arXiv subjects

Santiago Paternain

Publications and source records attributed to Santiago Paternain.

At least 37 records · Page 2Linked to original sources

arXiv2024

RL for Mitigating Cascading Failures: Targeted Exploration via Sensitivity Factors

Electricity grid's resiliency and climate change strongly impact one another due to an array of technical and policy-related decisions that impact both. This paper introduces a physics-informed machine learning-based framework to enhance grid's resiliency. Specifically, when encountering disruptive events, this paper designs remedial control actions to prevent blackouts. The proposed Physics-Guided Reinforcement Learning (PG-RL) framework determines effective real-time remedial line-switching actions, considering their impact on power balance, system security, and grid reliability. To identify an effective blackout mitigation policy, PG-RL leverages power-flow sensitivity factors to guide the RL exploration during agent training. Comprehensive evaluations using the Grid2Op platform demonstrate that incorporating physical signals into RL significantly improves resource utilization within electric grids and achieves better blackout mitigation policies - both of which are critical in addressing climate change.

cs.LG↗

arXiv2024

Transfer Learning for a Class of Cascade Dynamical Systems

This work considers the problem of transfer learning in the context of reinforcement learning. Specifically, we consider training a policy in a reduced order system and deploying it in the full state system. The motivation for this training strategy is that running simulations in the full-state system may take excessive time if the dynamics are complex. While transfer learning alleviates the computational issue, the transfer guarantees depend on the discrepancy between the two systems. In this work, we consider a class of cascade dynamical systems, where the dynamics of a subset of the state-space influence the rest of the states but not vice-versa. The reinforcement learning policy learns in a model that ignores the dynamics of these states and treats them as commanded inputs. In the full-state system, these dynamics are handled using a classic controller (e.g., a PID). These systems have vast applications in the control literature and their structure allows us to provide transfer guarantees that depend on the stability of the inner loop controller. Numerical experiments on a quadrotor support the theoretical findings.

cs.LG↗

arXiv2024

Data-driven Under Frequency Load Shedding Using Reinforcement Learning

Underfrequency load shedding (UFLS) is a critical control strategy in power systems aimed at maintaining system stability and preventing blackouts during severe frequency drops. Traditional UFLS schemes often rely on predefined rules and thresholds, which may not adapt effectively to the dynamic and complex nature of modern power grids. Reinforcement learning (RL) methods have been proposed to effectively handle the UFLS problem. However, training these RL agents is computationally burdensome due to solving multiple differential equations at each step of training. This computational burden also limits the effectiveness of the RL agents for use in real-time. To reduce the computational burden, a machine learning (ML) classifier is trained to capture the frequency response of the system to various disturbances. The RL agent is then trained using the classifier, thus avoiding multiple computations during each step of agent training. Key features of this approach include reduced training time, as well as faster real-time application compared to other RL agents, and its potential to improve system resilience by minimizing the amount of load shed while effectively stabilizing the frequency. Comparative studies with conventional UFLS schemes demonstrate that the RL-based strategy achieves superior performance while significantly reducing the time required. Simulation results on the IEEE 68-bus system validate the performance of the proposed RL method.

eess.SY↗

arXiv2024

Fast and Accurate Relative Motion Tracking for Dual Industrial Robots

Industrial robotic applications such as spraying, welding, and additive manufacturing frequently require fast, accurate, and uniform motion along a 3D spatial curve. To increase process throughput, some manufacturers propose a dual-robot setup to overcome the speed limitation of a single robot. Industrial robot motion is programmed through waypoints connected by motion primitives (Cartesian linear and circular paths and linear joint paths at constant Cartesian speed). The actual robot motion is affected by the blending between these motion primitives and the pose of the robot (an outstretched/near-singularity pose tends to have larger path tracking errors). Choosing the waypoints and the speed along each motion segment to achieve the performance requirement is challenging. At present, there is no automated solution, and laborious manual tuning by robot experts is needed to approach the desired performance. In this paper, we present a systematic three-step approach to designing and programming a dual robot system to optimize system performance. The first step is to select the relative placement between the two robots based on the specified relative motion path. The second step is to select the relative waypoints and the motion primitives. The final step is to update the waypoints iteratively based on the actual measured relative motion. Waypoint iteration is first executed in simulation and then completed using the actual robots. For performance assessment, we use the mean path speed subject to the relative position and orientation constraints and the path speed uniformity constraint. We have demonstrated the effectiveness of this method on two systems, a physical testbed of two ABB robots and a simulation testbed of two FANUC robots, for two challenging test curves.

