I have an objective function having parameters of power consumption (p) and latency (d). I want to minimize the power consumption given a latency constraint (seconds). The optimization problem can be expressed in terms of Lagrange function as follows:
f(p,d) = p + L*d
Where L is Lagrange variable. Since power consumption and latency are inversely proportional to each other and decreasing the former results in increasing the later, the objective function can also be written in terms of relative weights as:
f(p,d) = L*p + (1-L)*d
The questions is, "given a latency constraint of d seconds, how do I find an appropriate value of L that can minimize the variable p?". I want to use reinforcement learning for this purpose, where at each state, the system takes a decision and assigns a cost to the previous action in next state in terms of the above function. Every action results in certain power consumption and latency in processing the requests. The goal is to minimize the power consumption given a latency constraint. Any suggestions/hints in this respect will be highly appreciated.