# 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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### When can we unnest the minimizations/recursions in an value function(bellman optimality equation)?

When reading the following paper(page 4): An Approximate Dynamic Programming Approach for Dual Stochastic Model Predictive Control I could see that they were able to unnest the minimization's in the ...
35 views

### Optimal decision with continuous, stochastic signals and rewards

I am performing a task, where I have to decide which projects to pursue at a given point in time, where the projects have different horizons of 30 minutes. At a given point in time, forecasts are made ...
1 vote
17 views

### How can I prove that early termination in an MDP state is valid?

I have an MDP $M$ with transition function $p$, states $S$ and a state $s^0 \in S$. $s^0$ has the property that both the most optimistic trajectory (highest expected reward) and the most pessimistic ...
1 vote
58 views

### Is this a bandit problem or a MDP?

I am trying to understand if this problem can be casted both as a bandit problem as well as an MDP. Lets assume that we are trying to optimize sales $y_t$ based on investments $x_{1, t}, x_{2, t}$ ...
44 views

### UCB, Thompson sampling etc seems myopic/greedy for bandits?

When considering multi-armed bandits in different formats, UCB, $\epsilon$-greedy, thompson sampling etc seems so greedy/myopic in the sense that it solely considers reward for the current timestep. ...
52 views

### Why is R(s) more restrictive than R(s, a) in an MDP?

I am quite new to RL. I would like to know why a state-dependent reward function R(s) is more restrictive than a state-action-dependent reward function R(s, a)? And why is it that a policy can be ...
22 views

### How to decide on size of state space?

I'm in a reinforcement learning class and we're working on a dice game problem where you profit the number rolled for certain digits and lose all your money on certain other digits. You can choose to ...
84 views

### MDP to model finding an optimal sequence of actions with no other state data

I would like to build an RL agent who's objective is to find an N length sequence of actions to a reward where N is not known and the states are indistinguishable from each other (at least for it's ...
1 vote
108 views

### How can i cast this problem as an POMDP or an belief space MDP?

I am currently attempting to formulate my problem as either a Partially Observable Markov Decision Process (POMDP) or a Belief space MDP. My end goal is to gain insights into the proposed methods ...
19 views

### If the agent is at the same state but at different times and receives a different reward, wouldn't this be violating somehow the MDP assumption?

I've been trying to train an agent, I've received and read suggestions to improve its speed to reach the goal. The suggestion is to use a time penalty, for example, adding $-0.1$ to the reward each ...
1 vote
36 views

### How is the Markov property of a general state-space model derived?

Below is the derivation for the Markov property of a general state-space model. The red part is not clear. Could someone please explain the steps in the sequential derivation for the red part?
56 views

### Could you explain these 2 steps of the derivation of the Bellman equation as a recursive equation in Sutton & Barto?

I am reading the Sutton & Barto (2018) RL textbook. On page 59, it derives the recursive property of the state-value function as below. Could you explain the steps of third and fourth equality? ...
1 vote
26 views

### Can we use Low rank approximation in Markov decision process problem?

I am newbie in MDP.I have started reading Ronald Howard Dynamic Programming and MDP book as well as Sutton and Barto An Introduction to Reinforcement Learning. To my understanding MDP is a model based ...
1 vote
165 views

206 views

### Is it appropriate to represent 'total failure' as an absorbing state?

My understanding is that, in Markov decision processes, absorbing state are states which can transition only to themselves and that these transitions generate rewards of 0. I know that absorbing ...
53 views

### Does the policy search work if there is no state to state dependency through actions?

There is a game in which the state comes one after the other without depending on the agent's action. The agent gets a reward for its actions at the end of the game. The goal of the agent is to reach ...
73 views

### Does $S_{t+1}$ denote the future information in Q-learning?

In Q-learning, $Q(S_t,a)$ is updated by the Bellman equation. $Q(S_t,a) = r + \max_{a'}(Q(S_{t+1},a'))$ where $S_{t+1}$ is the future state. Let's say $S$ denotes the stock price, does it mean we are ...
53 views

### Does $R_{s}=E[R_{t}|S_{t}=s]$ indicate the reward we might expect on getting on average moving from any other state to $s$?

I'm trying to understand correctly what each "variable" in RL is and I'm not sure about $R_{s}$ the reward function. I used to think that it's the reward we may expect on average after ...
746 views

### Factors that affect the number of iterations of value iteration

I had an assumption that value iteration will take more iterations to converge if the map size increases/environment's complexity increases. I tried to verify this idea by running value iteration on ...
1 vote
177 views

### Are these two forms of the state value function the same?

Why are there different forms of the value function in reinforcement learning? Sutton & Barto (2nd edition, equation 3.14) define the state value function as follows v_{\pi}(s) = \displaystyle\...
1 vote
210 views

### Does the state space of an MDP change in these two examples?

In the classic Atari environments, like that introduced in the original DQN paper, the state space is the set of all possible images that the Atari emulator can produce (or more generally just any RGB ...
344 views

### Are multi agent or self-play environments always automatically POMDPs?

As part of my thesis, I'm working on a zero sum game with RL to train an agent. The game is a real-time game, a derivation of pong, one could imagine playing pong with both sides being foosball rods. ...
2k views

### Is there a fundamental difference between an environment being stochastic and being partially observable?

In AI literature, deterministic vs stochastic and being fully-observable vs partially observable are usually considered two distinct properties of the environment. I'm confused about this because what ...
93 views

### Is there a mathematical formalism to deal with a missing reward signal?

Typically, a Reinforcement Learning learning problem is formalized as finding an optimal policy for a Markov Decision Process (MDP). In many real-life situations, however, an agent can only get ...