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If you need robustness you can explicitly model an uncertainty set for your problem coefficients, and solve to optimality the robust optimization problem. That

If you need robustness you can explicitly model an uncertainty set for your problem coefficients, and solve to optimality the robust optimization problem. That way you know exactly your degree of “insurance” to uncertainty. You also know that this is the absolute best you can do in view of this uncertainty set.

taeric 3y ago
Right, I am asking if RL may be a somewhat easy way to get that in there? Since a lot of robustness is best known after a series of losses. That is, if you know what your total exposure to risk is, then LP is still ultimately the answer. If you don't, you need some way to monte carlo different scenarios to get an idea. And at that point, I feel you have backed yourself into RL?
- whatever1 3y ago
  Fair point, but there are no shortcuts. Either you will use domain knowledge and you will build a model-based approach (LP, IP, MINLP, CP/SAT, DP), or you will have to find terabytes of good quality samples to feed the RL beast, hoping it will approximate a good enough policy / value function. The main appeal of RL is for cases where an explicit model cannot be derived. Think of very complex chemical reactions or other system dynamics. There indeed, you can go with RL and cross your fingers. If your process is dangerous, we must also have a supervisor system, to ensure that the RL actions will not lead to catastrophic situations (from violating constraints). Like Teslas targeting firetrucks.
  - taeric 3y ago
    Absolutely! I said in another post that I assumed you'd use LP if your decision space was modeled in such a way that that can work, but RL if you instead have more of a simulator and a cost function. Even that, I grant, is over simplified. Mainly trying to find a way to use charity for that opening post. At face value, I don't know what they were getting at.
- graycat 3y ago
  Small point: If you want to do Monte Carlo on an LP (linear program), then using the simplex algorithm, for the first Monte Carlo trial, go ahead and find the optimal solution. Then for the rest of the trials, start with the optimal solution, the basic variables, and the matrix inverse of the basis matrix and from those find the next optimal solution -- that solution will nearly always come quite quickly. So, you will be able to have a good collection of Monte Carlo trials for surprisingly little more computing than for the first optimal solution.
  - taeric 3y ago
    I knew you can carry forward solutions in most solvers. I'd assume you would be changing constraints some, though I imagine most constraints would not be changed such that a lot of the discovered solution would still be good?
    - graycat 3y ago
      The change that would make finding the next solution maybe not quickly would be to the basis matrix and its inverse from the last solution. Still, finding a new basis inverse would be much faster than starting from just the whole problem. Yes, changes in the basis matrix could make that basis infeasible, but could attack that the usual way with artificial variables, and there may be still better ways. Changes in the costs c, the right hand side b, or the non-basic columns of matrix A would let the new solution be found usually quickly.

taeric 3y ago

Right, I am asking if RL may be a somewhat easy way to get that in there? Since a lot of robustness is best known after a series of losses. That is, if you know what your total exposure to risk is, then LP is still ultimately the answer. If you don't, you need some way to monte carlo different scenarios to get an idea. And at that point, I feel you have backed yourself into RL?

whatever1 3y ago
Fair point, but there are no shortcuts. Either you will use domain knowledge and you will build a model-based approach (LP, IP, MINLP, CP/SAT, DP), or you will have to find terabytes of good quality samples to feed the RL beast, hoping it will approximate a good enough policy / value function. The main appeal of RL is for cases where an explicit model cannot be derived. Think of very complex chemical reactions or other system dynamics. There indeed, you can go with RL and cross your fingers. If your process is dangerous, we must also have a supervisor system, to ensure that the RL actions will not lead to catastrophic situations (from violating constraints). Like Teslas targeting firetrucks.
- taeric 3y ago
  Absolutely! I said in another post that I assumed you'd use LP if your decision space was modeled in such a way that that can work, but RL if you instead have more of a simulator and a cost function. Even that, I grant, is over simplified. Mainly trying to find a way to use charity for that opening post. At face value, I don't know what they were getting at.
graycat 3y ago
Small point: If you want to do Monte Carlo on an LP (linear program), then using the simplex algorithm, for the first Monte Carlo trial, go ahead and find the optimal solution. Then for the rest of the trials, start with the optimal solution, the basic variables, and the matrix inverse of the basis matrix and from those find the next optimal solution -- that solution will nearly always come quite quickly. So, you will be able to have a good collection of Monte Carlo trials for surprisingly little more computing than for the first optimal solution.
- taeric 3y ago
  I knew you can carry forward solutions in most solvers. I'd assume you would be changing constraints some, though I imagine most constraints would not be changed such that a lot of the discovered solution would still be good?
  - graycat 3y ago
    The change that would make finding the next solution maybe not quickly would be to the basis matrix and its inverse from the last solution. Still, finding a new basis inverse would be much faster than starting from just the whole problem. Yes, changes in the basis matrix could make that basis infeasible, but could attack that the usual way with artificial variables, and there may be still better ways. Changes in the costs c, the right hand side b, or the non-basic columns of matrix A would let the new solution be found usually quickly.