Mouhacine Benosman

Xiangyuan Zhang, Saviz Mowlavi, Mouhacine Benosman et al.

We introduce the receding-horizon policy gradient (RHPG) algorithm, the first PG algorithm with provable global convergence in learning the optimal linear estimator designs, i.e., the Kalman filter (KF). Notably, the RHPG algorithm does not require any prior knowledge of the system for initialization and does not require the target system to be open-loop stable. The key of RHPG is that we integrate vanilla PG (or any other policy search directions) into a dynamic programming outer loop, which iteratively decomposes the infinite-horizon KF problem that is constrained and non-convex in the policy parameter into a sequence of static estimation problems that are unconstrained and strongly-convex, thus enabling global convergence. We further provide fine-grained analyses of the optimization landscape under RHPG and detail the convergence and sample complexity guarantees of the algorithm. This work serves as an initial attempt to develop reinforcement learning algorithms specifically for control applications with performance guarantees by utilizing classic control theory in both algorithmic design and theoretical analyses. Lastly, we validate our theories by deploying the RHPG algorithm to learn the Kalman filter design of a large-scale convection-diffusion model. We open-source the code repository at \url{https://github.com/xiangyuan-zhang/LearningKF}.

Xiangyuan Zhang, Weichao Mao, Saviz Mowlavi et al.

We introduce controlgym, a library of thirty-six industrial control settings, and ten infinite-dimensional partial differential equation (PDE)-based control problems. Integrated within the OpenAI Gym/Gymnasium (Gym) framework, controlgym allows direct applications of standard reinforcement learning (RL) algorithms like stable-baselines3. Our control environments complement those in Gym with continuous, unbounded action and observation spaces, motivated by real-world control applications. Moreover, the PDE control environments uniquely allow the users to extend the state dimensionality of the system to infinity while preserving the intrinsic dynamics. This feature is crucial for evaluating the scalability of RL algorithms for control. This project serves the learning for dynamics & control (L4DC) community, aiming to explore key questions: the convergence of RL algorithms in learning control policies; the stability and robustness issues of learning-based controllers; and the scalability of RL algorithms to high- and potentially infinite-dimensional systems. We open-source the controlgym project at https://github.com/xiangyuan-zhang/controlgym.

Weidong Cao, Mouhacine Benosman, Xuan Zhang et al. · tsinghua

The design automation of analog circuits is a longstanding challenge. This paper presents a reinforcement learning method enhanced by graph learning to automate the analog circuit parameter optimization at the pre-layout stage, i.e., finding device parameters to fulfill desired circuit specifications. Unlike all prior methods, our approach is inspired by human experts who rely on domain knowledge of analog circuit design (e.g., circuit topology and couplings between circuit specifications) to tackle the problem. By originally incorporating such key domain knowledge into policy training with a multimodal network, the method best learns the complex relations between circuit parameters and design targets, enabling optimal decisions in the optimization process. Experimental results on exemplary circuits show it achieves human-level design accuracy (99%) 1.5X efficiency of existing best-performing methods. Our method also shows better generalization ability to unseen specifications and optimality in circuit performance optimization. Moreover, it applies to design radio-frequency circuits on emerging semiconductor technologies, breaking the limitations of prior learning methods in designing conventional analog circuits.

Mouhacine Benosman

Artificial intelligence (AI), particularly in the form of large language models (LLMs) or chatbots, has become increasingly integrated into our daily lives. In the past five years, several LLMs have been introduced, including ChatGPT by OpenAI, Claude by Anthropic, and Llama by Meta, among others. These models have the potential to be employed across a wide range of human-machine interaction applications, such as chatbots for information retrieval, assistance in corporate hiring decisions, college admissions, financial loan approvals, parole determinations, and even in medical fields like psychotherapy delivered through chatbots. The key question is whether these chatbots will interact with humans in a bias-free manner or if they will further reinforce the existing pathological biases present in human-to-human interactions. If the latter is true, then how can we rigorously measure these biases? We address this challenge by introducing STAMP-LLM (Standardized Test and Assessment Measurement Protocol for LLMs), a psychometric-based principled two-phase framework for designing psychometric measures to evaluate chatbot biases: (i) a Definitional phase for construct mapping, item development, and expert review; and (ii) a Data/Analysis phase for protocol control (prompts/decoding), automated sampling, pre-specified scoring, and basic reliability/validity checks. We illustrate STAMP-LLM on racial bias using one explicit and two implicit measures.

