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Control schemes that learn using measurement data collected online areincreasingly promising for the control of complex and uncertain systems.However, in most approaches of this kind, learning is viewed as a side effectthat passively improves control performance, e.g., by updating a model of thesystem dynamics. Determining how improvements in control performance due tolearning can be actively exploited in the control synthesis is still an openresearch question. In this paper, we present AntLer, a design algorithm forlearning-based control laws that anticipates learning, i.e., that takes theimpact of future learning in uncertain dynamic settings explicitly intoaccount. AntLer expresses system uncertainty using a non-parametricprobabilistic model. Given a cost function that measures control performance,AntLer chooses the control parameters such that the expected cost of theclosed-loop system is minimized approximately. We show that AntLer approximatesan optimal solution arbitrarily accurately with probability one. Furthermore,we apply AntLer to a nonlinear system, which yields better results compared tothe case where learning is not anticipated.

Anticipating the Long-Term Effect of Online Learning in Control