model mismatch. To address this, we propose a robust co-design framework for agile fixed-wing UAVs that integrates parametric uncertainty and wind disturbances directly into the concurrent optimisation process. Our bi-level approach optimises physical design in a high-level loop while discovering nominal solutions via a constrained trajectory planner and evaluating performance across a stochastic Monte Carlo ensemble using feedback LQR control. Validated across three agile flight missions, our strategy consistently outperforms deterministic baselines. The results demonstrate that our robust co-design strategy inherently tailors aerodynamic features, such as wing placement and aspect ratio, to achieve an optimal trade-off between mission performance and disturbance rejection.

Nicolò Botteghi, Urban Fasel

Optimal control of parametric partial differential equations (PDEs) is crucial in many applications in engineering and science. In recent years, the progress in scientific machine learning has opened up new frontiers for the control of parametric PDEs. In particular, deep reinforcement learning (DRL) has the potential to solve high-dimensional and complex control problems in a large variety of applications. Most DRL methods rely on deep neural network (DNN) control policies. However, for many dynamical systems, DNN-based control policies tend to be over-parametrized, which means they need large amounts of training data, show limited robustness, and lack interpretability. In this work, we leverage dictionary learning and differentiable L$_0$ regularization to learn sparse, robust, and interpretable control policies for parametric PDEs. Our sparse policy architecture is agnostic to the DRL method and can be used in different policy-gradient and actor-critic DRL algorithms without changing their policy-optimization procedure. We test our approach on the challenging tasks of controlling parametric Kuramoto-Sivashinsky and convection-diffusion-reaction PDEs. We show that our method (1) outperforms baseline DNN-based DRL policies, (2) allows for the derivation of interpretable equations of the learned optimal control laws, and (3) generalizes to unseen parameters of the PDE without retraining the policies.

Nicolò Botteghi, Stefania Fresca, Mengwu Guo et al.

In this work, we devise a new, general-purpose reinforcement learning strategy for the optimal control of parametric partial differential equations (PDEs). Such problems frequently arise in applied sciences and engineering and entail a significant complexity when control and/or state variables are distributed in high-dimensional space or depend on varying parameters. Traditional numerical methods, relying on either iterative minimization algorithms or dynamic programming, while reliable, often become computationally infeasible. Indeed, in either way, the optimal control problem must be solved for each instance of the parameters, and this is out of reach when dealing with high-dimensional time-dependent and parametric PDEs. In this paper, we propose HypeRL, a deep reinforcement learning (DRL) framework to overcome the limitations shown by traditional methods. HypeRL aims at approximating the optimal control policy directly. Specifically, we employ an actor-critic DRL approach to learn an optimal feedback control strategy that can generalize across the range of variation of the parameters. To effectively learn such optimal control laws, encoding the parameter information into the DRL policy and value function neural networks (NNs) is essential. To do so, HypeRL uses two additional NNs, often called hypernetworks, to learn the weights and biases of the value function and the policy NNs. We validate the proposed approach on two PDE-constrained optimal control benchmarks, namely a 1D Kuramoto-Sivashinsky equation and a 2D Navier-Stokes equations, by showing that the knowledge of the PDE parameters and how this information is encoded, i.e., via a hypernetwork, is an essential ingredient for learning parameter-dependent control policies that can generalize effectively to unseen scenarios and for improving the sample efficiency of such policies.

Florian Wolf, Nicolò Botteghi, Urban Fasel et al.

Effectively controlling systems governed by Partial Differential Equations (PDEs) is crucial in several fields of Applied Sciences and Engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement Learning (RL), particularly Deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these issues, we propose a data-efficient, interpretable, and scalable Dyna-style Model-Based RL framework for PDE control, combining the Sparse Identification of Nonlinear Dynamics with Control (SINDy-C) algorithm and an autoencoder (AE) framework for the sake of dimensionality reduction of PDE states and actions. This novel approach enables fast rollouts, reducing the need for extensive environment interactions, and provides an interpretable latent space representation of the PDE forward dynamics. We validate our method on two PDE problems describing fluid flows - namely, the 1D Burgers equation and 2D Navier-Stokes equations - comparing it against a model-free baseline, and carrying out an extensive analysis of the learned dynamics.

Nicolò Botteghi, Matteo Tomasetto, Urban Fasel et al.

Deep reinforcement learning has recently emerged as a promising feedback control strategy for complex dynamical systems governed by partial differential equations (PDEs). When dealing with distributed, high-dimensional problems in state and control variables, multi-agent reinforcement learning (MARL) has been proposed as a scalable approach for breaking the curse of dimensionality. In particular, through decentralized training and execution, multiple agents cooperate to steer the system towards a target configuration, relying solely on local state and reward information. However, the principle of locality may become a limiting factor whenever a collective, nonlocal behavior of the agents is crucial to maximize the reward function, as typically happens in PDE-constrained optimal control problems. In this work, we propose HypeMARL: a decentralized MARL algorithm tailored to the control of high-dimensional, parametric, and distributed systems. HypeMARL employs hypernetworks to effectively parametrize the agents' policies and value functions with respect to the system parameters and the agents' relative positions, encoded by sinusoidal positional encoding. Through the application on challenging control problems, such as density and flow control, we show that HypeMARL (i) can effectively control systems through a collective behavior of the agents, outperforming state-of-the-art decentralized MARL, (ii) can efficiently deal with parametric dependencies, (iii) requires minimal hyperparameter tuning and (iv) can reduce the amount of expensive environment interactions by a factor of ~10 thanks to its model-based extension, MB-HypeMARL, which relies on computationally efficient deep learning-based surrogate models approximating the dynamics locally, with minimal deterioration of the policy performance.