James Queeney, Mouhacine Benosman

Many real-world domains require safe decision making in uncertain environments. In this work, we introduce a deep reinforcement learning framework for approaching this important problem. We consider a distribution over transition models, and apply a risk-averse perspective towards model uncertainty through the use of coherent distortion risk measures. We provide robustness guarantees for this framework by showing it is equivalent to a specific class of distributionally robust safe reinforcement learning problems. Unlike existing approaches to robustness in deep reinforcement learning, however, our formulation does not involve minimax optimization. This leads to an efficient, model-free implementation of our approach that only requires standard data collection from a single training environment. In experiments on continuous control tasks with safety constraints, we demonstrate that our framework produces robust performance and safety at deployment time across a range of perturbed test environments.

Anantharaman Subbaraman, Mouhacine Benosman

In this paper, we study a tracking control problem for linear time-invariant systems, with model parametric uncertainties, under input and states constraints. We apply the idea of modular design introduced in Benosman et al. 2014, to solve this problem in the model predictive control (MPC) framework. We propose to design an MPC with input-to-state stability (ISS) guarantee, and complement it with an extremum seeking (ES) algorithm to iteratively learn the model uncertainties. The obtained MPC algorithms can be classified as iterative learning control (ILC)-MPC.

Mouhacine Benosman, Jeff Borggaard, Boris Kramer

We present some results on stabilization for reduced-order models (ROMs) of partial differential equations. The stabilization is achieved using Lyapunov theory to design a new closure model that is robust to parametric uncertainties. The free parameters in the proposed ROM stabilization method are optimized using a model-free multi-parametric extremum seeking (MES) algorithm. The 3D Boussinesq equations provide a challenging numerical test-problem that is used to demonstrate the advantages of the proposed method.

Saviz Mowlavi, Mouhacine Benosman

In systems governed by nonlinear partial differential equations such as fluid flows, the design of state estimators such as Kalman filters relies on a reduced-order model (ROM) that projects the original high-dimensional dynamics onto a computationally tractable low-dimensional space. However, ROMs are prone to large errors, which negatively affects the performance of the estimator. Here, we introduce the reinforcement learning reduced-order estimator (RL-ROE), a ROM-based estimator in which the correction term that takes in the measurements is given by a nonlinear policy trained through reinforcement learning. The nonlinearity of the policy enables the RL-ROE to compensate efficiently for errors of the ROM, while still taking advantage of the imperfect knowledge of the dynamics. Using examples involving the Burgers and Navier-Stokes equations, we show that in the limit of very few sensors, the trained RL-ROE outperforms a Kalman filter designed using the same ROM. Moreover, it yields accurate high-dimensional state estimates for trajectories corresponding to various physical parameter values, without direct knowledge of the latter.

James Queeney, Xiaoyi Cai, Alexander Schperberg et al.

The reliable deployment of deep reinforcement learning in real-world settings requires the ability to generalize across a variety of conditions, including both in-distribution scenarios seen during training as well as novel out-of-distribution scenarios. In this work, we present a framework for dynamics generalization in deep reinforcement learning that unifies these two distinct types of generalization within a single architecture. We introduce a robust adaptation module that provides a mechanism for identifying and reacting to both in-distribution and out-of-distribution environment dynamics, along with a joint training pipeline that combines the goals of in-distribution adaptation and out-of-distribution robustness. Our algorithm GRAM achieves strong generalization performance across in-distribution and out-of-distribution scenarios upon deployment, which we demonstrate through extensive simulation and hardware locomotion experiments on a quadruped robot.

