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Questions tagged [monte-carlo]

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How to find the best exploration parameter in a Monte Carlo tree search?

I've developed a Monte Carlo tree search algorithm in checkers. Here is my question. What should be the value of $C$, the exploration parameter in the following formula described in Monte Carlo Tree ...
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88 views

Is MCTS an appropriate method for this problem size (large action/state space)?

I'm doing a research on a finite horizon decision problem 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 state $s(t)...
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1answer
43 views

How to decrease the confidence of a Monte Carlo algorithm in its answer?

Recall that a Monte Carlo algorithm is $p$-correct if it outputs a correct answer with probability at least $p$. In the case of decision problems, where the answer is binary, repeating the MC ...
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1answer
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Monte Carlo Algorithms : Are there any problems where two opposite Monte Carlo algorithms could solve it?

I started reading on Probabilistic algorithms and Monte-Carlo algorithms. Since a Monte-Carlo can only give a certain answer for either True or False, I was wondering if it's conceivable that for the ...
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39 views

Randomly construct linear combination that is within bounds over two basis

Given rank deficient matrix $A$, I want to randomly construct vectors $\vec{x}$ such that: $0 \le x_{j} \le 1$ $0 \le b_{j} \le 1$ where $\vec{b} = A\vec{x}$ Matrix $A$ is about 10 x 15. I want to ...
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58 views

Understanding On-policy First Visit Monte Carlo Control algorithm

I am going through the Monte Carlo methods, and it's going fine until now. However, I am actually studying the On-Policy First Visit Monte Carlo control for epsilon soft policies, which allows us to ...
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1answer
41 views

Pi approximation with Montecarlo: Why not just evenly distributed points?

With the randomised algorithm for Pi approximation (see https://www.geeksforgeeks.org/estimating-value-pi-using-monte-carlo/ ), I keep wondering why just using points with an even distance should'n ...
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Generate a random magic square on a large field

If consecutive natural numbers 1 .. n^2 are placed in a n*n grid so that sum of numbers in each column and in each row is a constant then we call it a magic square. I would like to generate magic ...
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How do you protect an AI from a human doing “illogical” moves?

Using a monte carlo approach and evalutation function. Some moves will deemed to be more advantageous than others. As a computer plays itself, it will generally go for the best moves possible. And ...
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1answer
293 views

What is the difference between Simulated Annealing and Monte-Carlo Simulations?

What is the difference between Simulated Annealing and Monte-Carlo Simulations? Is Simulated Annealing a specific type of Monte-Carlo simulation, or are they completely separate techniques?
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1answer
76 views

Do Nested Monte Carlo Algorithm always find the best score where score is the number of moves on the leftmost path

I am studying Nested Monte Carlo Algorithm addressing the problem of guiding the search toward better states when there is no available heuristic. It uses nested levels of random games in order ...
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260 views

How to estimate how many assignments satisfy a given DNF formula using Monte Carlo?

Admittedly, homework. For the purpose of this question: $\phi$ is a DNF formula similar to this one: $(x_1 \wedge \neg x_3 \wedge x_4) \vee (\neg x_1 \wedge x_2)$ Also $C_i$ is a clause in this ...
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1answer
188 views

What is partial expansion in Monte Carlo Tree Search?

I'm trying to understand the modification to the MCTS algorithm called Partial Expansion. From what I've been reading it enables one to not require all child nodes to have been expanded before ...
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1answer
2k views

Monte Carlo: what is a seed?

I have reached a chapter in the notes I am following where a program written in C++ is using a Monte Carlo method to estimate $\pi$. It mentions a 'seed', but does not say what this is. I have tried ...
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Card Shuffling, Bounding Mixing time using Paths and Flows

I've been struggling with a problem that is very similar to a 2014 question posted here. The question in particular is 3(1) and 3(2). To paraphrase, we are supposed to use paths and an encoding ...
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2answers
99 views

Monte Carlo algorithm: Element in array

Design a Monte Carlo algorithm that checks in constant time if a given element $x$ is in a $n$-dimensional vector $V$. Calculate the probability for a correct answer. Then suppose $n=10$, how many ...
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37 views

Not grasping Bayesian Monte Carlo

I've read several sources of information that describe the process of Bayesian Monte Carlo Quadrature but am just not understanding the details enough to be able to implement it. For instance two ...
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1answer
1k views

Generating values from a probability density function

If I have a probability density function, some f(x) which is >= 0 everywhere and integrates to 1, is there a method to generate random numbers using that PDF? I know there is the box-muller transform ...
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1answer
121 views

Monte Carlo Tree Search in connect 5 tree design

I'm trying to create a mcts ai for connect 5 algorithm. However, I'm confused on designing the tree. Here is a quick description of the algorithm: The initial state, S0 is the board state where the ...
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1answer
500 views

How does MCTS handle games with large numbers of poor moves?

