# Questions tagged [dynamic-programming]

Dynamic programming is a mathematical optimization/programming approach applicable if an optimal solution can be constructed efficiently from optimal solutions of its subproblems. A classic example is the Towers of Hanoi.

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### Special Case - How to generate a formula to calculate where next additional items in a set of items, in a particular row and at a particular index

I've tried to generate a simple formula to do this calculation but I've not successfully arrived at a working formula. Here, I have a list of items displayed in a grid. Let's use these symbols ...
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### Calculate probability of flipping coins with probabilities dependent on previous results

Let's say I have a biased coin that has a probability of 0.2 for heads and 0.8 for tails. If you flip it 6 times without getting a heads however, the probability of heads increases by 0.2 per non-...
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### Dynamic programming algorithm to maximize job execution steps on two machines

I have a problem that requires finding a plan to execute a job on two machines, A and B, or moving the job between machines to maximize the number of executed steps. Specifically, in each time ...
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### How can I prove the contraction property on a joint system of equations?

I'm studying a simple dynamic programming problem whose solution is a system of Bellman equations, and am running into some issues trying to prove the Contraction Mapping Theorem for the system as a ...
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### Value iteration, Bellman [closed]

can someone please explain how V2 values are calculated in this picture. I have a pretty good understanding of Bellman equation, or at least I think I do. But when I calculate it, my v2 Values turn ...
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### repeatedly XOR n-bit string - probability of getting all 1s

Start with n-bits of all 0s Each round, generate a n-bit string, delta, with probability of getting a 1 being p. Output of the ...
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### Random Dynamical System

there are two questions here, but I have no ideas at all about it, can you give a clue or book recommendation? 1 vote
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### A Basic Question of Continuous Time Macroeconomic Model (Variation of Constant to Solve an ODE)

I am going through the continuous time macro slides by Ben Moll (link is: https://benjaminmoll.com/wp-content/uploads/2019/07/Lecture2_ECO521.pdf), when deriving New keynesian model in continuous time,...
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1 vote
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### Mathematical Requirements for Dynamic Programming

As far as I understand, for Dynamic Programming to "work" (I think this means for Dynamic Programming to return a Globally Optimal Solution?), am optimization problem must have the two ...
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1 vote
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### Can Gradient Descent be "Combined" with Dynamic Programming?

In most applications of Gradient Descent (e.g. optimizing the Loss Functions of Neural Networks) - regardless of the "type" of Gradient Descent algorithm being used (e.g. Stochastic Gradient ...
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### Can Machine Learning models be considered as "Approximate Dynamic Programming"?

In the context of certain statistical/machine learning models, such as models that are trying to estimate "optimal policies" (e.g. reinforcement learning) - can we consider these models as &...
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