Questions tagged [markov-decision-process]
The markov-decision-process tag has no usage guidance.
41
questions
0
votes
0
answers
13
views
Learning Markov Decision Processes from Puterman's text with limited mathematical background
I am studying Markov Decision Processes (MDPs) using Puterman's classic text, but am finding it challenging due to my limited background in measure theory and Borel subsets. Additionally, the lack of ...
- 101
5
votes
1
answer
102
views
Is reinforcement learning conceptually equivalent to time-series with a latent dependent variable?
In reinforcement learning, there is a state $s_t$, an action $a_t$, and a policy $\pi(a|s)$ that maps states to the Probability Distribution Function (PDF) of actions. The goal is to choose the ...
- 807
0
votes
0
answers
15
views
What is state transition probability in an MDP? A matrix or a 3-D tensor?
I find the following written in places:
$P$ is a state transition probability matrix,
$P_{ss'}^{a} = P[S_{t+1} = s' | S_t = s, A_t = a]$ (notes by david silver - slide 24 and, sutton and barto)
How is ...
- 2,385
0
votes
0
answers
20
views
Can all MDPs be translated into MPs?
Say we have a Markov Decison Process (MDP) with countably infinite state space $S$, continuous action space $A$, well-defined transition matrix $T_a(s,s') = P(s'\mid s,a)$ and some stochastic policy $\...
- 1
1
vote
1
answer
56
views
Can two states have different actions in a deterministic policy? How to specify states which have probability linked with them in the policy?
The agent has two actions, a0 and a1, whose effects in each state σ0; . . . ; σ3 are described in Figure 1. The edges from actions are labeled with the probability that this transition occurs. For ...
- 11
0
votes
0
answers
28
views
How are RNNs trained for infinite horizon reinforcement learning
In the literature in case of POMDPs, the policy is conditioned on the state and the observation/belief, which should summarize the history of the states/actions taken so far.
To do so, usually a RNN ...
- 859
0
votes
1
answer
61
views
Can the observation function in a POMDP be a function of the previous state?
I would like to model my problem with a Partially Observable Markov Decision Process (POMDP) but I have as an observation the previous state $o_t = s_{t-1}$.
However, I see in all formal definitions ...
- 3
0
votes
1
answer
69
views
Existence of the optimal control in finite horizon MDP
For infinite horizon MDP with finite state and action space, there exists an optimal (stationary) policy. For finite horizon MDP with finite state and action space, does there exist an optimal policy? ...
- 21
0
votes
0
answers
39
views
How to estimate the order of a controlled Markov process from data?
Consider a non-stationary controlled Markov process represented by a sequence of states and actions $(s_0,a_0,\ldots,s_{T-1},a_{T-1},s_T)$ over a finite number of discrete time steps.
If the process ...
- 151
1
vote
0
answers
22
views
What theoretical guarantees are lost in modeling reward as a function of next state?
There are a couple of threads (1, 2) which address the dependency of reward on the next state in addition to the current state and action. Clearly, modeling the transition probability as a joint ...
- 11
1
vote
0
answers
15
views
Can we do Deep Reinforcement Learning with Disjoint Action Sets?
I'm defining a construction you can apply to a Markov decision process*, and it involves extending an equivalence relation from the the state space of the MDP to an equivalence relation on the action ...
1
vote
1
answer
19
views
Why $A_{t-1}$ in reinforcement learning history $H_t = O_1, R_1, A_1, ..., A_{t-1}, O_t, R_t$? [closed]
I learn with David Silver's slides reinforcement learning. His definition of the history $H_t$ is:
$H_t = O_1, R_1, A_1, ..., A_{t-1}, O_t, R_t$
$O =$ observations
$R =$ rewards
$A =$ actions
Why do ...
- 129
0
votes
1
answer
248
views
Estimated Optimal Policy vs True Optimal Policy
In an MDP / in Reinforcement Learning, the optimal policy is often defined as something similar to: a policy that maximizes the value of all states at the same time.
But I am not sure whether this ...
1
vote
0
answers
32
views
Fixed point of the Bellman operator for suboptimal policies
Consider an MDP and let the Bellman operator be defined as follows,
$$
(T^\pi_\gamma V)(s) = \sum_{a\in A}\pi(s)\big(r(s,a) + \gamma \sum_{s' \in S} p(s'\mid s,a) V(s')\big)
$$
where,
$\pi:S\to \...
- 141
0
votes
1
answer
117
views
In reinforcement learning, after an action, the state does not change
After conducting an action, the state of the agent may change into a new state, also may not change. So is it still reasonable to formulate the problem by MDP and solved it by reinforcement learning ...
3
votes
1
answer
226
views
Bellman Optimality Operator fixed point
I'm reading Szepesvári's book on RL. My question is concerning the proof of Theorem A.10 (p. 71).
Theorem
Let $V$ be the fixed point of $T^∗$ and assume that there is policy $π$ which is greedy w.r.t ...
- 43
2
votes
0
answers
213
views
Is random policy a stochastic policy?
I'm a student to start to study RL.
When I studied MDP and watched the gridworld example, I had one question.
In the gridworld, we usually assume that we can have four actions in any states, e.g. up, ...
- 53
1
vote
0
answers
583
views
Q-learning convergence with stochastic reward function
Every proof for convergence of Q-learning I can find assumes that the reward is a function $r(s, a, s')$ i.e. deterministic. However, MDPs are often defined with a stochastic reward, as exemplified in ...
- 131
1
vote
0
answers
625
views
Open AI Gym for TSP problem?
In a previous question I asked about use of Open AI Gym as a vehicle for modeling business problems as MDPs. A comment suggested that I start a new question with more refined scope. In general, I'm ...
- 2,501
1
vote
1
answer
28
views
What kind of model to optimize the allocation a ressource in the context of time to event outcome?
