arXiv subjects

Sebastien Gros

Publications and source records attributed to Sebastien Gros.

At least 19 recordsLinked to original sources

arXiv2026

Solving Markov Decision Processes with Future Information via MPC

Model Predictive Control (MPC) is widely used in industrial and robotic systems for enforcing constraints and embedding domain knowledge through finite-horizon optimization-based planning. However, despite these strengths, an MPC scheme typically does not yield optimal policies for sequential decision-making problems formulated as Markov Decision Processes (MDPs). Recent combinations of MPC with Reinforcement Learning (RL) alleviate this issue by treating MPC as a parameterized model of the optimal policy of an MDP and adjusting its parameters using data. While these approaches typically consider classical MDPs, many real-world problems include future information--such as forecasts, prices, or reference trajectories--at decision time, which must be included in the MDP state for optimal decision-making. Current MPC-RL approaches do not directly account for this augmented-state structure, raising the question of how to incorporate future information into MPC to obtain an optimal policy. This work establishes the structural requirements under which a parameterized MPC can exactly represent the optimal value functions and policy of an MDP with future information. We further demonstrate that such a parameterized MPC can serve as a structured function approximator, with its parameters learned using RL. The approach is illustrated on a point-mass racing task with future reference information.

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arXiv2026

MedGym:A Unified Continuous-Time Benchmark for Dynamic Medical Treatment Reinforcement Learning

Medical treatment recommendation poses several challenges to reinforcement learning (RL): patient physiology evolves in continuous time, measurements and interventions are performed at irregular intervals, and treatment effects vary substantially across individuals. Existing RL formulations and simulated environments, however, are based on discrete-time MDP or POMDP abstractions with fixed or pre-specified decision intervals. Thus, it remains difficult to evaluate whether RL methods can handle time-interval-dependent disease progression, personalized treatment response, and safety between consecutive measurement points. To address this gap, we introduce MedGym, a benchmark environment for dynamic treatment recommendation. MedGym models longitudinal patient evolution in a continuous-time framework and constructs a configurable medical RL benchmark from clinical data by using Physics-Informed Neural Networks. The resulting benchmark supports both offline and online RL, and enables direct comparison between discrete-time and continuous-time methods under irregular treatment timing and patient-specific dynamics. Besides, MedGym supports evaluation from clinically important perspectives, including personalization, trajectory-level safety, and the performance gap between model-based offline learning and online deployment. By providing a standardized and configurable benchmark for continuous-time dynamic treatment, MedGym aims to facilitate more realistic and informative evaluation of medical RL methods.

cs.LG↗

arXiv2026

Interaction-Limited Safe Continuous-Time RL for Dynamical Medical Treatment

Dynamic medical treatment requires deciding treatment intensity and intervention timing, while patient states evolve continuously and adverse events may occur between clinical interactions. Most existing treatment learning methods assume fixed schedules or enforce safety only at discrete decision points. We propose Interaction-Limited Safe Continuous-Time Reinforcement Learning, a framework that jointly optimizes treatment administration and clinical interaction timing under trajectory-level safety constraints. Our key idea is to reformulate the continuous time treatment problem as an option-based semi-Markov decision process, where each option specifies a continuous-time treatment policy and its duration. We develop a safety-tightening mechanism showing that suitably constructed constraints at interaction times guarantee safety over the full continuous-time trajectory with high probability. We further establish finite-sample guarantees for policy learning from logged treatment trajectories and introduce a practical data-driven conservative surrogate. Experiments show that the proposed adaptive interaction-timing mechanism improves both safety and treatment effectiveness over equidistant interaction schemes across different safe policy optimization methods.

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arXiv2026

Uncertainty Propagation under Residual Disturbances: A Smart-Home Case Study

This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a single quantity that can be estimated from data. Under mild assumptions, the resulting stochastic predictor is causal and distributionally consistent, enabling efficient uncertainty quantification through polynomial chaos expansions and higher-order Chebyshev inequalities. The proposed method is validated using experimental data from a smart home in Norway.