cs.RO↗

arXiv2024

Blackout Mitigation via Physics-guided RL

This paper considers the sequential design of remedial control actions in response to system anomalies for the ultimate objective of preventing blackouts. A physics-guided reinforcement learning (RL) framework is designed to identify effective sequences of real-time remedial look-ahead decisions accounting for the long-term impact on the system's stability. The paper considers a space of control actions that involve both discrete-valued transmission line-switching decisions (line reconnections and removals) and continuous-valued generator adjustments. To identify an effective blackout mitigation policy, a physics-guided approach is designed that uses power-flow sensitivity factors associated with the power transmission network to guide the RL exploration during agent training. Comprehensive empirical evaluations using the open-source Grid2Op platform demonstrate the notable advantages of incorporating physical signals into RL decisions, establishing the gains of the proposed physics-guided approach compared to its black box counterparts. One important observation is that strategically~\emph{removing} transmission lines, in conjunction with multiple real-time generator adjustments, often renders effective long-term decisions that are likely to prevent or delay blackouts.

eess.SY↗

arXiv2024

Real-Time Small-Signal Security Assessment Using Graph Neural Networks

Security assessment is one of the most crucial functions of a power system operator. However, growing complexity and unpredictability make this an increasingly complex and computationally difficult task. In recent times, machine learning methods have gained attention for their ability to handle complex modeling applications. Some methods proposed include deep learning using convolutional neural networks, decision trees, etc. While these methods generate promising results, most methods still require long training times and computational resources. This paper proposes a graph neural network (GNN) approach to the small-signal security assessment problem using data from Phasor Measurement Units (PMUs). Leveraging the inherently graphical structure of the power grid using GNNs, training times can be reduced and efficiency improved for real-time application. Also, using graph properties, optimal PMU placement is determined and the proposed method is shown to perform efficiently under partial observability with limited PMU data. Case studies with simulated data from the IEEE 68-bus system and the NPCC 140-bus system are used to verify the effectiveness of the proposed method.

eess.SY↗

arXiv2024

Multi-agent assignment via state augmented reinforcement learning

We address the conflicting requirements of a multi-agent assignment problem through constrained reinforcement learning, emphasizing the inadequacy of standard regularization techniques for this purpose. Instead, we recur to a state augmentation approach in which the oscillation of dual variables is exploited by agents to alternate between tasks. In addition, we coordinate the actions of the multiple agents acting on their local states through these multipliers, which are gossiped through a communication network, eliminating the need to access other agent states. By these means, we propose a distributed multi-agent assignment protocol with theoretical feasibility guarantees that we corroborate in a monitoring numerical experiment.

eess.SY↗

arXiv2024

Tensor and Matrix Low-Rank Value-Function Approximation in Reinforcement Learning

Value-function (VF) approximation is a central problem in Reinforcement Learning (RL). Classical non-parametric VF estimation suffers from the curse of dimensionality. As a result, parsimonious parametric models have been adopted to approximate VFs in high-dimensional spaces, with most efforts being focused on linear and neural-network-based approaches. Differently, this paper puts forth a a parsimonious non-parametric approach, where we use stochastic low-rank algorithms to estimate the VF matrix in an online and model-free fashion. Furthermore, as VFs tend to be multi-dimensional, we propose replacing the classical VF matrix representation with a tensor (multi-way array) representation and, then, use the PARAFAC decomposition to design an online model-free tensor low-rank algorithm. Different versions of the algorithms are proposed, their complexity is analyzed, and their performance is assessed numerically using standardized RL environments.

cs.LG↗

arXiv2024

Probabilistic Constraint for Safety-Critical Reinforcement Learning

In this paper, we consider the problem of learning safe policies for probabilistic-constrained reinforcement learning (RL). Specifically, a safe policy or controller is one that, with high probability, maintains the trajectory of the agent in a given safe set. We establish a connection between this probabilistic-constrained setting and the cumulative-constrained formulation that is frequently explored in the existing literature. We provide theoretical bounds elucidating that the probabilistic-constrained setting offers a better trade-off in terms of optimality and safety (constraint satisfaction). The challenge encountered when dealing with the probabilistic constraints, as explored in this work, arises from the absence of explicit expressions for their gradients. Our prior work provides such an explicit gradient expression for probabilistic constraints which we term Safe Policy Gradient-REINFORCE (SPG-REINFORCE). In this work, we provide an improved gradient SPG-Actor-Critic that leads to a lower variance than SPG-REINFORCE, which is substantiated by our theoretical results. A noteworthy aspect of both SPGs is their inherent algorithm independence, rendering them versatile for application across a range of policy-based algorithms. Furthermore, we propose a Safe Primal-Dual algorithm that can leverage both SPGs to learn safe policies. It is subsequently followed by theoretical analyses that encompass the convergence of the algorithm, as well as the near-optimality and feasibility on average. In addition, we test the proposed approaches by a series of empirical experiments. These experiments aim to examine and analyze the inherent trade-offs between the optimality and safety, and serve to substantiate the efficacy of two SPGs, as well as our theoretical contributions.