Xiaoyu Xie, Saviz Mowlavi, Mouhacine Benosman

Spatiotemporal modeling is critical for understanding complex systems across various scientific and engineering disciplines, but governing equations are often not fully known or computationally intractable due to inherent system complexity. Data-driven reduced-order models (ROMs) offer a promising approach for fast and accurate spatiotemporal forecasting by computing solutions in a compressed latent space. However, these models often neglect temporal correlations between consecutive snapshots when constructing the latent space, leading to suboptimal compression, jagged latent trajectories, and limited extrapolation ability over time. To address these issues, this paper introduces a continuous operator learning framework that incorporates jerk regularization into the learning of the compressed latent space. This jerk regularization promotes smoothness and sparsity of latent space dynamics, which not only yields enhanced accuracy and convergence speed but also helps identify intrinsic latent space coordinates. Consisting of an implicit neural representation (INR)-based autoencoder and a neural ODE latent dynamics model, the framework allows for inference at any desired spatial or temporal resolution. The effectiveness of this framework is demonstrated through a two-dimensional unsteady flow problem governed by the Navier-Stokes equations, highlighting its potential to expedite high-fidelity simulations in various scientific and engineering applications.

Xiangyuan Zhang, Saviz Mowlavi, Mouhacine Benosman et al.

Dimensionality reduction is crucial for controlling nonlinear partial differential equations (PDE) through a "reduce-then-design" strategy, which identifies a reduced-order model and then implements model-based control solutions. However, inaccuracies in the reduced-order modeling can substantially degrade controller performance, especially in PDEs with chaotic behavior. To address this issue, we augment the reduce-then-design procedure with a policy optimization (PO) step. The PO step fine-tunes the model-based controller to compensate for the modeling error from dimensionality reduction. This augmentation shifts the overall strategy into reduce-then-design-then-adapt, where the model-based controller serves as a warm start for PO. Specifically, we study the state-feedback tracking control of PDEs that aims to align the PDE state with a specific constant target subject to a linear-quadratic cost. Through extensive experiments, we show that a few iterations of PO can significantly improve the model-based controller performance. Our approach offers a cost-effective alternative to PDE control using end-to-end reinforcement learning.

Jonah Botvinick-Greenhouse, Wael H. Ali, Mouhacine Benosman et al.

We introduce adaptive-basis physics-informed neural networks (AB-PINNs), a novel approach to domain decomposition for training PINNs in which existing subdomains dynamically adapt to the intrinsic features of the unknown solution. Drawing inspiration from classical mesh refinement techniques, we also modify the domain decomposition on-the-fly throughout training by introducing new subdomains in regions of high residual loss, thereby providing additional expressive power where the solution of the differential equation is challenging to represent. Our flexible approach to domain decomposition is well-suited for multiscale problems, as different subdomains can learn to capture different scales of the underlying solution. Moreover, the ability to introduce new subdomains during training helps prevent convergence to unwanted local minima and can reduce the need for extensive hyperparameter tuning compared to static domain decomposition approaches. Throughout, we present comprehensive numerical results which demonstrate the effectiveness of AB-PINNs at solving a variety of complex multiscale partial differential equations.

Shounak Sural, Charles Kekeh, Wenliang Liu et al.

