Questions tagged [markov-decision-process]
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3
votes
1answer
24 views
Are successive actions independent?
The proof of the consistency of the per-decision importance sampling estimator assumes the independence of
$$\frac{\pi(A_t|S_t)}{b(A_t|S_t)}R_{t+1}\quad\text{ and }\quad \prod_{k=t+1}^{T-1}\frac{\pi(...
4
votes
1answer
93 views
How can we use linear programming to solve an MDP?
Apparently, we can solve an MDP (that is, we can find the optimal policy for a given MDP) using a linear programming formulation. What's the basic idea behind this approach? I think you should start ...
3
votes
0answers
34 views
What is a generalized MDP?
What is a generalized MDP? How is it different than a "regular" MDP? How does it generalise the notion of an MDP? Why do we need a generalised MDP? Do generalised MDPs have some practical usefulness ...
1
vote
1answer
27 views
Unable to understand the second iteration update in value iteration algorithm for solving MDP
I am trying to understand the value iteration method for Markov Decision Process(MDP) and I was referring ot UC Berkeley's slides titled Markov Decision Processes
and
Exact Solution Methods
On slide ...
2
votes
1answer
52 views
Does the observation function for POMDP always add up to 1?
I was reading in the article A tutorial on partially observable Markov decision processes (p. 120), by Michael L. Littman, that $\sum_{z \in Z}O(a, s',z) =1$, where $a$ is the action, $s'$ the next ...
3
votes
2answers
61 views
Difference in continuing and episodic cases in Sutton and Barto - Introduction to RL, exercise 3.5
Excercise 3.5 The equastions in Section 3.1 are for the continuing
case and need to be modified (very slightly) to apply to episodic
tasks. Show that you know the modifications needed by giving ...
4
votes
1answer
70 views
Should I model my problem as a semi-MDP?
I have a system (like a bank) that people (customers) are entered into the systems by a Poisson process, so the time between the arrival of people (two consecutive customers) will be a random variable....
0
votes
0answers
20 views
How can we estimate the transition model and reward function?
In reinforcement learning (RL), there are model-based and model-free algorithms. In short, model-based algorithms use a transition model (e.g. a probability distribution) and the reward function, even ...
3
votes
3answers
152 views
Can the rewards be stochastic when the transition model is deterministic?
Suppose we have a deterministic environment where knowing $s,a$ determines $s'$. Is it possible to get two different rewards $r\neq r'$ in some state $s_{\text{fixed}}$? Assume that $s_{\text{fixed}}$ ...
1
vote
1answer
48 views
Is the next state drawn from the joint distribution of the previous state and action?
Suppose $G_t$, the discounted return at time $t$ is defined as: $$ G_t \triangleq R_t+\gamma R_{t+1}+\gamma^{2}R_{t+2} + \cdots = \sum_{j=1}^{\infty} \gamma^{k}R_{t+k}$$
where $R_t$ is the reward at ...
1
vote
1answer
38 views
What is the relation between a policy which is the solution to a MDP and a policy like $\epsilon$-greedy?
In the context of reinforcement learning, a policy, $\pi$, is often defined as a function from the space of states, $\mathcal{S}$, to the space of actions, $\mathcal{A}$, that is, $\pi : \mathcal{S} \...
4
votes
2answers
54 views
How are the reward functions $R(s)$, $R(s, a)$ and $R(s, a, s')$ equivalent?
In this video, the lecturer states that $R(s)$, $R(s, a)$ and $R(s, a, s')$ are equivalent representations of the reward function. Intuitively, this is the case, according to the same lecturer, ...
1
vote
0answers
33 views
What limitations does the Markov property place on real time learning?
The Markov property is the dependence of a system's future state probability distribution solely on the present state, excluding any dependence on past system history.
The presence of the Markov ...
1
vote
2answers
191 views
Is Monte Carlo Tree Search appropriate for problems with large state and action spaces?
I'm doing a research on a finite-horizon Markov decision process with $t=1, \dots, 40$ periods. In every time step $t$, the (only) agent has to chose an action $a(t) \in A(t)$, while the agent is in ...
5
votes
1answer
63 views
What is the appropriate approach to playing a game with incomplete state information?
I have a steady hex-map and turn-based war game featuring WWII carrier battles. I would like to improve the fixed policy for the AI using reinforcement learning. I have some beginner's questions, ...
1
vote
1answer
103 views
Importance Sampling Ratio Probability
When reading Reinforcement Learning by Sutton and Barto, I came across the importance sampling ratio.
The first equation, I believe, describes the probability a particular sequence is obtained given ...
1
vote
0answers
21 views
How to generalize finite MDP to general MDP?
Suppose, for simplicity sake, to be in a discrete time domain with the action set being the same for all states $S \in \mathcal{S}$. Thus, in a finite Markov Decision Process, the sets $\mathcal{A}$, $...
3
votes
2answers
738 views
What is a time-step in a Markov Decision Process?
The “Discounted sum of future rewards” using
discount factor $\gamma$ is
$\gamma$ (reward in 1 time step) + $\gamma^2$ (reward in 2 time steps) + $\gamma^3$ (reward in 3 time steps) + ...
I am ...
