Questions tagged [monte-carlo-methods]

For questions related to the Monte Carlo methods in reinforcement learning and other AI sub-fields. ("Monte Carlo" refers to random sampling of the search space.)

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12
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2answers
8k views

What is the difference between First-Visit Monte-Carlo and Every-Visit Monte-Carlo Policy Evaluation?

I came across this 2 algorithms but I cannot understand the difference between these 2 both in terms of implementation as well as intuitionally. So what difference does the second point in both the ...
8
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1answer
166 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 ...
6
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1answer
191 views

Is this proof of $\epsilon$-greedy policy improvement correct?

The text book being referred to, in this question is "Reinforcement Learning: An introduction" by Richard Sutton and Andrew Barto (second edition, 2018). For your convenience, I have ...
6
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2answers
874 views

What is the intuition behind TD($\lambda$)?

I'd like to better understand temporal-difference learning. In particular, I'm wondering if it is prudent to think about TD($\lambda$) as a type of "truncated" Monte Carlo learning?
6
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1answer
656 views

MCTS: How to choose the final action from the root

When the time allotted to Monte Carlo tree search runs out, what action should be chosen from the root? The original UCT paper (2006) says bestAction in their ...
5
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1answer
153 views

Why do we need importance sampling?

I was studying the off-policy policy improvement method. Then I encountered importance sampling. I completely understood the mathematics behind the calculation, but I am wondering what is the ...
5
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2answers
341 views

How can we compute the ratio between the distributions if we don't know one of the distributions?

Here is my understanding of importance sampling. If we have two distributions $p(x)$ and $q(x)$, where we have a way of sampling from $p(x)$ but not from $q(x)$, but we want to compute the expectation ...
5
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1answer
76 views

In MCTS, what to do if I do not want to simulate till the end of the game?

I'm trying to implement MCTS with UCT for a board game and I'm kinda stuck. The state space is quite large (3e15), and I'd like to compute a good move in less than 2 seconds. I already have MCTS ...
5
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1answer
69 views

Why didn't champion of the Go game manage to win the last game against AlphaGo, after winning the 4th one?

In the documentary about the match, it is said that after losing the 4th game, AlphaGo came back stronger and started to play in a weird way (not human-like) and it was pretty impossible to be beaten. ...
4
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1answer
92 views

What does the term $|\mathcal{A}(s)|$ mean in the $\epsilon$-greedy policy?

I've been looking online for a while for a source that explains these computations but I can't find anywhere what does the $|A(s)|$ mean. I guess $A$ is the action set but I'm not sure about that ...
4
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1answer
130 views

How do temporal-difference and Monte Carlo methods work, if they do not have access to model?

In value iteration, we have a model of the environment's dynamics, i.e $p(s', r \mid s, a)$, which we use to update an estimate of the value function. In the case of temporal-difference and Monte ...
4
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1answer
2k views

Why is GLIE Monte-Carlo control an on-policy control?

In slide 16 of his lecture 5 of the course "Reinforcement Learning", David Silver introduced GLIE Monte-Carlo Control. But why is it an on-policy control? The sampling follows a policy $\pi$ while ...
4
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1answer
89 views

How does policy evaluation work for continuous state space model-free approaches?

How does policy evaluation work for continuous state space model-free approaches? Theoretically, a model-based approach for the discrete state and action space can be computed via dynamic programming ...
3
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2answers
198 views

Why is the target called “target” in Monte Carlo and TD learning if it is not the true target?

I was going through Sutton's book and, using sample-based learning for estimating the expectations, we have this formula $$ \text{new estimate} = \text{old estimate} + \alpha(\text{target} - \text{old ...
3
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1answer
111 views

Is the expected value we sample in TD-learning action-value Q or state-value V?

Both MC and TD are model-free and they both follow a sample trajectory (in the case of TD, the trajectory is cut-short) to estimate the return (we basically are sampling Q values). Other than that, ...
3
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1answer
72 views

How is the incremental update rule derived from the weighted importance sampling in off-policy Monte Carlo control?

Here's the approximated value using weighted importance sampling $$ V_{n} \doteq \frac{\sum_{k=1}^{n-1} W_{k} G_{k}}{\sum_{k=1}^{n-1} W_{k}}, \quad n \geq 2 $$ Here's the incremental update rule for ...
3
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1answer
234 views

How does Monte Carlo have high variance?

I was going through David Silver's lecture on reinforcement learning (lecture 4). At 51:22 he says that Monte Carlo (MC) methods have high variance and zero bias. I understand the zero bias part. It ...
3
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1answer
137 views

Why Monte Carlo epsilon-soft approach cannot compute $\max Q(s,a)$?

