  In this paper, we investigate the problem of power control for streaming
variable bit rate (VBR) videos over wireless links. A system model involving a
transmitter (e.g., a base station) that sends VBR video data to a receiver
(e.g., a mobile user) equipped with a playout buffer is adopted, as used in
dynamic adaptive streaming video applications. In this setting, we analyze
power control policies considering the following two objectives: 1) the
minimization of the transmit power consumption, and 2) the minimization of the
transmission completion time of the communication session. In order to play the
video without interruptions, the power control policy should also satisfy the
requirement that the VBR video data is delivered to the mobile user without
causing playout buffer underflow or overflows. A directional water-filling
algorithm, which provides a simple and concise interpretation of the necessary
optimality conditions, is identified as the optimal offline policy. Following
this, two online policies are proposed for power control based on channel side
information (CSI) prediction within a short time window. Dynamic programming is
employed to implement the optimal offline and the initial online power control
policies that minimize the transmit power consumption in the communication
session. Subsequently, reinforcement learning (RL) based approach is employed
for the second online power control policy. Via simulation results, we show
that the optimal offline power control policy that minimizes the overall power
consumption leads to substantial energy savings compared to the strategy of
minimizing the time duration of video streaming. We also demonstrate that the
RL algorithm performs better than the dynamic programming based online grouped
water-filling (GWF) strategy unless the channel is highly correlated.
