We design adaptive controller (learning rule) for a networked control system (NCS) in which data packets containing control information are transmitted across a lossy wireless channel. We propose Upper Confidence Bounds for Networked Control Systems (UCB-NCS), a learning rule that maintains confidence intervals for the estimates of plant parameters $(A_{(star)},B_{(star)})$, and channel reliability $p_{(star)}$, and utilizes the principle of optimism in the face of uncertainty while making control decisions. We provide non-asymptotic performance guarantees for UCB-NCS by analyzing its regret, i.e., performance gap from the scenario when $(A_{(star)},B_{(star)},p_{(star)})$ are known to the controller. We show that with a high probability the regret can be upper-bounded as $tilde{O}left(Csqrt{T}right)$footnote{Here $tilde{O}$ hides logarithmic factors.}, where $T$ is the operating time horizon of the system, and $C$ is a problem dependent constant.
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