# Questions tagged [markov-decision-process]

For questions related to the concept of Markov decision process (MDP), which is a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision-maker. The concept of MDP is useful for studying optimization problems solved via dynamic programming and reinforcement learning.

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### Reinforcement Learning for an environment that is non-markovian

I am a beginner in the field of Reinforcement Learning with only a couple of months of experience being in the field. Soon, I will start working on a project where we want to optimize the production ...
2answers
83 views

### Why is the optimal policy for an infinite horizon MDP deterministic?

Could someone please help me gain some intuition as to why the optimal policy for a Markov Decision Process in the infinite horizon case (agent acts forever) is deterministic?
0answers
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### What is an appropriate stop criteria for training on a non-stationary environment in reinforcement learning?

I'm currently studying reinforcement learning (RL) and would like to understand non-stationary environments better. So for stationary environments, the Q-values of all state-action pairs converge ...
2answers
781 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 ...
2answers
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### Is there a natural way to define the terminal state from the MDP transition probabilities $p(s',r|s,a)$?

I'm learning the basics of RL and I'm struggling to understand the notion of terminal state in MDPs. To ask my question straightforwardly: is there a natural way to define the terminal state from the ...
0answers
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### Are there any known disadvantages of implementing vanilla Q-learning on a discretized-state space environment?

For an RL problem on a continuous state space, the states could be discretized into buckets and these buckets used in implementing the Q-table. I see that is what is done here. However, according to ...
1answer
69 views

### What is a good convergence criterion for Q-learning in a stochastic environment?

I have a stochastic environment and I'm implementing a Q-table for the learning that happens on the environment. The code is shown below. In short, there are ten states (0, 1, 2,...,9), and three ...
1answer
82 views

### Does stochasticity of an environment necessarily mean non-stationarity in MDPs?

Is a stochastic environment necessarily also non-stationary? To elaborate, consider a two-state environment ($s_1$ and $s_2$), with two actions $a_1$ and $a_2$. In $s_1$, taking action $a_1$ has a ...
1answer
82 views

### What is the difference between Bayes-adaptive MDP and a Belief-MDP in Reinforcement Learning?

I have been reading a few papers in this area recently and I keep coming across these two terms. As far as I'm aware, Belief-MDPs are when you cast a POMDP as a regular MDP with a continuous state ...
1answer
70 views

### Why can we take the action $a$ from the next state $s'$ in the max part of the Q-learning update rule, if that action doesn't lead to any reward?

I'm using OpenAI's cartpole environment. First of all, is this environment not Markov? Knowing that, my main question concerns Q-learning and off-policy methods: For me, there is something weird in ...
1answer
121 views

### How can we find the value function by solving a system of linear equations without knowing the policy?

An MDP is a Markov Reward Process with decisions, it’s an environment in which all states are Markov. This is what we want to solve. An MDP is a tuple $(S, A, P, R, \gamma)$, where $S$ is our state ...
2answers
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### Should we feed a greater fraction of terminal states to the value network so that their values are learned first?

The basis of Q-learning is recursive (similar to dynamic programming), where only the absolute value of the terminal state is known. Shouldn't it make sense to feed the model a greater proportion of ...
0answers
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### What trait of a planning problem makes reinforcement learning a well suited solution?

Planning problems have been the first problems studied at the dawn of AI (Shakey the robot). Graph search (e.g. A*) and planning (e.g. GraphPlan) algorithms can be very efficient at generating a plan. ...
1answer
60 views

### How should I implement the state transition when it is a Gaussian distribution?

I am reading this paper Anxiety, Avoidance and Sequential Evaluation and is confused about the implementation of a specific lab study. Namely, the authors model what is called the Balloon task using a ...
1answer
63 views

### How can I go from $R(s)$ to $R(s,a)$ in this specific MDP?

I'm trying to implement a research paper, as explained in this other post, here the author of the paper assumed R as a function of both states and actions, while the code (and the MDP) I'm using to ...
1answer
162 views

### How to fill in missing transitions when sampling an MDP transition table?

I have a simulator modelling a relatively complex scenario. I extract ~12 discrete features from the simulator state which forms the basis for my MDP state space. Suppose I am estimating the ...
2answers
252 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, ...
1answer
945 views

### Is my understanding of the differences between MDP, Semi MDP and POMDP correct?

I just wanted to confirm that my understanding of the different Markov Decision Processes are correct, because they are the fundamentals of reinforcement learning. Also, I read a few literature ...
2answers
154 views

### Are perfect and imperfect information games modelled as fully and partially observable environments, respectively?

In perfect information games, the agent can see all the moves performed in the past. Besides, it can observe the next action that will be put into practice by the opponent. In this case, can we say ...
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270 views

### Why does having a fixed policy change a Markov Decision Process to a Markov Reward Process?

If a policy is fixed, it is said that a Markov Decision Process (MDP) becomes a Markov Reward Process (MRP). Why is this so? Aren't the transitions and rewards still parameterized by the action and ...
1answer
280 views

### How do I convert an MDP with the reward function in the form $R(s,a,s')$ to and an MDP with a reward function in the form $R(s,a)$?

The AIMA book has an exercise about showing that an MDP with rewards of the form $r(s, a, s')$ can be converted to an MDP with rewards $r(s, a)$, and to an MDP with rewards $r(s)$ with equivalent ...
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### Can you convert a MDP problem to a Contextual Multi-Arm Bandits problem?

I'm trying to get a better understanding of Multi-Arm Bandits, Contextual Multi-Arm Bandits and Markov Decision Process. Basically, Multi-Arm Bandits is a special case of Contextual Multi-Arm Bandits ...
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801 views

### What is the reward system of reinforcement learning?

Can you describe this reward system in more detail? I understand that the environment sends a signal indicating whether or not the action taken by the agent was 'good' or not, but it seems too simple. ...
2answers
2k views

### What is a time-step in a Markov Decision Process?

The "discounted sum of future rewards" (or return) using discount factor $\gamma$ is $$\gamma^1 r_1 +\gamma^2 r_2 + \gamma^3 r_2 + \dots \tag{1}\label{1}$$ where $r_i$ is the reward received ...
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### How can I encode states where the environment consists of multiple identical elements, but each is characterised by different features?

I am quite new to Deep Reinforcement Learning, and I'm trying to define states in a Reinforcement Learning problem. The environment consists of multiple identical elements, and each one of them is ...
1answer
205 views

### Is the state transition matrix known to the agents in a Markov decision processes?

The question is more or less in the title. A Markov decision process consists of a state space, a set of actions, the transition probabilities and the reward function. If I now take an agent's point ...