Optimism-Based Adaptive Regulation of Linear-Quadratic Systems

The main challenge for adaptive regulation of linear-quadratic systems is the tradeoff between identification and control. An policy needs to address both estimation unknown dynamics parameters (exploration), as well underlying system (exploitation). To this end, optimism-based methods that bias in favor optimistic approximations true parameter are employed literature. A number asymptotic results have been established, but their finite-time counterparts few, with important restrictions. This article establishes worst-case regret policies. presented high probability upper bounds optimal up logarithmic factors. nonasymptotic analysis requires following very mild assumptions: stabilizability system's dynamics, limiting degree heaviness noise distribution. establish such bounds, certain novel techniques developed comprehensively probabilistic behavior dependent random matrices heavy-tailed distributions.