Questions tagged [markov-decision-process]
For questions related to Markov decision processes (MDPs), which model decision making in time-varying and usually stochastic environments.
21
questions
1
vote
0
answers
35
views
LP programming of a Markov Decision Model
I am doing my thesis and I encounter the following issue last weeks, without solving it yet: I am trying to formulate a Markov Decision Process as an LP formulation, considering 2 items. (In the ...
2
votes
0
answers
121
views
Is OCN=DOCN decidable?
One-Counter Nets (OCNs) are finite-state machines equipped with an integer counter that
cannot decrease below zero and cannot be explicitly tested for zero.
An OCN $A$ over alphabet $\sum$ accepts a ...
- 21
0
votes
1
answer
102
views
Analytic international relations
Here is the Saudi-Israel game framework as a Stack Exchange question with MathJax:
game-theory markov-processes
How can I model the dynamics of Saudi-Israel relations using a stochastic game with ...
- 1
0
votes
0
answers
43
views
Creating a simple class in python for doing simulation of MDP
I am currently learning Python and doing object-oriented programming. I am trying to create a simulation for MDP.
My problem statement is: "I have four stages of process. Each stage has two ...
- 29
3
votes
1
answer
225
views
Optimization for Stochastic Simulations
This questions stems from my original question here. I have a system, where each 'run' is a simulation of agents switching between tasks (or states) as in a Markov Chain. I would like to find ways to ...
- 325
1
vote
1
answer
111
views
(OR-Tools) Custom Function to Evaluate Intermediate Solutons
I have a system with $k$ tasks, where each task is a state in a Markov chain. I am working on allocating agents to each task. I would like to achieve a specific distribution of the agents among these ...
- 325
0
votes
1
answer
178
views
How to model history-dependent dynamic program?
Suppose there is a dynamic program that the state of the problem grows over time (more info is added to the state of the problem over time) and at each time, we need all historical data, full history, ...
- 2,150
1
vote
0
answers
46
views
How to check if the state of a dynamic program is Markovian or not?
Based on Markov chain context, we say a stochastic process is Markovian if the state at time $t+1$, $S_{t+1}$ just depends on the state in the previous step, that is, $\Pr\left( S_{t+1}|S_1, S_2, \...
- 2,150
2
votes
1
answer
331
views
Understanding MDP's Dual Linear Program
I'm trying to understand a proof in Puterman'05 (Markov Decision Processes: Discrete Stochastic Systems). My question is within Theorem 6.9.1 pertaining to the equivalence of solutions to the primal (...
- 23
2
votes
0
answers
31
views
MDP model for a unique system
Let's assume that we have a system where there are two exogenous factors, name $a$ and $b$, that can affect the system state. At each decision epoch either $a$ or $b$ occurs and it is not possible ...
- 21
1
vote
0
answers
107
views
Markov Chain - Stationary or Borderline distribution [closed]
I have a Markov chain problem below, where :
The problem
An urn initially contains 3 black balls and 1 red ball. The balls are indistinguishable to the touch. One ball is randomly drawn.
If this ball ...
- 73
4
votes
0
answers
49
views
Equilibria in two player, finite horizon, zero sum stochastic game
Suppose we have a two player, finite horizon, zero sum stochastic game (a.k.a. "competitive MDP"). The game is defined over a finite set of state $S$. At each decision epoch $t\in\{1,\dots,T\}$ (for ...
- 2,047
3
votes
1
answer
115
views
Queuing Theoretic Model with Memory
Consider a telephone company which receives call request at some arrival rate and serves each request with some service rate. This can be modeled using a Poisson Process. However I wish to model the ...
- 897
8
votes
1
answer
172
views
Can I use an MDP for a stochastic inventory model when my demand distribution is non-stationary?
Most formulations of Markov Decision Processes for stochastic inventory models I've come across assume a fixed demand distribution.
But in my case I have a time series forecast with a non stationary ...
- 2,089
12
votes
3
answers
1k
views
Number of aircraft to operate in an airline company
Suppose that an airline company has X planes, in general the companies keep a number of these aircraft (say 80% of X) in reserve in case of hazards. My question is how the airline companies compute ...
- 229
12
votes
1
answer
134
views
Model or State Uncertainty in Queueing Model due to uncertain arrival rate
Introduction
I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy via Value or ...
- 463
11
votes
1
answer
346
views
Algorithm for workforce scheduling for call volumes
I am trying to solve a workforce scheduling and optimization problem.
Available data:
daily level forecasted call volumes,
shift schedules,
resource utilization at the aggregate level,
AHT at ...
10
votes
2
answers
4k
views
Infinite horizon versus finite horizon MDP
When can we approximate a finite horizon MDP with infinite horizon?
Can we use infinite horizon stochastic shortest path problem on a directed acyclic graph?
- 101
9
votes
0
answers
211
views
For the solution of complex gaming are we to leave behind approximation and fixed algorithms in favor of agents?
For an evolutionary extensive form game is the use of multi-agent systems a necessity or can more traditional approximate Nash equilibria and mean-field interactions suffice?
Few games can be ...
- 2,098
12
votes
1
answer
169
views
Open source Markov decision process solvers
Which sources are out there that provide reliable and fast MDP solvers? I prefer that the library is callable from C++ but other languages are fine too.
There is indeed an abundance of repositories ...
- 2,461
8
votes
1
answer
379
views
Convergence rate value iteration
Value iteration is one of the most commonly used methods to solve Markov decision processes. Its convergence rate obviously depends on the number of states and actions. However, the convergence rate ...
- 2,461