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A linear programming (LP) problem is essentially just, for positive integers m and n and real or rational matrices 1 by n c n by 1 x m by n A m by 1 b 1 by

A linear programming (LP) problem is essentially just, for positive integers m and n and real or rational matrices 1 by n c n by 1 x m by n A m by 1 b 1 by 1 z, maximize z = cx subject to Ax = b, x >= 0 That is, an LP is a fully precisely stated problem in math. There is no randomness, ambiguity, flexibility, uncertainty, etc. Now when move to the real world and have a problem, e.g., in mixing animal feed, cracking crude oil, we have some real world considerations that are not really LP. But in some cases, maybe it appears, after some examination, that we can take the real problem and formulate it as an LP. The formulation may have some of these real considerations, but once we have our LP, all we can hope to get from the LP is the usual LP results -- an optimal solution, maybe infinitely many alternate optima (other solutions also optimal), some sensitivity analysis on how much we could change some of the input data and have the solution we found remain optimal, and some more, but none of this goes very far on resolving the real world issues of randomness, etc. So, sure, maybe we (1) several times adjust the input data and solve the LP again, (2) move to non-linear programming (quadratic programming, the Kuhn-Tucker conditions, etc.) or integer linear programming, or (3) have some models of the randomness and move to optimization under uncertainty, e.g., stochastic dynamic programming. Main point: There is (A) the math and (B) the real world, and the two are not the same. Hopefully the real world problem can be solved nicely with some math, but we should know when we jump from the (a) real problem to the (b) math problem and have good understandings of the relevant issues of both (a) and (b). For a (crude) analogy, the math, e.g., LP is just a tool. E.g., recently somehow my plastic mail box got whacked with some cracked plastic and a hole in the top. Fixes used some tools, tape measure, hand saw, bridge saw, circle saw, hand planer, wire brush, electric drill, epoxy glue, spray paint, ... -- but none of these were directly "mailbox fixes" but just tools useful in fixing the mailbox. In this analogy, the math is not a real fix but just some tools that might yield a real fix.

taeric 3y ago
Right, I get what an LP is. As I said in the other thread, I'm mainly trying to use charity to the opening post to find a way it can be meaningful. With an idea that mayhap you could use RL to try and explore a solution space that you don't know the penalty for non-compliance to a solution. Specifically, use LP to craft a plan in an iteration of scenarios that is varying a cost function through iterations. I suspect I'm fumbling in the multi period planning realm more so than the RL one, here. I further suspect, though, that it is more "if you can formalize your problem such that LP solves it, use LP." That is, the opening post was largely just nonsensical?

taeric 3y ago

Right, I get what an LP is. As I said in the other thread, I'm mainly trying to use charity to the opening post to find a way it can be meaningful. With an idea that mayhap you could use RL to try and explore a solution space that you don't know the penalty for non-compliance to a solution. Specifically, use LP to craft a plan in an iteration of scenarios that is varying a cost function through iterations. I suspect I'm fumbling in the multi period planning realm more so than the RL one, here. I further suspect, though, that it is more "if you can formalize your problem such that LP solves it, use LP." That is, the opening post was largely just nonsensical?