Questions tagged [markov-decision-process]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
1 vote
0 answers
13 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
0 votes
0 answers
17 views

Markov's Decision Process - calculate value in each iteration

I have the following decision tree: I calculated the value of the plan using the following paramenters (given): {𝑆0 → 𝑎1 , 𝑆1 → 𝑎3 , 𝑆2 → 𝑎4 }, Discount factor (𝛾)= 0.2 I used this formula to ...
1 vote
0 answers
10 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 ...
  • 11
1 vote
1 answer
15 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 ...
0 votes
0 answers
42 views

Can I restrict action space based on state in DDPG?

I am working on a RL based recommender system using the DDPG algorithm and wanted to restrict the action space (possible recommedations) based in the user. I have tried using the restricted action ...
0 votes
1 answer
41 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
25 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 \...
  • 121
0 votes
0 answers
9 views

Markov decison process: equality of two expressions

For a Markov decision process, are the following two expressions equal? If yes, why? Eq1: $E_{\pi}[R_{t+1}+\gamma q(S_{t+1}, A_{t+1})|S_t=s, A_t=a]$ Eq2: $E[R_{t+1}+\gamma v_\pi(S_{t+1})|S_t=s, A_t=a]$...
0 votes
0 answers
85 views

First-Visit Monte Carlo Prediction Algorithm Walkthrough

I'm currently reading the fifth chapter of Sutton and Barto Reinforcement Learning. I don't quite understand how the first-visit Monte Carlo prediction algorithm works, for estimating $V\approx v_{\pi}...
0 votes
0 answers
32 views

introduction to POMDPs?

Any recommendations for spinning up on partially observable markov decision processes and related modeling methods? We're starting a project to match trainees with sparring partners in a way that ...
0 votes
0 answers
11 views

The relationship of the value function between two approximate MDP

Considering the original MDP , where 0 < γ < 1 is the discounting factor. Now I assume an approximate MDP , which is identical to the original M, except that the transition probability . If we ...
0 votes
1 answer
69 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 ...
1 vote
0 answers
78 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 ...
1 vote
0 answers
66 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, ...
1 vote
0 answers
333 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
297 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 ...
  • 1,728
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
0 votes
1 answer
1k 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 ...
  • 155
1 vote
0 answers
112 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: ...
1 vote
1 answer
206 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 ...
2 votes
1 answer
166 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 ...
  • 200
2 votes
1 answer
139 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
47 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 ...
  • 181
0 votes
2 answers
309 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
287 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
4 votes
1 answer
4k 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. ...
  • 2,501
3 votes
1 answer
158 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 ...
1 vote
1 answer
620 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
1 vote
0 answers
186 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 ...
  • 11
0 votes
1 answer
121 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?
  • 139
0 votes
0 answers
56 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 ...
1 vote
1 answer
139 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
6k 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 ...
  • 691
3 votes
1 answer
837 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 ...
  • 691
3 votes
0 answers
40 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 ...
0 votes
0 answers
46 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 ...
  • 2,655
1 vote
0 answers
46 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
3 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 "...
  • 181