I have a list of N patients that are competing for one treatment at each time. A treatment becomes available at times t=1,...,T.
I want to build a model that can take the time-varying characteristics ...
- 11
1
vote
1
answer
2k
views
Whats exactly deterministic and non deterministic in deterministic and nondeterministic MDP policies?
Consider below Markov Decision Process:
Blue hexagons are states and orange circles are actions. I have rather simple confusion.
What will be nature of deterministic and non deterministic MDPs? This ...
- 205
1
vote
0
answers
154
views
Optimal action-value as function of optimal value. Proof
Currently reading through Algorithms for Reinforcement Learning, I think these notes are good, but there're bits that are a bit unclear, and I have few questions that I think are quite basic:
...
- 213
1
vote
1
answer
355
views
Equivalent definitions of Markov Decision Process
I'm currently reading through Sutton's Reinforcement Learning where in Chapter 3 the notion of MDP is defined.
What it seems to me the author is saying is that an MDP is completely defined by means of ...
- 213
2
votes
1
answer
262
views
Is a policy $\pi(s)$ on Markov decision process a random variable?
Citing Wikipedia:
The goal in a Markov decision process is to find a good "policy" for
the decision maker: a function $\pi$ that specifies the action
$\pi(s)$ that the decision maker will ...
- 242
2
votes
1
answer
258
views
How to solve a Markov Decision Problem with State Transition Matrix and Reward Matrix
I'm stuck in solving a simple dynamic probabilistic model. I have Three states {Sunny, Cloudy, Rainy}.
I have the ...
- 75
1
vote
0
answers
63
views
does it make sense to define average reward in finite horizon
I am new to reinforcement learning but there is a situation I am considering using average reward instead of sum reward as objective for a finite horizon application problem.
Specifically, there are ...
- 211
-1
votes
1
answer
507
views
How to calculate the probability Matrix (Alpha) for Regular Markov chains
Pardon me for being a novice here. In the image attached, eq 3.1 represents the transition matrix (it's pretty clear). I am not able to comprehend the eq 3.2, alpha*P = alpha, as well as the further ...
1
vote
0
answers
515
views
Bellmans equation and existence of optimal policy for MDPs
I'm trying to understand the proof of existence of an optimal policy from this question
Why is there always at least one policy that is better than or equal to all other policies?
by Lovelris.
-
...
- 121
5
votes
1
answer
6k
views
What is the difference between Reinforcement Learning(RL) and Markov Decision Process(MDP)?
What is the difference between a Reinforcement Learning(RL) and a Markov Decision Process(MDP)?
I believed I understood the principles of both, but now when I need to compare the two I feel lost. ...
- 2,785
3
votes
1
answer
340
views
States in Bandit Problems
I am wondering if there is an interpretation of the Bandit Problem with more than one states. I know that there are versions which views each slot machine as an independent Markovian machines and as ...
- 105
1
vote
1
answer
935
views
Calculating Value State matrix for a finite MDP without limit condition
In the book "Reinforcement Learning" From Andrew Sutton and Barto there is an example given for the Bellman equations:
Figure 3.2 (left) shows a rectangular gridworld representation of a simple ...
- 113
2
votes
1
answer
473
views
Large state space and Markov decision process
I am working on a project where I have an MDP but with a very large state space (each state is described by a tuple (a,b,c,d) where a,b,c,d are integers in the range [0, 1000]).
My goal is to compute ...
- 21
0
votes
1
answer
185
views
Does an optimal value function exist for an MDP with continous state and action spaces?
If the state set $\mathcal{S}$ and action set $\mathcal{A}$ of a Markov Decision Process are infinite does an optimal value function $v_\pi(s)$ exist?
- 149
0
votes
0
answers
93
views
Can someone explain how an action reward function is calculated in markov decision process
In his second lecture on Reinforcement Learning, David Silver, writes the expression for reward function(for MDP) as:
Why do we need to calculate the expected value? Because if we are in state s1 and ...
- 121
1
vote
1
answer
269
views
How to model transition probability if action does not lead to a state change (in MDP)?
An MDP (markov decision process) is defined as a set of states $S$, actions space $A$, Transition Probabilities $T$ and Rewards $R$. An action $a$ in a state $s$ usually result in a change of state ...
3
votes
1
answer
8k
views
Dyna-Q Algorithm Reinforcement Learning
In step(f) of the Dyna-Q algorithm we plan by taking random samples from the experience/model for some steps.
Wouldn't it be more efficient if we construct an MDP from experience by computing the ...
- 731
3
votes
1
answer
1k
views
UCB Exploration in Reinforcement Learning
I have two questions regarding the upper confidence bounds (UCB) exploration in reinforcement learning:
UCB exploration is derived from Hoeffding's inequality which assumes that the reward is bounded ...
- 731
3
votes
0
answers
47
views
Model or State Uncertainty in Queueing Model due to uncertain arrival rate
$\textbf{Introduction}$
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 ...
- 213
0
votes
0
answers
69
views
What is the point of doing simulation on Markov Chain?
I am studying Markov Chain and I am currently reading about simulation on Markov Chain but I can't see the point of simulation on Markov Chain. What does simulation mean in Markov Chain and what can ...
- 3,165
1
vote
0
answers
85
views
How to increase the total number of iterations it takes to converge a MDP?
I was reading about Policy Iteration. What are the factors that influence the total number of iterations the algorithm takes to converge?
For a given MDP which converges in 3 iterations, what setting ...
- 111
5
votes
2
answers
4k
views
Uniqueness of the optimal value function for an MDP
Suppose we have a Markov decision process with a finite state set and a finite action set. We calculate the expected reward with a discount of $\gamma \in [0,1]$.
In chapter 3.8 of the book "...
- 211