All of us set certain goals and try to achieve them. What is the best way to keep track if you have taken the right decision? Here is a quick method to keep track of your progress. Consider that you set a goal today, and you are trying to optimize all the actions in order to reduce the total cost. The cost here can be due to time, money, effort, social costs and others.
The idea is to incorporate a method to reach the optimum in a step by step manner that uses only the local information. We query that : "If I assume that I am optimal in the future, what action needs to be taken today to ensure a global optimum". This leads us to the answer that, the best way is to determine the best that you can do today, with the assumption that from tomorrow we are going to be optimal. This seems to be very suited to our current practice also. While we drive a car we put the gear to the right speed, so that we can endure the local roads and the nearby traffic. The goal might be distant but we always have to act optimally to reach there. While spending we ensure that the basic needs for today is met. The savings also are done accordingly. Take the simple game of tic-tac-toe, here we are trying to see the local information in the game and trying to win or in most situations stop the opponent from winning !
This approach of dynamic policy is widely employed in control systems and communication. There are two things that we consider in this optimization problem, one is the value or the cost that is incurred due to our decision (actions) and the second is the policy that we have come up with. So remember at the beginning of each day try to see that you are going to be optimum for 'today', because tomorrow will "take care for itself".
The idea is to incorporate a method to reach the optimum in a step by step manner that uses only the local information. We query that : "If I assume that I am optimal in the future, what action needs to be taken today to ensure a global optimum". This leads us to the answer that, the best way is to determine the best that you can do today, with the assumption that from tomorrow we are going to be optimal. This seems to be very suited to our current practice also. While we drive a car we put the gear to the right speed, so that we can endure the local roads and the nearby traffic. The goal might be distant but we always have to act optimally to reach there. While spending we ensure that the basic needs for today is met. The savings also are done accordingly. Take the simple game of tic-tac-toe, here we are trying to see the local information in the game and trying to win or in most situations stop the opponent from winning !
Courtesy : http://experimental.designforfun.com
This approach of dynamic policy is widely employed in control systems and communication. There are two things that we consider in this optimization problem, one is the value or the cost that is incurred due to our decision (actions) and the second is the policy that we have come up with. So remember at the beginning of each day try to see that you are going to be optimum for 'today', because tomorrow will "take care for itself".
[Topic Courtesy : Introduction to Stochastic Optimization, IITB]
