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Thompson Sampling for Linear-Quadratic Control Problems
We consider the exploration-exploitation tradeoff in linear quadratic (L...
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Finite Time Analysis of Optimal Adaptive Policies for Linear-Quadratic Systems
We consider the classical problem of control of linear systems with quad...
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Robust Learning-Based Control via Bootstrapped Multiplicative Noise
Despite decades of research and recent progress in adaptive control and ...
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Optimistic Agents are Asymptotically Optimal
We use optimism to introduce generic asymptotically optimal reinforcemen...
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Finite-Sample Analyses for Fully Decentralized Multi-Agent Reinforcement Learning
Despite the increasing interest in multi-agent reinforcement learning (M...
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A Tour of Reinforcement Learning: The View from Continuous Control
This manuscript surveys reinforcement learning from the perspective of o...
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Input Perturbations for Adaptive Regulation and Learning
Design of adaptive algorithms for simultaneous regulation and estimation...
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Exact Asymptotics for Linear Quadratic Adaptive Control
Recent progress in reinforcement learning has led to remarkable performance in a range of applications, but its deployment in high-stakes settings remains quite rare. One reason is a limited understanding of the behavior of reinforcement algorithms, both in terms of their regret and their ability to learn the underlying system dynamics—existing work is focused almost exclusively on characterizing rates, with little attention paid to the constants multiplying those rates that can be critically important in practice. To start to address this challenge, we study perhaps the simplest non-bandit reinforcement learning problem: linear quadratic adaptive control (LQAC). By carefully combining recent finite-sample performance bounds for the LQAC problem with a particular (less-recent) martingale central limit theorem, we are able to derive asymptotically-exact expressions for the regret, estimation error, and prediction error of a rate-optimal stepwise-updating LQAC algorithm. In simulations on both stable and unstable systems, we find that our asymptotic theory also describes the algorithm's finite-sample behavior remarkably well.
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