I am new to Reinforcement learning and am currently reading up on the estimation of Q $\pi(s, a)$ values using MC epsilon-soft approach and chanced upon this algorithm. The link to the algorithm is ...
3
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1answer
228 views

In Monte Carlo learning, what do you do when an end state is reached, after having recorded the previously visited states and taken actions?

When you train a model using Monte Carlo-based learning the state and action taken at each step is recorded, and then at some point an end state is reached and the agent receives some reward - what do ...
3
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1answer
112 views

Why is Monte Carlo used as the tree search algorithm for AlphaGo?

Could a better algorithm other than Monte Carlo be used for the AlphaGo computer? Why didn't the DeepMind team think of choosing another kind of algorithm rather than spending time on their neural ...
3
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1answer
125 views

Why is an average of all returns used to update the value in the first-visit MC control?

In Sutton & Barto's Reinforcement Learning: An Introduction, in page 83 (101 of the pdf), there is a description of first-visit MC control. In the phase where they update $Q(s, a)$, they do an ...
3
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0answers
42 views

Why do we update $W$ with $\frac{1}{\mu (A_t | S_t)}$ instead of $\frac{\pi (A_t | S_t)}{\mu (A_t | S_t)}$ in off-policy Monte Carlo control?

I had the same question when I am reading the RL textbook from Sutton Bartol as posted here. Why do we update $W$ with $\frac{1}{\mu (A_t | S_t)}$ instead of $\frac{\pi (A_t | S_t)}{\mu (A_t | S_t)}$?...
2
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1answer
90 views

Into which subcategories can reinforcement learning be divided?

In the course of a scientific work, I will discuss the different types of reinforcement learning. However, I have difficulties to find these different types. So, into which subcategories can ...
2
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2answers
156 views

With Monte Carlo off-policy learning what do we correct by using importance sampling?

I do not understand the link of importance sampling to Monte Carlo off-policy learning. We estimate a value using sampling on whole episodes, and we take these values to construct the target policy. ...
2
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1answer
133 views

In what RL algorithm category is MiniMax?

Q-learning is a temporal-difference method and Monte Carlo tree search is a Monte Carlo method. In what category is MiniMax?
2
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1answer
1k views

Monte-Carlo, every-visit gridworld, exploring starts, python code gets stuck in foreverloop in episode generation

I've been trying to implement policy improvement for Q(s,a) function as per Sutton&Barto reinforcement learning book. The original algorithm with first-visit MonteCarlo is pictured below. I ...
2
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1answer
129 views

Do we need the transition probability function when calculating the importance sampling ratio?

I am reading the book titled "Reinforcement Learning: An Introduction" (by Sutton and Barto). I am at chapter 5, which is about Monte Carlo methods, but now I am quite confused. There is one thing I ...
2
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1answer
320 views

What is the bias-variance trade-off in reinforcement learning?

I am watching DeepMind's video lecture series on reinforcement learning, and when I was watching the video of model-free RL, the instructor said the Monte Carlo methods have less bias than temporal-...
2
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1answer
121 views

What does the figure “Blackjack Value Function…” from Sutton represent?

I came across this graph in David Silver's youtube lecture and Sutton's book on reinforcement learning. Can anyone help me understand the graph? From the graph, for 10000 episodes what i see is ...
2
votes
1answer
310 views

What is the relation between Monte Carlo and model-free algorithms?

Monte Carlo (MC) methods are methods that use some form of randomness or sampling. For example, we can use an MC method to approximate the area of a circle inside a square: we generate random 2D ...
2
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1answer
54 views

In off-policy MC control algorithm by Sutton & Barto, why do we perform a last update when sample action is inconsistent with target policy?

I have a question about the $W$ term in the off-policy MC control algorithm on Page 111 of Sutton & Barto. I have also included it in the figure below. My question: shouldn't the check $A_{t} = \...
2
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2answers
382 views

How does Monte Carlo Exploring Starts work?

I'm having trouble understanding the 5th step in the flowchart. For the 5th step, the 'update the Q function by taking the average of returns' is confusing. From what I understand, the Q function ...
2
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1answer
80 views

Similarities and differences between UCT algorithms in (i), (ii), (iii) and (iv)?

I am trying to understand the similarities and differences between: (i) the UCT algorithm in Kocsis and Szepesvári (2006); (ii) the UCT algorithm in Section 3.3 of Browne et al (2012); (iii) the MCTS ...
2
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0answers
61 views

How can I use Monte Carlo Dropout in a pre-trained CNN model?