cs.LG↗

arXiv2024

Adaptive Primal-Dual Method for Safe Reinforcement Learning

Primal-dual methods have a natural application in Safe Reinforcement Learning (SRL), posed as a constrained policy optimization problem. In practice however, applying primal-dual methods to SRL is challenging, due to the inter-dependency of the learning rate (LR) and Lagrangian multipliers (dual variables) each time an embedded unconstrained RL problem is solved. In this paper, we propose, analyze and evaluate adaptive primal-dual (APD) methods for SRL, where two adaptive LRs are adjusted to the Lagrangian multipliers so as to optimize the policy in each iteration. We theoretically establish the convergence, optimality and feasibility of the APD algorithm. Finally, we conduct numerical evaluation of the practical APD algorithm with four well-known environments in Bullet-Safey-Gym employing two state-of-the-art SRL algorithms: PPO-Lagrangian and DDPG-Lagrangian. All experiments show that the practical APD algorithm outperforms (or achieves comparable performance) and attains more stable training than the constant LR cases. Additionally, we substantiate the robustness of selecting the two adaptive LRs by empirical evidence.

cs.LG↗

arXiv2024

Learning Non-myopic Power Allocation in Constrained Scenarios

We propose a learning-based framework for efficient power allocation in ad hoc interference networks under episodic constraints. The problem of optimal power allocation -- for maximizing a given network utility metric -- under instantaneous constraints has recently gained significant popularity. Several learnable algorithms have been proposed to obtain fast, effective, and near-optimal performance. However, a more realistic scenario arises when the utility metric has to be optimized for an entire episode under time-coupled constraints. In this case, the instantaneous power needs to be regulated so that the given utility can be optimized over an entire sequence of wireless network realizations while satisfying the constraint at all times. Solving each instance independently will be myopic as the long-term constraint cannot modulate such a solution. Instead, we frame this as a constrained and sequential decision-making problem, and employ an actor-critic algorithm to obtain the constraint-aware power allocation at each step. We present experimental analyses to illustrate the effectiveness of our method in terms of superior episodic network-utility performance and its efficiency in terms of time and computational complexity.

eess.SP↗

arXiv2023

State Augmented Constrained Reinforcement Learning: Overcoming the Limitations of Learning with Rewards

A common formulation of constrained reinforcement learning involves multiple rewards that must individually accumulate to given thresholds. In this class of problems, we show a simple example in which the desired optimal policy cannot be induced by any weighted linear combination of rewards. Hence, there exist constrained reinforcement learning problems for which neither regularized nor classical primal-dual methods yield optimal policies. This work addresses this shortcoming by augmenting the state with Lagrange multipliers and reinterpreting primal-dual methods as the portion of the dynamics that drives the multipliers evolution. This approach provides a systematic state augmentation procedure that is guaranteed to solve reinforcement learning problems with constraints. Thus, as we illustrate by an example, while previous methods can fail at finding optimal policies, running the dual dynamics while executing the augmented policy yields an algorithm that provably samples actions from the optimal policy.

cs.LG↗

arXiv2023

Policy Gradients for Probabilistic Constrained Reinforcement Learning

This paper considers the problem of learning safe policies in the context of reinforcement learning (RL). In particular, we consider the notion of probabilistic safety. This is, we aim to design policies that maintain the state of the system in a safe set with high probability. This notion differs from cumulative constraints often considered in the literature. The challenge of working with probabilistic safety is the lack of expressions for their gradients. Indeed, policy optimization algorithms rely on gradients of the objective function and the constraints. To the best of our knowledge, this work is the first one providing such explicit gradient expressions for probabilistic constraints. It is worth noting that the gradient of this family of constraints can be applied to various policy-based algorithms. We demonstrate empirically that it is possible to handle probabilistic constraints in a continuous navigation problem.