I am trying to understand how pure Monte Carlo tree search (https://en.wikipedia.org/wiki/Monte_Carlo_tree_search) handles games where random playout will likely result in a loss easily avoided by ...
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2answers
148 views

UCT1 Algorithm: What does “total number of simulations” mean?

When reading up on the UCT1 algorithm (I'm writing a Monte Carlo tree search), I'm having trouble with the formula. $$\frac{w_i}{n_i} + \sqrt{\frac{\ln t}{n_i}}$$ Wikipedia, this guy, and this guy all ...
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336 views

How does the Monte Carlo Tree Search Algorithm Decide When to Expand?

I understand that the MCTS algorithm expands its tree after it has selected the best route to take. However, how does it decide when to end selection and then expand the tree? It cannot just traverse ...
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What did Dijkstra think about Monte Carlo algorithms? [closed]

In A Discipline of Programming, Dijkstra wrote: Two circumstances have changed the scene since then.* The one is the insight that, even in the case of fully deterministic machines, program testing ...
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1answer
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How can we get a Las Vegas algorithm from a Monte Carlo one?

I am trying to solve some exercises on random algorithms from this book, randomized algorithms. This is not a homework. I am only trying to improve my skills. Here is the exercise: Exercise 1.3: ...
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1answer
451 views

How do multiple branches from one node occur with the Monte Carlo Tree Search?

I think I understand the Monte Carlo Tree search. It goes through the tree until it reaches a leaf node, where it branches (creates a child node). However, the branching only occurs at the leaf nodes (...
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What use does the predictor stage in a particle filter have?

Im a bit confused about the particle filter. I understand the generic particle filter algorithm but in some literature say particle filter has predictor stage which is not mentioned in the generic ...
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1answer
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What is a proper way of solving a multibody nonlinear problem?

I encountered some system of ~5000 random nodes connected by ~8000 non-hookean springs, with ~1300 nodes at the boundary fixed as the "wall", the potential of the springs are of the form $dx*e^{(dx/a)}...
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1answer
355 views

Approximate Bayesian Computation VS Monte Carlo Simulation

I am a little confused about the differences between Approximation Bayesian Computation (ABC) and Monte Carlo Methods (MCM). Citing from wikipedia: Approximate Bayesian computation (ABC) ...
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1answer
66 views

How to simulate this randomized “finite” sum? [closed]

Consider the the Geometric Brownian motion $\qquad dX_t=\mu X_t dt+\sigma X_t dW_t$, with $X_0=1$, $\mu=0.2$, and $\sigma=0.30$. for each $n=1,2,3,..$ let $h_n=1/n$, and let $X^n_n$ be the final ...
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2answers
265 views

Adversarial Monte Carlo Tree Search Asymmetry

Monte Carlo Tree Search with UCT is praised for it's asymmetric tree growth, growing promising subtrees more than non-promising ones. But in a 2-player adversarial game, when a win at one node is a ...
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1answer
106 views

Minimizing total distance to a point from a set of points

I've read about a problem: There are $n$ houses that are placed randomly. Place a parking lot so that the (straight-line) distance to all houses is minimal. I've written a Monte-Carlo algorithm, ...
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1answer
2k views

Algorithm for finding best combination of elements

Say I have a very large, arbitrary number of variables, each of which I can assign to be type A, B, or C. The types come with expenses: Type A's are the least expensive, and C's are the most ...
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1answer
169 views

Do RP algorithms exist?

I think I understand the RP complexity class (along with coRP, BPP, and ZPP). However, I can't seem to think of how an RP algorithm might be formulated. How can the random coin flip possibilities ...
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1answer
713 views

Understanding Monte Carlo Probabilities

I am trying to get a good grasp on Monte Carlo (MC) algorithms, but I feel I am missing something fundamental. What I don't understand is how MC improves its confidence of giving the correct solution ...
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1answer
123 views

Advantage of the Monte Carlo method over a regular periodic sampling [closed]

I am unclear on when to use the Monte Carlo random sampling method for algorithm design. The classic example that I keep seeing is using random points within some bounding rectangle to determine the ...