  A wireless system with multiple channels is considered, where each channel
has several transmission states. A user learns about the instantaneous state of
an available channel by transmitting a control packet in it. Since probing all
channels consumes significant energy and time, a user needs to determine what
and how much information it needs to acquire about the instantaneous states of
the available channels so that it can maximize its transmission rate. This
motivates the study of the trade-off between the cost of information
acquisition and its value towards improving the transmission rate.
  A simple model is presented for studying this information acquisition and
exploitation trade-off when the channels are multi-state, with different
distributions and information acquisition costs. The objective is to maximize a
utility function which depends on both the cost and value of information.
Solution techniques are presented for computing near-optimal policies with
succinct representation in polynomial time. These policies provably achieve at
least a fixed constant factor of the optimal utility on any problem instance,
and in addition, have natural characterizations. The techniques are based on
exploiting the structure of the optimal policy, and use of Lagrangean
relaxations which simplify the space of approximately optimal solutions.
