Approximate Global Convergence of Independent Learning in Multi-Agent Systems

Independent learning (IL), despite being a popular approach in practice to achieve scalability in large-scale multi-agent systems, usually lacks global convergence guarantees. In this paper, we study two representative algorithms, independent $Q$-learning and independent natural actor-critic, within value-based and policy-based frameworks, and provide the first finite-sample analysis for approximate global convergence. The results imply a sample complexity of $\tilde{\mathcal{O}}(\epsilon^{-2})$ up to an error term that captures the dependence among agents and characterizes the fundamental limit of IL in achieving global convergence. To establish the result, we develop a novel approach for analyzing IL by constructing a separable Markov decision process (MDP) for convergence analysis and then bounding the gap due to model difference between the separable MDP and the original one. Moreover, we conduct numerical experiments using a synthetic MDP and an electric vehicle charging example to verify our theoretical findings and to demonstrate the practical applicability of IL.

Diffusion for Natural Image Matting

We aim to leverage diffusion to address the challenging image matting task. However, the presence of high computational overhead and the inconsistency of noise sampling between the training and inference processes pose significant obstacles to achieving this goal. In this paper, we present DiffMatte, a solution designed to effectively overcome these challenges. First, DiffMatte decouples the decoder from the intricately coupled matting network design, involving only one lightweight decoder in the iterations of the diffusion process. With such a strategy, DiffMatte mitigates the growth of computational overhead as the number of samples increases. Second, we employ a self-aligned training strategy with uniform time intervals, ensuring a consistent noise sampling between training and inference across the entire time domain. Our DiffMatte is designed with flexibility in mind and can seamlessly integrate into various modern matting architectures. Extensive experimental results demonstrate that DiffMatte not only reaches the state-of-the-art level on the Composition-1k test set, surpassing the best methods in the past by 5% and 15% in the SAD metric and MSE metric respectively, but also show stronger generalization ability in other benchmarks.

Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictions

We study the tradeoff between consistency and robustness in the context of a single-trajectory time-varying Markov Decision Process (MDP) with untrusted machine-learned advice. Our work departs from the typical approach of treating advice as coming from black-box sources by instead considering a setting where additional information about how the advice is generated is available. We prove a first-of-its-kind consistency and robustness tradeoff given Q-value advice under a general MDP model that includes both continuous and discrete state/action spaces. Our results highlight that utilizing Q-value advice enables dynamic pursuit of the better of machine-learned advice and a robust baseline, thus result in near-optimal performance guarantees, which provably improves what can be obtained solely with black-box advice.

Convergence Rates for Localized Actor-Critic in Networked Markov Potential Games

We introduce a class of networked Markov potential games where agents are associated with nodes in a network. Each agent has its own local potential function, and the reward of each agent depends only on the states and actions of agents within a $\kappa$-hop neighborhood. In this context, we propose a localized actor-critic algorithm. The algorithm is scalable since each agent uses only local information and does not need access to the global state. Further, the algorithm overcomes the curse of dimensionality through the use of function approximation. Our main results provide finite-sample guarantees up to a localization error and a function approximation error. Specifically, we achieve an $\tilde{\mathcal{O}}(\epsilon^{-4})$ sample complexity measured by the averaged Nash regret. This is the first finite-sample bound for multi-agent competitive games that does not depend on the number of agents.

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.

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.

Online Optimization with Feedback Delay and Nonlinear Switching Cost

We study a variant of online optimization in which the learner receives $k$-round $\textit{delayed feedback}$ about hitting cost and there is a multi-step nonlinear switching cost, i.e., costs depend on multiple previous actions in a nonlinear manner. Our main result shows that a novel Iterative Regularized Online Balanced Descent (iROBD) algorithm has a constant, dimension-free competitive ratio that is $O(L^{2k})$, where $L$ is the Lipschitz constant of the switching cost. Additionally, we provide lower bounds that illustrate the Lipschitz condition is required and the dependencies on $k$ and $L$ are tight. Finally, via reductions, we show that this setting is closely related to online control problems with delay, nonlinear dynamics, and adversarial disturbances, where iROBD directly offers constant-competitive online policies.

Scalable Multi-Agent Reinforcement Learning for Networked Systems with Average Reward

It has long been recognized that multi-agent reinforcement learning (MARL) faces significant scalability issues due to the fact that the size of the state and action spaces are exponentially large in the number of agents. In this paper, we identify a rich class of networked MARL problems where the model exhibits a local dependence structure that allows it to be solved in a scalable manner. Specifically, we propose a Scalable Actor-Critic (SAC) method that can learn a near optimal localized policy for optimizing the average reward with complexity scaling with the state-action space size of local neighborhoods, as opposed to the entire network. Our result centers around identifying and exploiting an exponential decay property that ensures the effect of agents on each other decays exponentially fast in their graph distance.

Distributed Reinforcement Learning in Multi-Agent Networked Systems

We study distributed reinforcement learning (RL) for a network of agents. The objective is to find localized policies that maximize the (discounted) global reward. In general, scalability is a challenge in this setting because the size of the global state/action space can be exponential in the number of agents. Scalable algorithms are only known in cases where dependencies are local, e.g., between neighbors. In this work, we propose a Scalable Actor Critic framework that applies in settings where the dependencies are non-local and provide a finite-time error bound that shows how the convergence rate depends on the depth of the dependencies in the network. Additionally, as a byproduct of our analysis, we obtain novel finite-time convergence results for a general stochastic approximation scheme and for temporal difference learning with state aggregation that apply beyond the setting of RL in networked systems.