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I'm given: the current state of the system S, for which the objective function C can be calculated. There's also a set of possible actions a1, a2, .... . Each action leads to a change in the state. The objective function can both increase and decrease in value. The goal is to minimize the objective function. Based on the outcome of application of a(i) I calculate the historical performance of each action and try to use them to predict the possible future performance of an action. There are many difficulties: 1. a(i) * a(j) != a(j) * a(i), which means applying a(i) first and a2(j) next is not the same as the other way around 2. The state of the system changes after applying actions to it, so a1 can perform better in the beginning and much worse at the end

Is there any machine learning algorithm which can 1. predict the performance of a(i) based on its past performance? 2. find the best sequence of actions which can help finding the likely combinations of actions for quicker objective function decrease?

Can reinforcement learning be used for this task?

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Yes, this sounds like a classic scenario of reinforcement learning. You should model your state transitions as a dynamic Bayesian Network. I recommend the method described in this paper.

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