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arXiv2025

CORL: Reinforcement Learning of MILP Policies Solved via Branch and Bound

Combinatorial sequential decision making problems are typically modeled as mixed integer linear programs (MILPs) and solved via branch and bound (B&B) algorithms. The inherent difficulty of modeling MILPs that accurately represent stochastic real world problems leads to suboptimal performance in the real world. Recently, machine learning methods have been applied to build MILP models for decision quality rather than how accurately they model the real world problem. However, these approaches typically rely on supervised learning, assume access to true optimal decisions, and use surrogates for the MILP gradients. In this work, we introduce a proof of concept CORL framework that end to end fine tunes an MILP scheme using reinforcement learning (RL) on real world data to maximize its operational performance. We enable this by casting an MILP solved by B&B as a differentiable stochastic policy compatible with RL. We validate the CORL method in a simple illustrative combinatorial sequential decision making example.

cs.AI↗

arXiv2025

Sample-Efficient Model-Free Policy Gradient Methods for Stochastic LQR via Robust Linear Regression

Policy gradient algorithms are widely used in reinforcement learning and belong to the class of approximate dynamic programming methods. This paper studies two key policy gradient algorithms, the Natural Policy Gradient and the Gauss-Newton Method, for solving the Linear Quadratic Regulator (LQR) problem in unknown stochastic linear systems. The main challenge lies in obtaining a consistent gradient estimate from noisy data due to errors-in-variables in linear regression. This issue is addressed by employing a primal-dual estimation procedure. Using this novel gradient estimation scheme, the paper establishes convergence guarantees with a sample complexity of order O(1/epsilon). Theoretical results are further supported by numerical experiments, which demonstrate the effectiveness of the proposed algorithms.

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arXiv2025

Quasi-Newton Compatible Actor-Critic for Deterministic Policies

In this paper, we propose a second-order deterministic actor-critic framework in reinforcement learning that extends the classical deterministic policy gradient method to exploit curvature information of the performance function. Building on the concept of compatible function approximation for the critic, we introduce a quadratic critic that simultaneously preserves the true policy gradient and an approximation of the performance Hessian. A least-squares temporal difference learning scheme is then developed to estimate the quadratic critic parameters efficiently. This construction enables a quasi-Newton actor update using information learned by the critic, yielding faster convergence compared to first-order methods. The proposed approach is general and applicable to any differentiable policy class. Numerical examples demonstrate that the method achieves improved convergence and performance over standard deterministic actor-critic baselines.

cs.LG↗

arXiv2025

Bi-Level Reinforcement Learning Pathway for Sim-to-Real Optimality

Training Reinforcement Learning (RL) policies using simulation models before deployment in real-world environments is a common strategy when real-world interaction is expensive. This approach is used in sim-to-real RL and in dyna-style model-based RL. A key limitation of this approach is that the policies trained in simulation often perform poorly in the real world due to discrepancies between the simulation model and the real-world environment, referred to as the sim-to-real gap. This gap reflects the objective mismatch: simulation models are typically constructed for predictive accuracy, whereas policies are trained to maximize task performance. Since the policy learned in simulation is implicitly defined by the simulation parameters, understanding the sensitivity of the learned policy to these parameters enables gradient-based adaptation of the simulation model to improve real-world policy performance. Motivated by this, we derive the sensitivity of locally converged policies trained with Stochastic Policy Gradient (SPG) methods in an actor-critic setting, which is the most widely used approach in RL. Based on this sensitivity analysis, we formulate a bi-level RL approach that can address the objective mismatch problem by learning simulation parameters using gradients of real-world policy performance, thereby directly coupling simulation model adaptation with policy performance. We provide a thorough convergence analysis of the proposed bi-level RL approach and illustrate the concept through a proof-of-concept bi-level PPO algorithm.

cs.LG↗

arXiv2025

Efficient Multi-Objective Constrained Bayesian Optimization of Bridge Girder

The buildings and construction sector is a significant source of greenhouse gas emissions, with cement production alone contributing 7~\% of global emissions and the industry as a whole accounting for approximately 37~\%. Reducing emissions by optimizing structural design can achieve significant global benefits. This article introduces an efficient multi-objective constrained Bayesian optimization approach to address this challenge. Rather than attempting to determine the full set of non-dominated solutions with arbitrary trade-offs, the approach searches for a solution matching a specified trade-off. Structural design is typically conducted using computationally expensive finite element simulations, whereas Bayesian optimization offers an efficient approach for optimizing problems that involve such high-cost simulations. The proposed method integrates proper orthogonal decomposition for dimensionality reduction of simulation results with Kriging partial least squares to enhance efficiency. Constrained expected improvement is used as an acquisition function for Bayesian optimization. The approach is demonstrated through a case study of a two-lane, three-span post-tensioned concrete bridge girder, incorporating fifteen design variables and nine constraints. A comparison with conventional design methods demonstrates the potential of this optimization approach to achieve substantial cost reductions, with savings of approximately 10\% to 15\% in financial costs and about 20\% in environmental costs for the case study, while ensuring structural integrity.

cs.CE↗

arXiv2025

Safe Reinforcement Learning using Action Projection: Safeguard the Policy or the Environment?