Long-horizon motion forecasting for multiple autonomous robots is challenging due to non-linear agent interactions, compounding prediction errors, and continuous-time evolution of dynamics. Learned dynamics of such a system can be useful in various applications such as travel time prediction, prediction-guided planning and generative simulation. In this work, we aim to develop an efficient trajectory forecasting model conditioned on multi-agent goals. Motivated by the recent success of physics-guided deep learning for partially known dynamical systems, we develop a model based on neural Controlled Differential Equations (CDEs) for long-horizon motion forecasting. Unlike discrete-time methods such as RNNs and transformers, neural CDEs operate in continuous time, allowing us to combine physics-informed constraints and biases to jointly model multi-robot dynamics. Our approach, named PINCoDE (Physics-Informed Neural Controlled Differential Equations), learns differential equation parameters that can be used to predict the trajectories of a multi-agent system starting from an initial condition. PINCoDE is conditioned on future goals and enforces physics constraints for robot motion over extended periods of time. We adopt a strategy that scales our model from 10 robots to 100 robots without the need for additional model parameters, while producing predictions with an average ADE below 0.5 m for a 1-minute horizon. Furthermore, progressive training with curriculum learning for our PINCoDE model results in a 2.7X reduction of forecasted pose error over 4 minute horizons compared to analytical models.

Usman A. Khan, Mouhacine Benosman, Wenliang Liu et al.

In this paper, we propose a novel methodology for path planning and scheduling for multi-robot navigation that is based on optimal transport theory and model predictive control. We consider a setup where $N$ robots are tasked to navigate to $M$ targets in a common space with obstacles. Mapping robots to targets first and then planning paths can result in overlapping paths that lead to deadlocks. We derive a strategy based on optimal transport that not only provides minimum cost paths from robots to targets but also guarantees non-overlapping trajectories. We achieve this by discretizing the space of interest into $K$ cells and by imposing a ${K\times K}$ cost structure that describes the cost of transitioning from one cell to another. Optimal transport then provides \textit{optimal and non-overlapping} cell transitions for the robots to reach the targets that can be readily deployed without any scheduling considerations. The proposed solution requires $\unicode{x1D4AA}(K^3\log K)$ computations in the worst-case and $\unicode{x1D4AA}(K^2\log K)$ for well-behaved problems. To further accommodate potentially overlapping trajectories (unavoidable in certain situations) as well as robot dynamics, we show that a temporal structure can be integrated into optimal transport with the help of \textit{replans} and \textit{model predictive control}.

Weidong Cao, Mouhacine Benosman, Xuan Zhang et al.

The design automation of analog circuits is a longstanding challenge in the integrated circuit field. This paper presents a deep reinforcement learning method to expedite the design of analog circuits at the pre-layout stage, where the goal is to find device parameters to fulfill desired circuit specifications. Our approach is inspired by experienced human designers who rely on domain knowledge of analog circuit design (e.g., circuit topology and couplings between circuit specifications) to tackle the problem. Unlike all prior methods, our method originally incorporates such key domain knowledge into policy learning with a graph-based policy network, thereby best modeling the relations between circuit parameters and design targets. Experimental results on exemplary circuits show it achieves human-level design accuracy (~99%) with 1.5x efficiency of existing best-performing methods. Our method also shows better generalization ability to unseen specifications and optimality in circuit performance optimization. Moreover, it applies to designing diverse analog circuits across different semiconductor technologies, breaking the limitations of prior ad-hoc methods in designing one particular type of analog circuits with conventional semiconductor technology.

Reazul Hasan Russel, Mouhacine Benosman, Jeroen Van Baar et al.

Safety and robustness are two desired properties for any reinforcement learning algorithm. CMDPs can handle additional safety constraints and RMDPs can perform well under model uncertainties. In this paper, we propose to unite these two frameworks resulting in robust constrained MDPs (RCMDPs). The motivation is to develop a framework that can satisfy safety constraints while also simultaneously offer robustness to model uncertainties. We develop the RCMDP objective, derive gradient update formula to optimize this objective and then propose policy gradient based algorithms. We also independently propose Lyapunov based reward shaping for RCMDPs, yielding better stability and convergence properties.