In Monte Carlo Dropout (MCD), I know that I should enable dropout during training and testing, then get multiple predictions for the same input $x$ by performing multiple forward passes with $x$, then,...
2
votes
1answer
183 views

How to apply hyperparameter optimization on Monte Carlo Tree Search?

I have a basic MCTS agent for the game of Hex (a turn based game). I want to tune the parameters of UCT (the Cp parameter) and the number of rollouts parameter. Where do I have to begin? The problem ...
2
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0answers
41 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 ...
2
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0answers
43 views

How to show Monte Carlo methods converge to an estimate which minimizes mean squared error?

In chapter six of Sutton and Barto (p.128), they claim Monte Carlo methods converge to an estimate minimizing the mean squared error. How can this be shown formally? Bump
2
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1answer
288 views

How is Monte Carlo different from model-based methods?

I was going through an article where it is mentioned: The Monte-Carlo methods require only knowledge base (history/past experiences)—sample sequences of (states, actions and rewards) from the ...
2
votes
2answers
116 views

How to stop evaluation phase in reinforcement learning with epsilon-greedy Monte Carlo agent?

I have implemented an epsilon-greedy Monte Carlo reinforcement learning agent like suggested in Sutton and Barto's RL book (page 101). As far as I understood epsilon-greedy agents so far, the ...
2
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0answers
18 views

How is GARB implemented in PGRD-DL to calculate gradients w.r.t. internal rewards?

In section 3 of this paper the author outlines how GARB was adapted to reduce the variance in updating parameters to an internal reward function estimator. I have read it a number of times and ...
2
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0answers
413 views

Difficulty understanding Monte Carlo policy evaluation (state-value) for gridworld

I've been trying to read Sutton & Barto book chapter 5.1, but I'm still a bit confused about the procedure of using Monte Carlo policy evaluation (p.92), and now I just cant proceed anymore coding ...
1
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1answer
120 views

Why does Monte Carlo policy evaluation relies on action-value function rather than state-value function?

Here is David Silver's lecture on that. Look at 9:30 to 10:30. He says that, since it is model-free learning, the environment's dynamics are unknown, so the action-value function $Q$ is used. But ...
1
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1answer
49 views

When showing that the policy improvement theorem applies to MC control, why is $q_{\pi_{k}}\left(s, \pi_{k}(s)\right) \geq v_{\pi_{k}}(s)$ true?

When discussing why the policy improvement theorem is true, when we do Monte Carlo control by updating greedily, it says on page 98 of Sutton and Barto's book (2nd edition) that: $$ \begin{aligned} ...
1
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1answer
58 views

When updating the state-action value in the Monte Carlo method, is the return the same for each state-action pair?

Referring to this post, in the following formula to update the state-action value $$ Q(s,a) = Q(s,a) + \alpha (G − Q(s,a)),$$ is the value of $G$ (the return) the same for every state-action $(s,a)$ ...
1
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1answer
94 views

Why are state-values alone not sufficient in determining a policy (without a model)?

"If a model is not available, then it is particularly useful to estimate action values (the values of state-action pairs) rather than state values. With a model, state values alone are sufficient ...
1
vote
1answer
52 views

Understanding the W term in off policy monte carlo learning

In Sutton and Barto's RL textbook they included the following pseudocode for off policy Monte Carlo learning. I am a little confused, however, because to me it looks like the W term will become ...
1
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1answer
38 views

In the cross-entropy method, should I select state-action pairs by their immediate reward or by the episode reward?

I am trying to understand the code mechanics when selecting the elite states and elite actions. It appears clear to me that they are those that appear in the episodes with the rewards bigger than the ...
1
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1answer
118 views

How exactly is Monte Carlo counterfactual regret minimization with external sampling implemented?

I have read many papers, such as this or this, explaining how external sampling works, but I still don't understand how the algorithm works. I understand you divide $Q$, which is the set of all ...
1
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1answer
74 views

Unclear definition of a “leaf” and diverging UTC values in the Monte Carlo Tree Search

I have two questions regarding the Selection and Expansion steps in the Monte Carlo Tree Search Algorithm. In order to state the questions, I recall the algorithm that I believe is the one most ...
1
vote
1answer
70 views

AI to play a solo card game

I would like to create an AI for the 1 player version of the card game called "The Game" by Steffen Benndorf (rules here: https://nsv.de/wp-content/uploads/2018/05/the-game-english.pdf). The ...