7 Commits

Author SHA1 Message Date
Arthur Lu
f40301cac9 delete gym-wordle, fix some issues in letter_guess gym, add wandb integration 2024-03-19 16:49:01 -07:00
Ethan Shapiro
fc197acb6e started new letter guess environment 2024-03-19 11:52:10 -07:00
Ethan Shapiro
e799c14ece new reward scheme 2024-03-18 11:25:14 -07:00
Ethan Shapiro
bbe9a1891c updated wordle to gymnasium env 2024-03-15 18:19:58 -07:00
Arthur Lu
9172326013 upload wordle env, fix indexing issue in wordle env, attempt to improve reward (no improvement) 2024-03-14 16:47:11 -07:00
Arthur Lu
4836be8121 remove debug prints 2024-03-14 15:00:19 -07:00
Arthur Lu
5672169073 copy the wordle env locally and fix the obs return 2024-03-14 14:49:17 -07:00
13 changed files with 392055 additions and 47 deletions

4
.gitignore vendored
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@@ -1,2 +1,6 @@
**/data/* **/data/*
**/*.zip **/*.zip
**/__pycache__
/env
**/runs/*
**/wandb/*

2996
dqn_letter_gssr.ipynb Normal file

File diff suppressed because it is too large Load Diff

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@@ -2,64 +2,308 @@
"cells": [ "cells": [
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": 1,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"import gym\n", "import gym\n",
"import gym_wordle\n", "import gym_wordle\n",
"from stable_baselines3 import DQN\n", "from stable_baselines3 import DQN, PPO, common\n",
"import numpy as np\n", "import numpy as np\n",
"import tqdm" "import tqdm"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": 2,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<Monitor<WordleEnv instance>>\n"
]
}
],
"source": [ "source": [
"env = gym.make(\"Wordle-v0\")\n", "env = gym_wordle.wordle.WordleEnv()\n",
"env = common.monitor.Monitor(env)\n",
"\n", "\n",
"print(env)" "print(env)"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 35, "execution_count": 3,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using cuda device\n",
"Wrapping the env in a DummyVecEnv.\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "6921a0721569456abf5bceac7e7b6b34",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Output()"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"----------------------------------\n",
"| rollout/ | |\n",
"| ep_len_mean | 4.97 |\n",
"| ep_rew_mean | -63.8 |\n",
"| exploration_rate | 0.05 |\n",
"| time/ | |\n",
"| episodes | 10000 |\n",
"| fps | 1628 |\n",
"| time_elapsed | 30 |\n",
"| total_timesteps | 49995 |\n",
"----------------------------------\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"----------------------------------\n",
"| rollout/ | |\n",
"| ep_len_mean | 5 |\n",
"| ep_rew_mean | -70.5 |\n",
"| exploration_rate | 0.05 |\n",
"| time/ | |\n",
"| episodes | 20000 |\n",
"| fps | 662 |\n",
"| time_elapsed | 150 |\n",
"| total_timesteps | 99992 |\n",
"| train/ | |\n",
"| learning_rate | 0.0001 |\n",
"| loss | 11.7 |\n",
"| n_updates | 12497 |\n",
"----------------------------------\n"
]
},
{
"data": {
"text/html": [
"<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
],
"text/plain": []
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
"</pre>\n"
],
"text/plain": [
"\n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"<stable_baselines3.dqn.dqn.DQN at 0x1bfd6cc0210>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [ "source": [
"total_timesteps = 100000\n", "total_timesteps = 100_000\n",
"model = DQN(\"MlpPolicy\", env, verbose=0)\n", "model = DQN(\"MlpPolicy\", env, verbose=1, device='cuda')\n",
"model.learn(total_timesteps=total_timesteps, progress_bar=True)" "model.learn(total_timesteps=total_timesteps, log_interval=10_000, progress_bar=True)"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": null, "execution_count": 4,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"def test(model):\n", "model.save(\"dqn_new_state\")"
"\n", ]
" end_rewards = []\n", },
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"c:\\Repository\\cse151b-final-project\\env\\Lib\\site-packages\\stable_baselines3\\common\\save_util.py:166: UserWarning: Could not deserialize object lr_schedule. Consider using `custom_objects` argument to replace this object.\n",
"Exception: code() argument 13 must be str, not int\n",
" warnings.warn(\n",
"c:\\Repository\\cse151b-final-project\\env\\Lib\\site-packages\\stable_baselines3\\common\\save_util.py:166: UserWarning: Could not deserialize object exploration_schedule. Consider using `custom_objects` argument to replace this object.\n",
"Exception: code() argument 13 must be str, not int\n",
" warnings.warn(\n"
]
}
],
"source": [
"# model = DQN.load(\"dqn_wordle\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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" 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 0. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
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" 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 1.\n",
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" 0. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
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" 1. 1. 0. 0. 0. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 1. 1. 0. 0. 0. 0. 0. 0. 0.\n",
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" 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
" 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
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" 1. 1. 1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 1.\n",
" 1. 1. 1. 1. 1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0.\n",
" 0. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
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"[1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 1. 1. 1.\n",
" 1. 1. 1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 1.\n",
" 1. 1. 1. 1. 1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 0.\n",
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" 1. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 0. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0.\n",
" 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
"0\n"
]
}
],
"source": [
"env = gym_wordle.wordle.WordleEnv()\n",
"\n", "\n",
"for i in range(1000):\n", "for i in range(1000):\n",
" \n", " \n",
" state = env.reset()\n", " state, info = env.reset()\n",
"\n", "\n",
" done = False\n", " done = False\n",
"\n", "\n",
" wins = 0\n",
"\n",
" while not done:\n", " while not done:\n",
"\n", "\n",
" action, _states = model.predict(state, deterministic=True)\n", " action, _states = model.predict(state, deterministic=True)\n",
"\n", "\n",
" state, reward, done, info = env.step(action)\n", " state, reward, done, truncated, info = env.step(action)\n",
"\n", "\n",
" end_rewards.append(reward == 0)\n", " print(state)\n",
" if info[\"correct\"]:\n",
" wins += 1\n",
"\n", "\n",
" return np.sum(end_rewards) / len(end_rewards)" "print(wins)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([1., 0., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
" 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 0., 1., 1.,\n",
" 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
" 1., 1., 0., 1., 1., 1., 0., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
" 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 0., 1., 1., 1., 0., 1.,\n",
" 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
" 1., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
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" 0., 0., 0., 0., 0., 0., 0., 1.]),\n",
" -50)"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"state, reward"
] ]
}, },
{ {
@@ -67,27 +311,7 @@
"execution_count": null, "execution_count": null,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": []
"model.save(\"dqn_wordle\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"model = DQN.load(\"dqn_wordle\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"print(test(model))"
]
} }
], ],
"metadata": { "metadata": {
@@ -106,7 +330,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.10" "version": "3.11.5"
} }
}, },
"nbformat": 4, "nbformat": 4,