Projection-based safety filters, which modify unsafe actions by mapping them to the closest safe alternative, are widely used to enforce safety constraints in reinforcement learning (RL). Two integration strategies are commonly considered: Safe environment RL (SE-RL), where the safeguard is treated as part of the environment, and safe policy RL (SP-RL), where it is embedded within the policy through differentiable optimization layers. Despite their practical relevance in safety-critical settings, a formal understanding of their differences is lacking. In this work, we present a theoretical comparison of SE-RL and SP-RL. We identify a key distinction in how each approach is affected by action aliasing, a phenomenon in which multiple unsafe actions are projected to the same safe action, causing information loss in the policy gradients. In SE-RL, this effect is implicitly approximated by the critic, while in SP-RL, it manifests directly as rank-deficient Jacobians during backpropagation through the safeguard. Our contributions are threefold: (i) a unified formalization of SE-RL and SP-RL in the context of actor-critic algorithms, (ii) a theoretical analysis of their respective policy gradient estimates, highlighting the role of action aliasing, and (iii) a comparative study of mitigation strategies, including a novel penalty-based improvement for SP-RL that aligns with established SE-RL practices. Empirical results support our theoretical predictions, showing that action aliasing is more detrimental for SP-RL than for SE-RL. However, with appropriate improvement strategies, SP-RL can match or outperform improved SE-RL across a range of environments. These findings provide actionable insights for choosing and refining projection-based safe RL methods based on task characteristics.

cs.LG↗

arXiv2025

Computationally efficient Gauss-Newton reinforcement learning for model predictive control

Model predictive control (MPC) is widely used in process control due to its interpretability and ability to handle constraints. As a parametric policy in reinforcement learning (RL), MPC offers strong initial performance and low data requirements compared to black-box policies like neural networks. However, most RL methods rely on first-order updates, which scale well to large parameter spaces but converge at most linearly, making them inefficient when each policy update requires solving an optimal control problem, as is the case with MPC. While MPC policies are typically low parameterized and thus amenable to second-order approaches, existing second-order methods demand second-order policy derivatives, which can be computationally intractable. This work introduces a Gauss-Newton approximation of the deterministic policy Hessian that eliminates the need for second-order policy derivatives, enabling superlinear convergence with minimal computational overhead. To further improve robustness, we propose a momentum-based Hessian averaging scheme for stable training under noisy estimates coupled with an adaptive trustregion. We demonstrate the effectiveness of the approach on a nonlinear continuously stirred tank reactor (CSTR), showing faster convergence and improved data efficiency over state-of-the-art firstorder methods and deep RL approaches.

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arXiv2025

Mission-Aligned Learning-Informed Control of Autonomous Systems: Formulation and Foundations

Research, innovation and practical capital investment have been increasing rapidly toward the realization of autonomous physical agents. This includes industrial and service robots, unmanned aerial vehicles, embedded control devices, and a number of other realizations of cybernetic/mechatronic implementations of intelligent autonomous devices. In this paper, we consider a stylized version of robotic care, which would normally involve a two-level Reinforcement Learning procedure that trains a policy for both lower level physical movement decisions as well as higher level conceptual tasks and their sub-components. In order to deliver greater safety and reliability in the system, we present the general formulation of this as a two-level optimization scheme which incorporates control at the lower level, and classical planning at the higher level, integrated with a capacity for learning. This synergistic integration of multiple methodologies -- control, classical planning, and RL -- presents an opportunity for greater insight for algorithm development, leading to more efficient and reliable performance. Here, the notion of reliability pertains to physical safety and interpretability into an otherwise black box operation of autonomous agents, concerning users and regulators. This work presents the necessary background and general formulation of the optimization framework, detailing each component and its integration with the others.

math.OC↗

arXiv2025

Offline Guarded Safe Reinforcement Learning for Medical Treatment Optimization Strategies