cs.LG↗

arXiv2022

Constrained Learning with Non-Convex Losses

Though learning has become a core component of modern information processing, there is now ample evidence that it can lead to biased, unsafe, and prejudiced systems. The need to impose requirements on learning is therefore paramount, especially as it reaches critical applications in social, industrial, and medical domains. However, the non-convexity of most modern statistical problems is only exacerbated by the introduction of constraints. Whereas good unconstrained solutions can often be learned using empirical risk minimization, even obtaining a model that satisfies statistical constraints can be challenging. All the more so, a good one. In this paper, we overcome this issue by learning in the empirical dual domain, where constrained statistical learning problems become unconstrained and deterministic. We analyze the generalization properties of this approach by bounding the empirical duality gap -- i.e., the difference between our approximate, tractable solution and the solution of the original (non-convex) statistical problem -- and provide a practical constrained learning algorithm. These results establish a constrained counterpart to classical learning theory, enabling the explicit use of constraints in learning. We illustrate this theory and algorithm in rate-constrained learning applications arising in fairness and adversarial robustness.

cs.LG↗

arXiv2022

Navigation of a Quadratic Potential with Ellipsoidal Obstacles

Given a convex quadratic potential of which its minimum is the agent's goal and a Euclidean space populated with ellipsoidal obstacles, one can construct a Rimon-Koditschek (RK) artificial potential to navigate. Its negative gradient attracts the agent toward the goal and repels the agent away from the boundary of the obstacles. This is a popular approach to navigation problems since it can be implemented with local spatial information that is acquired during operation time. However, navigation is only successful in situations where the obstacles are not too eccentric (flat). This paper proposes a modification to gradient dynamics that allows successful navigation of an environment with a quadratic cost and ellipsoidal obstacles regardless of their eccentricity. This is accomplished by altering gradient dynamics with a Hessian correction that is intended to imitate worlds with spherical obstacles in which RK potentials are known to work. The resulting dynamics simplify by the quadratic form of the obstacles. Convergence to the goal and obstacle avoidance is established from almost every initial position (up to a set of measure one) in the free space, with mild conditions on the location of the target. Results are corroborated empirically with numerical simulations.

math.OC↗

arXiv2022

Safe Policies for Reinforcement Learning via Primal-Dual Methods

In this paper, we study the learning of safe policies in the setting of reinforcement learning problems. This is, we aim to control a Markov Decision Process (MDP) of which we do not know the transition probabilities, but we have access to sample trajectories through experience. We define safety as the agent remaining in a desired safe set with high probability during the operation time. We therefore consider a constrained MDP where the constraints are probabilistic. Since there is no straightforward way to optimize the policy with respect to the probabilistic constraint in a reinforcement learning framework, we propose an ergodic relaxation of the problem. The advantages of the proposed relaxation are threefold. (i) The safety guarantees are maintained in the case of episodic tasks and they are kept up to a given time horizon for continuing tasks. (ii) The constrained optimization problem despite its non-convexity has arbitrarily small duality gap if the parametrization of the policy is rich enough. (iii) The gradients of the Lagrangian associated with the safe-learning problem can be easily computed using standard policy gradient results and stochastic approximation tools. Leveraging these advantages, we establish that primal-dual algorithms are able to find policies that are safe and optimal. We test the proposed approach in a navigation task in a continuous domain. The numerical results show that our algorithm is capable of dynamically adapting the policy to the environment and the required safety levels.

eess.SY↗

arXiv2021

Towards Safe Continuing Task Reinforcement Learning

Safety is a critical feature of controller design for physical systems. When designing control policies, several approaches to guarantee this aspect of autonomy have been proposed, such as robust controllers or control barrier functions. However, these solutions strongly rely on the model of the system being available to the designer. As a parallel development, reinforcement learning provides model-agnostic control solutions but in general, it lacks the theoretical guarantees required for safety. Recent advances show that under mild conditions, control policies can be learned via reinforcement learning, which can be guaranteed to be safe by imposing these requirements as constraints of an optimization problem. However, to transfer from learning safety to learning safely, there are two hurdles that need to be overcome: (i) it has to be possible to learn the policy without having to re-initialize the system; and (ii) the rollouts of the system need to be in themselves safe. In this paper, we tackle the first issue, proposing an algorithm capable of operating in the continuing task setting without the need of restarts. We evaluate our approach in a numerical example, which shows the capabilities of the proposed approach in learning safe policies via safe exploration.

cs.LG↗

arXiv2021

Sufficiently Accurate Model Learning for Planning

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions. This can be improved using prior knowledge about the task at hand, which can be encoded in the form of constraints. This turns the unconstrained model learning problem into a constrained one. These constraints allow models with finite capacity to focus their expressive power on important aspects of the system. This can lead to models that are better suited for certain tasks. This paper introduces the constrained Sufficiently Accurate model learning approach, provides examples of such problems, and presents a theorem on how close some approximate solutions can be. The approximate solution quality will depend on the function parameterization, loss and constraint function smoothness, and the number of samples in model learning.

cs.AI↗