5. Finally, after solving a large number of states, we found that the optimal guess to make in a state is often a possible solution to the state itself; that is, if a" is the argmin for a given state s, in Eq. (1), a majority of the time we observe that a* € s₁. As such, while iterating through actions, we first evaluate those that lie in s, first. The Algorithm In this subsection, we provide descriptions of the algorithm used to generate the transition function and corresponding probabilities, as well as the algorithm used to calculate V (s) with the aforementioned optimizations. Algorithm 1 Get Transition Information Input: State se, String action Output: Dictionary[Set-Float] next_states transition_info + Dict() for solutions, do tile_coloring get_coloring(action, solution) Stemp + Set() for temp_solution E s, do if is valid solution (action, tile_coloring, temp_solution) then Stemp-add (solution) end if end for transition info[Stemp]+= end for return transition info ▷ Coloring from action given solution We conclude this section by discussing the limits of feasibility. The current form of Wordle - with 6 rounds, 5 letter words, and a guess and solution space of sizes 10,657 and 2,315, respectively - took days to solve via an efficient C++ implementation of the algorithm, parallelized across a 64-core computer. From inspection of (1), we see that scalability is primarily dictated by the number of rounds, vocabulary size, and word length. Thus, for instance, if we were tasked with solving a variant of Wordle with 7 rounds, the current form of the algorithm would likely not scale (because of the exponential blow-up of (1)) and thus further optimizations would need to be implemented (such as constraining the policy to 5 or 6 rounds, or proving time-independence of the value function, which we do not do or use in this paper). However, increasing the vocabulary size within moderation would

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Concept explainers

Question

100%

What does the pseudocode for this algorithm in the image attached mean in plain English? (Algorithm 1 — the image attached came from a Computer Science whitepaper with keywords: [Exact] Dynamic Programming, Optimal Decision Trees, Reinforcement Learning, Artificial Intelligence, Interpretability). Please explain with either Python Java code if possible (or any programming language). Also, where can I find a reference that explains all the notation used in this pseudocode found in the image? I see this type of notation frequently but can’t find a key or a reference that explains what type of symbols these all are (except for a few of them which I know to be math symbols). Much of this notation I can’t find a reference to explain what it means anywhere, please advise and thanks in advance.

8
5. Finally, after solving a large number of states, we found that the optimal guess to make in a
state is often a possible solution to the state itself; that is, if a* is the argmin for a given state
s, in Eq. (1), a majority of the time we observe that a* € s₁. As such, while iterating through
actions, we first evaluate those that lie in s, first.
The Algorithm
In this subsection, we provide descriptions of the algorithm used to generate the transition function and
corresponding probabilities, as well as the algorithm used to calculate V (s) with the aforementioned
optimizations.
Algorithm 1 Get Transition Information
Input: State St, String action
Bertsimas and Paskov: An Ezact and Interpretable Solution to Wordle
Output: Dictionary[Set-Float] next_states
transition_info + Dict()
for solutions, do
tile_coloring get_coloring(action, solution)
Stemp + Set()
for temp_solution est do
end if
if is_valid_solution (action, tile_coloring, temp_solution) then
Stemp.add(solution)
end for
transition_info[Stemp] + =
end for
return transition_info
▷ Coloring from action given solution
We conclude this section by discussing the limits of feasibility. The current form of Wordle- with
6 rounds, 5 letter words, and a guess and solution space of sizes 10,657 and 2,315, respectively-
took days to solve via an efficient C++ implementation of the algorithm, parallelized across a 64-core
computer. From inspection of (1), we see that scalability is primarily dictated by the number of
rounds, vocabulary size, and word length. Thus, for instance, if we were tasked with solving a variant
of Wordle with 7 rounds, the current form of the algorithm would likely not scale (because of the
exponential blow-up of (1)) and thus further optimizations would need to be implemented (such as
constraining the policy to 5 or 6 rounds, or proving time-independence of the value function, which
we do not do or use in this paper). However, increasing the vocabulary size within moderation would

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions