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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1answer
30 views

Why is learning $s'$ from $s,a$ a kernel density estimation problem but learning $r$ from $s,a$ is just regression?

In David Silver's 8th lecture he talks about model learning and says that learning $r$ from $s,a$ is a regression problem whereas learning $s'$ from $s,a$ is a kernel density estimation. His ...
3
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1answer
68 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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2answers
174 views

Why is the policy not a part of the MDP definition?

I'm reading an article on reinforcement learning, and I don't understand why the agent's policy $\pi$ is not part of definition of Markov Decision process(MDP): Bu, Lucian, Robert Babu, and ...
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0answers
50 views

Can we use a Gaussian process to approximate the belief distribution at every instant in a POMDP?

Suppose $x_{t+1} \sim \mathbb{P}(\cdot | x_t, a_t)$ denotes the state transition dynamics in a reinforcement learning (RL) problem. Let $y_{t+1} = \mathbb{P}(\cdot | x_{t+1})$ denote the noisy ...
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1answer
125 views

How can blackjack be formulated as a Markov decision process?

I am reading sutton barton's reinforcement learning textbook and have come across the finite Markov decision process (MDP) example of the blackjack game (Example 5.1). Isn't the environment ...
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0answers
24 views

State-of-the-art algorithms not working on a custom RL environment

I'm trying to train a RL agent on a custom, highly stochastic environment (MDP). In order to do so I'm using existing implementations of state-of-the-art RL algorithms as provided by Stable Baselines. ...
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1answer
25 views

What is the difference between the state transition of an MDP and an action-value?

Let's say we have MDP where we have a state transition matrix. How is this state transition different from action value in reinforcement learning? Is the state transition in MDP stochastic ...
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34 views

How are the classical MDP and the object-oriented MDP views different?

I've been reading the attached paper - which aims to model entities in the world as objects, including the learning agent itself! To say the least, the goal is to navigate through what seems like a ...
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3answers
60 views

Why does it make sense to study MDPs with finite state and action spaces?

In the standard Markov Decision Process (MDP) formalization of the reinforcement-learning (RL) problem (Sutton & Barto, 1998), a decision maker interacts with an environment consisting of finite ...
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1answer
27 views

Can optimizing for immediate reward result in a policy maximizing the return?

The goal of a reinforcement learning agent is to maximize the expected return which is often a discounted sum of future rewards. The return indeed is a very noisy random variable as future rewards ...
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0answers
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Relationship between the reward rate and the sampled reward in a Semi-Markov Decision Process

In the paper: Reinforcement learning methods for continuous-time Markov decision problems, the authors provide the following update rule for the Q-learning algorithm, when applied to Semi-Markov ...
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2answers
122 views

Formula for expected rewards for state–action–next-state triples as a three-argument function

While reading about reinforcement learning, I have come across the following expression for expected rewards in terms of a summation, the denominator of which I am not able to account for. The ...
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0answers
22 views

How can I formalise a non-zero-sum game of $N$ agent as Markov game?

I coded a non-zero-sum game of $N$ agents in a discrete dynamic environment to RL with Q-learning and DQN agents. It's like a marathon. Only two actions are available per agent: $\{ G \text{ (move ...
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0answers
12 views

Posterior sampling reinforcement learning is not exploring enough

In posterior sampling reinforcement learning (PSRL), an agent maintains a "belief distribution" over MDPs. At the start of each episode, PSRL samples an MDP from this distribution, and then follows ...
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28 views

How is the state-visitation frequency computed in “Maximum Entropy Inverse Reinforcement Learning”?

I am trying to understand the formulation of the maximum entropy Inverse RL method by Brian Ziebart. Particularly, I am stuck on how to understand the computation of state - visitation frequencies. ...
3
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1answer
49 views

What is the intuition behind grid-based solutions to POMDPs?

After spending some time reading about POMDP, I'm still having a hard time understanding how grid-based solutions work. I understand the finite horizon brute-force solution, where you have your ...
2
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0answers
17 views

How should I define the reward function for the Connect Four game?

I'm creating an RL application for the game Connect Four. I've researched the different strategies for the game and which positions are more favourable to lead to a win. Should I be assigning ...
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0answers
28 views

Why can the core reinforcement learning algorithms be applied to POMDPs?

Why can an AI, like AlphaStar, work in StarCraft, although the environment is only partially observable? As far as I know, there are no theoretical results on RL in the POMDP environment, but it ...
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0answers
37 views

Efficient algorithm to obtain near optimal policies for an MDP

Given a discrete, finite Markov Decision Process (MDP) with its usual parameters $(S, A, T, R, \gamma)$, it is possible to obtain the optimal policy $\pi^{*}$ and the optimal value function $V^{*}$ ...
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0answers
13 views

What are the most common non-Markov RL paradigms?

I am interested in doing model-free RL but not using the Markov assumptions typical for MDPs or POMDPs. What are alternative paradigms that don't rely on the Markov assumptions? Are there any common ...
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0answers
22 views

How to draw backup diagram when reward is in expectation but next state is iterated?

I am working through Sutton and Barto's RL book. So far in the text, when backup diagrams are drawn, the reward and next state are iterated together (i.e. the equations always have $\sum_{s',r}$), ...
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1answer
37 views

Why isn't the implementation of my policy evaluation for a simple MDP converging?

I am trying to code out a policy evaluation algorithm to find the $V^\pi(s)$ for all states. The following diagram below shows the MDP. In this case i let p = q = 0.5. the rewards for each states ...
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1answer
37 views

How is the Markovian property consistent in reinforcement learning based scheduling?

In Reinforcement Learning, an MDP model incorporates the Markovian property. A lot of scheduling applications in a lot of disciplines use reinforcement learning (mostly deep RL) to learn scheduling ...
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0answers
38 views

How to understand and visualize a trained RL agent's policy when the state space is high dimensional?

What are typical ways to understand and visualize a trained RL agent's policy when the state space is of high dimension (but not images)? For example, suppose state and action are denoted by $s=(...
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1answer
42 views

Policy invariance under affine transformations of the reward function?

In the context of a Markov decision process, this paper says "it is well-known that the optimal policy is invariant to positive affine transformation of the reward function". On the other hand, ...
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1answer
140 views

How can I constraint the actions with dependent coordinates?

I am working on a customized RL environment where each action is represented as a tuple $a = (a_1,a_2,\cdots,a_n)$ such that certain condition must be satisfied for entries of $a$ (for instance, $a_1+...
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1answer
13 views

Unable to understand V* at infinite time horizon using Bellman equation for solving MDP

I've been following the Berkeley cs188's assignment (I'm not taking the course). Currently, they don't show the solution in the gradescope unless I get it correct. My reasoning was $V^*(a)$ = 10 ...
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0answers
42 views

Are there reinforcement learning algorithms not based on Markov decision processes?

Are all RL algorithms based on the MDP? If not, could you give examples of some which aren't? I've looked elsewhere, but I haven't seen it explicitly said.
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0answers
52 views

Formulation of a Markov Decision Process Problem

Given a list of $N$ questions. If question $i$ is answered correctly (given probability $p_i$), we receive reward $R_i$; if not the quiz terminates. Find the optimal order of questions to maximize ...
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0answers
36 views

Why is this Monte Carlo approach scalable for a growing number of states variables and action variables?

I am reading a research paper on the formulation of MDP problems to ICU treatment decision making: Treatment Recommendation in Critical Care: A Scalable and Interpretable Approach in Partially ...
6
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1answer
104 views

Interesting examples of discrete stochastic games

SGs are a generalization of MDPs to multiple agents. Like this previous question on MDPs, are there any interesting examples of zero-sum, discrete SGs—preferably with small state and action spaces? I'...
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62 views

What is the difference between value iteration and policy iteration? [duplicate]

In reinforcement learning, what is the difference between policy iteration and value iteration? As much as I understand, in value iteration, you use the Bellman equation to solve for the optimal ...
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0answers
32 views

How do I determine the optimal policy in a bandit problem with missing contexts?

Suppose I learn an optimal policy $\pi(a|c)$ for a contextual multi-armed bandit problem, where the context $c$ is a composite of multiple context variables $c = c_1, c_2, c_3$. For example, the ...
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0answers
20 views

Finding total number of states in a POMDP

I've been working on a question that is posed in a document I've been reading, that models qualifying for a job as a POMDP. In this model, a person takes 3 exams, and must pass all of them in order to ...
4
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1answer
80 views

How to assign rewards in a non-Markovian environment?