Reazul Hasan Russel, Mouhacine Benosman, Jeroen Van Baar

In this paper, we focus on the problem of robustifying reinforcement learning (RL) algorithms with respect to model uncertainties. Indeed, in the framework of model-based RL, we propose to merge the theory of constrained Markov decision process (CMDP), with the theory of robust Markov decision process (RMDP), leading to a formulation of robust constrained-MDPs (RCMDP). This formulation, simple in essence, allows us to design RL algorithms that are robust in performance, and provides constraint satisfaction guarantees, with respect to uncertainties in the system's states transition probabilities. The need for RCMPDs is important for real-life applications of RL. For instance, such formulation can play an important role for policy transfer from simulation to real world (Sim2Real) in safety critical applications, which would benefit from performance and safety guarantees which are robust w.r.t model uncertainty. We first propose the general problem formulation under the concept of RCMDP, and then propose a Lagrangian formulation of the optimal problem, leading to a robust-constrained policy gradient RL algorithm. We finally validate this concept on the inventory management problem.

Siqi Zhang, Mouhacine Benosman, Orlando Romero

In this study, we investigate the performance of two novel first-order optimization algorithms, namely the rescaled-gradient flow (RGF) and the signed-gradient flow (SGF). These algorithms are derived from the forward Euler discretization of finite-time convergent flows, comprised of non-Lipschitz dynamical systems, which locally converge to the minima of gradient-dominated functions. We first characterize the closeness between the continuous flows and the discretizations, then we proceed to present (linear) convergence guarantees of the discrete algorithms (in the general and the stochastic case). Furthermore, in cases where problem parameters remain unknown or exhibit non-uniformity, we further integrate the line-search strategy with RGF/SGF and provide convergence analysis in this setting. We then apply the proposed algorithms to academic examples and deep neural network training, our results show that our schemes demonstrate faster convergences against standard optimization alternatives.

Ankush Chakrabarty, Mouhacine Benosman

Data generated from dynamical systems with unknown dynamics enable the learning of state observers that are: robust to modeling error, computationally tractable to design, and capable of operating with guaranteed performance. In this paper, a modular design methodology is formulated, that consists of three design phases: (i) an initial robust observer design that enables one to learn the dynamics without allowing the state estimation error to diverge (hence, safe); (ii) a learning phase wherein the unmodeled components are estimated using Bayesian optimization and Gaussian processes; and, (iii) a re-design phase that leverages the learned dynamics to improve convergence rate of the state estimation error. The potential of our proposed learning-based observer is demonstrated on a benchmark nonlinear system. Additionally, certificates of guaranteed estimation performance are provided.

Patrik Kolaric, Devesh K. Jha, Arvind U. Raghunathan et al.

The goal of this paper is to present a method for simultaneous trajectory and local stabilizing policy optimization to generate local policies for trajectory-centric model-based reinforcement learning (MBRL). This is motivated by the fact that global policy optimization for non-linear systems could be a very challenging problem both algorithmically and numerically. However, a lot of robotic manipulation tasks are trajectory-centric, and thus do not require a global model or policy. Due to inaccuracies in the learned model estimates, an open-loop trajectory optimization process mostly results in very poor performance when used on the real system. Motivated by these problems, we try to formulate the problem of trajectory optimization and local policy synthesis as a single optimization problem. It is then solved simultaneously as an instance of nonlinear programming. We provide some results for analysis as well as achieved performance of the proposed technique under some simplifying assumptions.

Orlando Romero, Mouhacine Benosman

In this paper, we propose two discontinuous dynamical systems in continuous time with guaranteed prescribed finite-time local convergence to strict local minima of a given cost function. Our approach consists of exploiting a Lyapunov-based differential inequality for differential inclusions, which leads to finite-time stability and thus finite-time convergence with a provable bound on the settling time. In particular, for exact solutions to the aforementioned differential inequality, the settling-time bound is also exact, thus achieving prescribed finite-time convergence. We thus construct a class of discontinuous dynamical systems, of second order with respect to the cost function, that serve as continuous-time optimization algorithms with finite-time convergence and prescribed convergence time. Finally, we illustrate our results on the Rosenbrock function.