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.Preprint. Under review.
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 κ-hop neighborhood, the agents are able to learn a policy with an optimality gap that decays polynomially in κ. 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 κ. Numerical simulations demonstrate the effectiveness of LPI.
We study a variant of online optimization in which the learner receives 𝑘-round 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 nonlinear 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 constantcompetitive online policies. This extended abstract is an abridged version of [2]. CCS CONCEPTS• Computing methodologies → Online learning settings.
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 certifying a black-box control policy with stability using 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 λ-confident policy, with a coefficient λ indicating the confidence in a black-box policy, and prove its stability. With bounded nonlinearity, in addition, we show that the adaptive λ-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 λ-confident policy and verify its efficacy in case studies about the Cart-Pole problem and a real-world electric vehicle (EV) charging problem with covariate shift due to COVID-19.INDEX TERMS black-box policy, stability, nonlinear control, covariate shift
We study a variant of online optimization in which the learner receives k-rounddelayed 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.
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