I am quite new to the Reinforcement Learning domain and I am curious about something. It seems to be the case that the majority of current research assumes Markovian environments, that is, future ...
2
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1answer
85 views

Solving a Multi-Armed, “Multi-Bandit” Problem

This is the problem: I have 66 slot-machines and for each of them I have 7 possible actions/arms to choose from. At each trial, I have to choose one of 7 actions for each and every one of the 66 slots....
2
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1answer
31 views

Why feed actions in later layer in Q network?

I read the DDPG paper, in which the authors state that the actions are fed only later to their Q network: Actions were not included until the 2nd hidden layer of Q. (Sec 7, Experiment Details) So ...
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0answers
98 views

What is the state of the art AI training technique for imperfect information 2 player turn based games?

As far as I can tell (correct me if I'm wrong), Alphazero (with MCTS and neural network heuristic function RL) is the state of the art training method for turn based, deterministic, perfect ...
2
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1answer
60 views

Markov property in maze solving problem in reinforcement learning

By definition, every state in RL has Markov property, which means that the future state depends only on the current state, not the past states. However, I saw that in some case we can define a state ...
3
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1answer
74 views

Why does having a fixed policy change a Markov Decision Process (MDP) to a Markov Reward Process (MRP)?

If a policy is fixed, it is said that an MDP becomes an MRP. Why is this so? Aren't the transitions and rewards still parameterized by the action and current state? In other words, aren't the ...
5
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1answer
39 views

Is the agent aware of a possible different set of actions for each state?

I have a use case where the set of actions is different for different states. Is the agent aware of what actions are valid for which states or is the agent only aware of the entire action space (in ...
3
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1answer
88 views

Can someone please help me validate my MDP?

Problem Statement : I have a system with four states - S1 through S4 where S1 is the beginning state and S4 is the end/terminal state. The next state is always better than the previous state i.e if ...
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0answers
38 views

Finding optimal Value function and Policy for an MDP

I am solving an RL MDP problem which is model based. I have an MDP which has four possible states S1-S4 and four different actions A1-A4, with S4 being terminal state and S1 is the beginning state. ...
6
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1answer
141 views

Benchmarks for reinforcement learning in discrete MDPs

To compare the performance of various algorithms for perfect information games, reasonable benchmarks include reversi and m,n,k-games (generalized tic-tac-toe). For imperfect information games, ...
3
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1answer
48 views

Can I have different rewards for a single action based on which state it transitions to?

I am working on an MDP where there are four states and ten actions. I am supposed to derive the optimal policy to reach the desired state. At any state, a particular action can take you to any of the ...
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0answers
15 views

Derivation for Value Iteration of CVaR

I am reading a paper named Risk-sensitive and Robust Decision-making: a CVaR Optimization Approach. In appendix A.3 they provide a proof for their Theorem $4$. The $n=1$ case for equation (11) is ...
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1answer
354 views

How to stay a up-to-date researcher in ML/RL community?

As a student who wants to work on machine learning, I would like to know how it is possible to start my studies and how to follow it to stay up-to-date. For example, I am willing to work on RL and MAB ...
4
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1answer
45 views

Why are state transitions in MDPs probabilistic rather than deterministic?

I've read that for MDPs the state transition function $P_a(s, s')$ is a probability. This seems strange to me for modeling because most environments (like video games) are deterministic. Now, I'd ...
5
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2answers
411 views

Why am I getting the incorrect value of lambda?

I am trying to solve for lambda using Temporal Difference Learning I am trying to figure out what lambda I need, to make TD(λ)=TD(1) but I get the incorrect value of lambda. Here is how I did: <...
5
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2answers
74 views

Reinforcement learning with uniformly random dynamics

Suppose I have an MDP $(S, A, p, R)$ where the $p(s_j|s_i,a_i)$ is uniform, i.e given an state $s_i$ and an action $a_i$ all states $s_j$ are equally probable. Now I want to find an optimal policy ...