129
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@@ -0,0 +1,129 @@
# Byte-compiled / optimized / DLL files
__pycache__/
*.py[cod]
*$py.class
# C extensions
*.so
# Distribution / packaging
.Python
build/
develop-eggs/
dist/
downloads/
eggs/
.eggs/
lib/
lib64/
parts/
sdist/
var/
wheels/
pip-wheel-metadata/
share/python-wheels/
*.egg-info/
.installed.cfg
*.egg
MANIFEST
# PyInstaller
# Usually these files are written by a python script from a template
# before PyInstaller builds the exe, so as to inject date/other infos into it.
*.manifest
*.spec
# Installer logs
pip-log.txt
pip-delete-this-directory.txt
# Unit test / coverage reports
htmlcov/
.tox/
.nox/
.coverage
.coverage.*
.cache
nosetests.xml
coverage.xml
*.cover
*.py,cover
.hypothesis/
.pytest_cache/
# Translations
*.mo
*.pot
# Django stuff:
*.log
local_settings.py
db.sqlite3
db.sqlite3-journal
# Flask stuff:
instance/
.webassets-cache
# Scrapy stuff:
.scrapy
# Sphinx documentation
docs/_build/
# PyBuilder
target/
# Jupyter Notebook
.ipynb_checkpoints
# IPython
profile_default/
ipython_config.py
# pyenv
.python-version
# pipenv
# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
# However, in case of collaboration, if having platform-specific dependencies or dependencies
# having no cross-platform support, pipenv may install dependencies that don't work, or not
# install all needed dependencies.
#Pipfile.lock
# PEP 582; used by e.g. github.com/David-OConnor/pyflow
__pypackages__/
# Celery stuff
celerybeat-schedule
celerybeat.pid
# SageMath parsed files
*.sage.py
# Environments
.env
.venv
env/
venv/
ENV/
env.bak/
venv.bak/
# Spyder project settings
.spyderproject
.spyproject
# Rope project settings
.ropeproject
# mkdocs documentation
/site
# mypy
.mypy_cache/
.dmypy.json
dmypy.json
# Pyre type checker
.pyre/

11
eric_wordle/README.md Normal file
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@@ -0,0 +1,11 @@
# N-dle Solver
A solver designed to beat New York Time's Wordle (link [here](https://www.nytimes.com/games/wordle/index.html)). If you are bored enough, can extend to solve the more general N-dle problem (for quordle, octordle, etc.)
I originally made this out of frustration for the game (and my own lack of lingual talent). One day, my friend thought she could beat my bot. To her dismay, she learned that she is no better than a machine. Let's see if you can do any better (the average number of attempts is 3.6).
## Usage:
1. Run `python main.py --n 1`
2. Follow the prompts
Currently only supports solving for 1 word at a time (i.e. wordle).