When applying offline reinforcement learning (RL) in healthcare scenarios, the out-of-distribution (OOD) issues pose significant risks, as inappropriate generalization beyond clinical expertise can result in potentially harmful recommendations. While existing methods like conservative Q-learning (CQL) attempt to address the OOD issue, their effectiveness is limited by only constraining action selection by suppressing uncertain actions. This action-only regularization imitates clinician actions that prioritize short-term rewards, but it fails to regulate downstream state trajectories, thereby limiting the discovery of improved long-term treatment strategies. To safely improve policy beyond clinician recommendations while ensuring that state-action trajectories remain in-distribution, we propose \textit{Offline Guarded Safe Reinforcement Learning} ($\mathsf{OGSRL}$), a theoretically grounded model-based offline RL framework. $\mathsf{OGSRL}$ introduces a novel dual constraint mechanism for improving policy with reliability and safety. First, the OOD guardian is established to specify clinically validated regions for safe policy exploration. By constraining optimization within these regions, it enables the reliable exploration of treatment strategies that outperform clinician behavior by leveraging the full patient state history, without drifting into unsupported state-action trajectories. Second, we introduce a safety cost constraint that encodes medical knowledge about physiological safety boundaries, providing domain-specific safeguards even in areas where training data might contain potentially unsafe interventions. Notably, we provide theoretical guarantees on safety and near-optimality: policies that satisfy these constraints remain in safe and reliable regions and achieve performance close to the best possible policy supported by the data.

cs.LG↗

arXiv2025

Differentiable Nonlinear Model Predictive Control

The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms. This paper discusses the computation of solution sensitivities of general nonlinear programs (NLPs) using the implicit function theorem (IFT) and smoothed optimality conditions treated in interior-point methods (IPM). We detail sensitivity computation within a sequential quadratic programming (SQP) method which employs an IPM for the quadratic subproblems. Previous works presented in the machine learning community are limited to convex or unconstrained formulations, or lack an implementation for efficient sensitivity evaluation. The publication is accompanied by an efficient open-source implementation within the acados framework, providing both forward and adjoint sensitivities for general optimal control problems, achieving speedups exceeding 3x over the state-of-the-art solvers mpc.pytorch and cvxpygen.

math.OC↗

arXiv2025

Data-Driven Distributionally Robust Control for Interacting Agents under Logical Constraints

In this paper, we propose a distributionally robust control synthesis for an agent with stochastic dynamics that interacts with other agents under uncertainties and constraints expressed by signal temporal logic (STL). We formulate the control synthesis as a chance-constrained program (CCP) with STL specifications that must be satisfied with high probability under all uncertainty tubes induced by the other agents. To tackle the CCP, we propose two methods based on concentration of measure (CoM) theory and conditional value at risk (CVaR) and compare the required assumptions and resulting optimizations. These approaches convert the CCP into an expectation-constrained program (ECP), which is simpler to solve than the original CCP. To estimate the expectation using a finite set of observed data, we adopt a distributionally robust optimization (DRO) approach. The underlying DRO can be approximated as a robust data-driven optimization that provides a probabilistic under-approximation to the original ECP, where the probability depends on the number of samples. Therefore, under feasibility, the original STL constraints are satisfied with two layers of designed confidence: the confidence of the chance constraint and the confidence of the approximated data-driven optimization, which depends on the number of samples. We then provide details on solving the resulting robust data-driven optimization numerically. Finally, we compare the two proposed approaches through case studies.

eess.SY↗

arXiv2025

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.

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arXiv2025

Optimization-based Coordination of Traffic Lights and Automated Vehicles at Intersections

This paper tackles the challenge of coordinating traffic lights and automated vehicles at signalized intersections, formulated as a constrained finite-horizon optimal control problem. The problem falls into the category of mixed-integer nonlinear programming, posing challenges for solving large instances. To address this, we introduce a decomposition approach consisting of an upper-level problem for traffic light timing allocation and a set of lower-level problems that generate appropriate commands for automated vehicles in each intersection movement. By leveraging solutions from the lower-level problems and employing parametric optimization techniques, we solve the upper-level problem using a standard sequential quadratic programming approach. The paper concludes by presenting an illustrative numerical example that highlights the effectiveness of our algorithm compared to scenarios where no coordination between traffic lights and vehicles exists.

math.OC↗

arXiv2025

MPC4RL -- A Software Package for Reinforcement Learning based on Model Predictive Control

In this paper, we present an early software integrating Reinforcement Learning (RL) with Model Predictive Control (MPC). Our aim is to make recent theoretical contributions from the literature more accessible to both the RL and MPC communities. We combine standard software tools developed by the RL community, such as Gymnasium, stable-baselines3, or CleanRL with the acados toolbox, a widely-used software package for efficient MPC algorithms. Our core contribution is MPC4RL, an open-source Python package that supports learning-enhanced MPC schemes for existing acados implementations. The package is designed to be modular, extensible, and user-friendly, facilitating the tuning of MPC algorithms for a broad range of control problems. It is available on GitHub.

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