Nicolò Botteghi, Luuk Grefte, Mannes Poel et al.

Inspection and maintenance are two crucial aspects of industrial pipeline plants. While robotics has made tremendous progress in the mechanic design of in-pipe inspection robots, the autonomous control of such robots is still a big open challenge due to the high number of actuators and the complex manoeuvres required. To address this problem, we investigate the usage of Deep Reinforcement Learning for achieving autonomous navigation of in-pipe robots in pipeline networks with complex topologies. Moreover, we introduce a hierarchical policy decomposition based on Hierarchical Reinforcement Learning to learn robust high-level navigation skills. We show that the hierarchical structure introduced in the policy is fundamental for solving the navigation task through pipes and necessary for achieving navigation performances superior to human-level control.

Nicolò Botteghi, Mannes Poel, Beril Sirmacek et al.

Deep Reinforcement Learning has shown its ability in solving complicated problems directly from high-dimensional observations. However, in end-to-end settings, Reinforcement Learning algorithms are not sample-efficient and requires long training times and quantities of data. In this work, we proposed a framework for sample-efficient Reinforcement Learning that take advantage of state and action representations to transform a high-dimensional problem into a low-dimensional one. Moreover, we seek to find the optimal policy mapping latent states to latent actions. Because now the policy is learned on abstract representations, we enforce, using auxiliary loss functions, the lifting of such policy to the original problem domain. Results show that the novel framework can efficiently learn low-dimensional and interpretable state and action representations and the optimal latent policy.

Nicolò Botteghi, Khaled Alaa, Mannes Poel et al.

Autonomous robots require high degrees of cognitive and motoric intelligence to come into our everyday life. In non-structured environments and in the presence of uncertainties, such degrees of intelligence are not easy to obtain. Reinforcement learning algorithms have proven to be capable of solving complicated robotics tasks in an end-to-end fashion without any need for hand-crafted features or policies. Especially in the context of robotics, in which the cost of real-world data is usually extremely high, reinforcement learning solutions achieving high sample efficiency are needed. In this paper, we propose a framework combining the learning of a low-dimensional state representation, from high-dimensional observations coming from the robot's raw sensory readings, with the learning of the optimal policy, given the learned state representation. We evaluate our framework in the context of mobile robot navigation in the case of continuous state and action spaces. Moreover, we study the problem of transferring what learned in the simulated virtual environment to the real robot without further retraining using real-world data in the presence of visual and depth distractors, such as lighting changes and moving obstacles.

Nicolò Botteghi, Ruben Obbink, Daan Geijs et al.

Reinforcement Learning has been able to solve many complicated robotics tasks without any need for feature engineering in an end-to-end fashion. However, learning the optimal policy directly from the sensory inputs, i.e the observations, often requires processing and storage of a huge amount of data. In the context of robotics, the cost of data from real robotics hardware is usually very high, thus solutions that achieve high sample-efficiency are needed. We propose a method that aims at learning a mapping from the observations into a lower-dimensional state space. This mapping is learned with unsupervised learning using loss functions shaped to incorporate prior knowledge of the environment and the task. Using the samples from the state space, the optimal policy is quickly and efficiently learned. We test the method on several mobile robot navigation tasks in a simulation environment and also on a real robot.

Nicolò Botteghi, Beril Sirmacek, Khaled A. A. Mustafa et al.

We present a map-less path planning algorithm based on Deep Reinforcement Learning (DRL) for mobile robots navigating in unknown environment that only relies on 40-dimensional raw laser data and odometry information. The planner is trained using a reward function shaped based on the online knowledge of the map of the training environment, obtained using grid-based Rao-Blackwellized particle filter, in an attempt to enhance the obstacle awareness of the agent. The agent is trained in a complex simulated environment and evaluated in two unseen ones. We show that the policy trained using the introduced reward function not only outperforms standard reward functions in terms of convergence speed, by a reduction of 36.9\% of the iteration steps, and reduction of the collision samples, but it also drastically improves the behaviour of the agent in unseen environments, respectively by 23\% in a simpler workspace and by 45\% in a more clustered one. Furthermore, the policy trained in the simulation environment can be directly and successfully transferred to the real robot. A video of our experiments can be found at: https://youtu.be/UEV7W6e6ZqI

Beril Sirmacek, Nicolò Botteghi, Santiago Sanchez Escalonilla Plaza

Recently, semantic video segmentation gained high attention especially for supporting autonomous driving systems. Deep learning methods made it possible to implement real time segmentation and object identification algorithms on videos. However, most of the available approaches process each video frame independently disregarding their sequential relation in time. Therefore their results suddenly miss some of the object segments in some of the frames even if they were detected properly in the earlier frames. Herein we propose two sequential probabilistic video frame analysis approaches to improve the segmentation performance of the existing algorithms. Our experiments show that using the information of the past frames we increase the performance and consistency of the state of the art algorithms.