Global Convergence of Localized Policy Iteration in Networked Multi-Agent Reinforcement Learning

We study a multi-agent reinforcement learning (MARL) problem where the agents interact over a given network. The goal of the agents is to cooperatively maximize the average of their entropy-regularized long-term rewards. To overcome the curse of dimensionality and to reduce communication, we propose a Localized Policy Iteration (LPI) algorithm that provably learns a near-globally-optimal policy using only local information. In particular, we show that, despite restricting each agent's attention to only its $\kappa$-hop neighborhood, the agents are able to learn a policy with an optimality gap that decays polynomially in $\kappa$. In addition, we show the finite-sample convergence of LPI to the global optimal policy, which explicitly captures the trade-off between optimality and computational complexity in choosing $\kappa$. Numerical simulations demonstrate the effectiveness of LPI.

KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems

Learning a dynamical system requires stabilizing the unknown dynamics to avoid state blow-ups. However, current reinforcement learning (RL) methods lack stabilization guarantees, which limits their applicability for the control of safety-critical systems. We propose a model-based RL framework with formal stability guarantees, Krasovskii Constrained RL (KCRL), that adopts Krasovskii's family of Lyapunov functions as a stability constraint. The proposed method learns the system dynamics up to a confidence interval using feature representation, e.g. Random Fourier Features. It then solves a constrained policy optimization problem with a stability constraint based on Krasovskii's method using a primal-dual approach to recover a stabilizing policy. We show that KCRL is guaranteed to learn a stabilizing policy in a finite number of interactions with the underlying unknown system. We also derive the sample complexity upper bound for stabilization of unknown nonlinear dynamical systems via the KCRL framework.

Equipping Black-Box Policies with Model-Based Advice for Stable Nonlinear Control

Machine-learned black-box policies are ubiquitous for nonlinear control problems. Meanwhile, crude model information is often available for these problems from, e.g., linear approximations of nonlinear dynamics. We study the problem of equipping a black-box control policy with model-based advice for nonlinear control on a single trajectory. We first show a general negative result that a naive convex combination of a black-box policy and a linear model-based policy can lead to instability, even if the two policies are both stabilizing. We then propose an adaptive $\lambda$-confident policy, with a coefficient $\lambda$ indicating the confidence in a black-box policy, and prove its stability. With bounded nonlinearity, in addition, we show that the adaptive $\lambda$-confident policy achieves a bounded competitive ratio when a black-box policy is near-optimal. Finally, we propose an online learning approach to implement the adaptive $\lambda$-confident policy and verify its efficacy in case studies about the CartPole problem and a real-world electric vehicle (EV) charging problem with data bias due to COVID-19.

Near-Optimal Distributed Linear-Quadratic Regulator for Networked Systems

This paper studies the trade-off between the degree of decentralization and the performance of a distributed controller in a linear-quadratic control setting. We study a system of interconnected agents over a graph and a distributed controller, called $\kappa$-distributed control, which lets the agents make control decisions based on the state information within distance $\kappa$ on the underlying graph. This controller can tune its degree of decentralization using the parameter $\kappa$ and thus allows a characterization of the relationship between decentralization and performance. We show that under mild assumptions, including stabilizability, detectability, and a polynomially growing graph condition, the performance difference between $\kappa$-distributed control and centralized optimal control becomes exponentially small in $\kappa$. This result reveals that distributed control can achieve near-optimal performance with a moderate degree of decentralization, and thus it is an effective controller architecture for large-scale networked systems.

Decentralized Graph-Based Multi-Agent Reinforcement Learning Using Reward Machines

In multi-agent reinforcement learning (MARL), it is challenging for a collection of agents to learn complex temporally extended tasks. The difficulties lie in computational complexity and how to learn the high-level ideas behind reward functions. We study the graph-based Markov Decision Process (MDP) where the dynamics of neighboring agents are coupled. We use a reward machine (RM) to encode each agent's task and expose reward function internal structures. RM has the capacity to describe high-level knowledge and encode non-Markovian reward functions. We propose a decentralized learning algorithm to tackle computational complexity, called decentralized graph-based reinforcement learning using reward machines (DGRM), that equips each agent with a localized policy, allowing agents to make decisions independently, based on the information available to the agents. DGRM uses the actor-critic structure, and we introduce the tabular Q-function for discrete state problems. We show that the dependency of Q-function on other agents decreases exponentially as the distance between them increases. Furthermore, the complexity of DGRM is related to the local information size of the largest $\kappa$-hop neighborhood, and DGRM can find an $O(\rho^{\kappa+1})$-approximation of a stationary point of the objective function. To further improve efficiency, we also propose the deep DGRM algorithm, using deep neural networks to approximate the Q-function and policy function to solve large-scale or continuous state problems. The effectiveness of the proposed DGRM algorithm is evaluated by two case studies, UAV package delivery and COVID-19 pandemic mitigation. Experimental results show that local information is sufficient for DGRM and agents can accomplish complex tasks with the help of RM. DGRM improves the global accumulated reward by 119% compared to the baseline in the case of COVID-19 pandemic mitigation.

Stable Online Control of Linear Time-Varying Systems

Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.

Stable Online Control of LTV Systems Stable Online Control of Linear Time-Varying Systems

Linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in control theory. However, existing approaches that guarantee stability typically lead to significantly sub-optimal cumulative control cost in online settings where only current or short-term system information is available. In this work, we propose an efficient online control algorithm, COvariance Constrained Online Linear Quadratic (COCO-LQ) control, that guarantees input-to-state stability for a large class of LTV systems while also minimizing the control cost. The proposed method incorporates a state covariance constraint into the semi-definite programming (SDP) formulation of the LQ optimal controller. We empirically demonstrate the performance of COCO-LQ in both synthetic experiments and a power system frequency control example.

Reinforcement Learning for Decision-Making and Control in Power Systems: Tutorial, Review, and Vision

With large-scale integration of renewable generation and ubiquitous distributed energy resources (DERs), modern power systems confront a series of new challenges in operation and control, such as growing complexity, increasing uncertainty, and aggravating volatility. While the upside is that more and more data are available owing to the widely-deployed smart meters, smart sensors, and upgraded communication networks. As a result, data-driven control techniques, especially reinforcement learning (RL), have attracted surging attention in recent years. In this paper, we focus on RL and aim to provide a tutorial on various RL techniques and how they can be applied to the decision-making and control in power systems. In particular, we select three key applications, including frequency regulation, voltage control, and energy management, for illustration, and present the typical ways to model and tackle them with RL methods. We conclude by emphasizing two critical issues in the application of RL, i.e., safety and scalability. Several potential future directions are discussed as well.