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Question 1

0votes

0answers

23views

Max–min assignment on a DAG when nodes have candidate values with compatibility constraints

I have a DAG where every node has a (usually small) set of candidate integers. A candidate a is compatible with b if (a | b) or (b | a). For every root I want to choose one candidate per node to ...

user5109988

81

askedNov 20 at 8:58

Question 2

0votes

0answers

32views

Determiniing max roundness of number in an array

I'm trying to solve the following Codeforces question (https://codeforces.com/contest/837/problem/D), and I feel like I have a solution that's very close but is probably still over the time constraint....

redLotus31415

35

askedNov 15 at 19:35

Question 3

0votes

0answers

29views

Continuity of an optimal stopping value with discontinuous gain function.

I am trying to approach this homework on optimal stopping. Suppose we have an optimal stopping problem where we observe the process $$dm_t = \frac{1}{1+t}dW_t,$$where $W_t$ is a standard Brownian ...

Abhi V

117

askedSep 24 at 15:00

Question 4

1vote

0answers

51views

Why is "double overshooting" not the optimal strategy in this kind of acceleration problem

https://leetcode.com/problems/race-car/description/I'm working on a problem where we need to reach a target position t on a number line by accelerating. The acceleration on step k is k.Let's say we ...

vignesh suresh

31

askedSep 21 at 15:59

Question 5

0votes

3answers

212views

How do I find the straightest path through 3D rectangles?

I'm mainly a programmer, not a mathematician, so please bear with me.I have a sequence of rectangles in 3D space. Each one has a specified pose: position, an orientation (rotation in 3D), and a width ...

Luke B.

111

askedSep 10 at 19:17

Question 6

0votes

0answers

16views

Prove concavity for a discrete MDP using Induction

Hi I am new to MDP and need to do a modeling for my project. I am really not comfortable with the entire abstraction of optimizing actions so I really need some help!! Thank you all in advance!!!The ...

Ari

1

askedAug 13 at 22:28

Question 7

3votes

1answer

155views

Counting the number of non-bypassing yet possibly intersecting path pairs on a grid

Consider an integer lattice path beginning at the origin with each step going rightwards or upwards. That is, a valid path starts at $(0,0)$, ends at $(m,n)$, and each step is a vector of the form $R=(...

Hyakutake

687

askedApr 28 at 6:36

Question 8

0votes

0answers

32views

Uniqueness of interior fixed point in a dynamic programming problem with strictly concave objective

Consider the following dynamic programming problem:$$V(s)=\max_{s'\in[0,1]}F\left(s,s'\right)+\beta V(s').$$Here $\beta\in[0,1)$ is the discount rate, $s\in\mathbb{R}$, and$F:\mathbb{R}^{2}\...

Andres

95

askedApr 5 at 20:07

Question 9

-1votes

1answer

142views

Is there any easy way to calculate total number of combination of a permutation of n such that all adjacent element's sum is composite?

A permutation of length $n$ is a sequence where every number from $1$ to $n$ comes exactly $1$ times, so permutation of $5 \mapsto 1,2,3,4,5$ but $1,1,2,3,5$ is not a permutation of $5$.Now we try to ...

Al Kaoser.

11

askedApr 1 at 3:56

Question 10

0votes

0answers

116views

Dynamic Programming

I am struggling with the following problem.A college student has 7 days remaining before final examinations begin in her four courses, and she wants to allocate this study time as effectively as ...

ryan

1

askedFeb 13 at 22:35

Question 11

0votes

0answers

54views

Optimal stopping time in discrete time, deterministic setup

I want to solve a very simple optimal stopping time problem. Let us assume that an agent derives some "utility" in each period t, equal to $u_{t}$. This is assumed to decay geometrically: $...

Balázs Markó

115

askedFeb 13 at 10:49

Question 12

1vote

1answer

114views

How to prove optimal substructure in dynamic programming?

There are 2 requirements for a problem to be considered for dynamic programming:overlapping sub-problemsoptimal sub-structureMajority of dp problems are modeled as recursive functions where the ...

Self

11

askedJan 30 at 4:58

Question 13

0votes

1answer

60views

Prove that $π^*(s | a) = δ(a, \arg\max_{a\in A} Q(s, a))$ is an optimal policy.

In a Markov Decision Process, a policy is a probability distribution over which actions to take given states:$$\pi(a \mid s) = \mathbb{P}(A_t = a \mid S_t = s)$$The state-value of a state $s_t$ when ...

Lysandre Terrisse

95

askedJan 17 at 4:24

Question 14

2votes

0answers

113views

Maximize expected stopping time of a random walk with absorbing barriers

Consider a discrete-time random process $\{X_t\}$ $(t = 0, 1, 2, \cdots)$ on the lattice $\mathbb{Z}^M$. Starting from the point $X_0 = (X^1_0, \cdots, X^M_0)$ satisfying$$X^1_0 + \cdots + X^M_0 = N ...

username

717

askedDec 14, 2024 at 7:56

Question 15

4votes

0answers

141views

Guessing a subset by submitting subsets and getting back the sizes of the intersections

Let $p>q$ be positive integers, set $P=\{1,2,...,p\}$, and $Q\subset P$ be an unknown set of $q$ elements.In every step, we can guess a set $T\subset P$ and then know the size $|T\cap Q|$ of its ...

LLLL

41

askedDec 13, 2024 at 15:44

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Questions tagged [dynamic-programming]

Max–min assignment on a DAG when nodes have candidate values with compatibility constraints

Determiniing max roundness of number in an array

Continuity of an optimal stopping value with discontinuous gain function.

Why is "double overshooting" not the optimal strategy in this kind of acceleration problem

How do I find the straightest path through 3D rectangles?

Prove concavity for a discrete MDP using Induction

Counting the number of non-bypassing yet possibly intersecting path pairs on a grid

Uniqueness of interior fixed point in a dynamic programming problem with strictly concave objective

Is there any easy way to calculate total number of combination of a permutation of n such that all adjacent element's sum is composite?

Dynamic Programming

Optimal stopping time in discrete time, deterministic setup

How to prove optimal substructure in dynamic programming?

Prove that $π^*(s | a) = δ(a, \arg\max_{a\in A} Q(s, a))$ is an optimal policy.

Maximize expected stopping time of a random walk with absorbing barriers

Guessing a subset by submitting subsets and getting back the sizes of the intersections

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