126
eric_wordle/ai.py Normal file
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@@ -0,0 +1,126 @@
import re
import string
import numpy as np
class AI:
def __init__(self, vocab_file, num_letters=5, num_guesses=6):
self.vocab_file = vocab_file
self.num_letters = num_letters
self.num_guesses = 6
self.vocab, self.vocab_scores, self.letter_scores = self.get_vocab(self.vocab_file)
self.best_words = sorted(list(self.vocab_scores.items()), key=lambda tup: tup[1])[::-1]
self.domains = None
self.possible_letters = None
self.reset()
def solve(self):
num_guesses = 0
while [len(e) for e in self.domains] != [1 for _ in range(self.num_letters)]:
num_guesses += 1
word = self.sample()
# # Always start with these two words
# if num_guesses == 1:
# word = 'soare'
# elif num_guesses == 2:
# word = 'culti'
print('-----------------------------------------------')
print(f'Guess #{num_guesses}/{self.num_guesses}: {word}')
print('-----------------------------------------------')
self.arc_consistency(word)
print(f'You did it! The word is {"".join([e[0] for e in self.domains])}')
def arc_consistency(self, word):
print(f'Performing arc consistency check on {word}...')
print(f'Specify 0 for completely nonexistent letter at the specified index, 1 for existent letter but incorrect index, and 2 for correct letter at correct index.')
results = []
# Collect results
for l in word:
while True:
result = input(f'{l}: ')
if result not in ['0', '1', '2']:
print('Incorrect option. Try again.')
continue
results.append(result)
break
self.possible_letters += [word[i] for i in range(len(word)) if results[i] == '1']
for i in range(len(word)):
if results[i] == '0':
if word[i] in self.possible_letters:
if word[i] in self.domains[i]:
self.domains[i].remove(word[i])
else:
for j in range(len(self.domains)):
if word[i] in self.domains[j] and len(self.domains[j]) > 1:
self.domains[j].remove(word[i])
if results[i] == '1':
if word[i] in self.domains[i]:
self.domains[i].remove(word[i])
if results[i] == '2':
self.domains[i] = [word[i]]
def reset(self):
self.domains = [list(string.ascii_lowercase) for _ in range(self.num_letters)]
self.possible_letters = []
def sample(self):
"""
Samples a best word given the current domains
:return:
"""
# Compile a regex of possible words with the current domain
regex_string = ''
for domain in self.domains:
regex_string += ''.join(['[', ''.join(domain), ']', '{1}'])
pattern = re.compile(regex_string)
# From the words with the highest scores, only return the best word that match the regex pattern
for word, _ in self.best_words:
if pattern.match(word) and False not in [e in word for e in self.possible_letters]:
return word
def get_vocab(self, vocab_file):
vocab = []
with open(vocab_file, 'r') as f:
for l in f:
vocab.append(l.strip())
# Count letter frequencies at each index
letter_freqs = [{letter: 0 for letter in string.ascii_lowercase} for _ in range(self.num_letters)]
for word in vocab:
for i, l in enumerate(word):
letter_freqs[i][l] += 1
# Assign a score to each letter at each index by the probability of it appearing
letter_scores = [{letter: 0 for letter in string.ascii_lowercase} for _ in range(self.num_letters)]
for i in range(len(letter_scores)):
max_freq = np.max(list(letter_freqs[i].values()))
for l in letter_scores[i].keys():
letter_scores[i][l] = letter_freqs[i][l] / max_freq
# Find a sorted list of words ranked by sum of letter scores
vocab_scores = {} # (score, word)
for word in vocab:
score = 0
for i, l in enumerate(word):
score += letter_scores[i][l]
# # Optimization: If repeating letters, deduct a couple points
# if len(set(word)) < len(word):
# score -= 0.25 * (len(word) - len(set(word)))
vocab_scores[word] = score
return vocab, vocab_scores, letter_scores

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import string
import numpy as np
words = []
with open('words.txt', 'r') as f:
for l in f:
words.append(l.strip())
# Count letter frequencies at each index
letter_freqs = [{letter: 0 for letter in string.ascii_lowercase} for _ in range(5)]
for word in words:
for i, l in enumerate(word):
letter_freqs[i][l] += 1
# Assign a score to each letter at each index by the probability of it appearing
letter_scores = [{letter: 0 for letter in string.ascii_lowercase} for _ in range(5)]
for i in range(len(letter_scores)):
max_freq = np.max(list(letter_freqs[i].values()))
for l in letter_scores[i].keys():
letter_scores[i][l] = letter_freqs[i][l] / max_freq
# Find a sorted list of words ranked by sum of letter scores
word_scores = [] # (score, word)
for word in words:
score = 0
for i, l in enumerate(word):
score += letter_scores[i][l]
word_scores.append((score, word))
sorted_by_second = sorted(word_scores, key=lambda tup: tup[0])[::-1]
print(sorted_by_second[:10])
for i, (score, word) in enumerate(sorted_by_second):
if word == 'soare':
print(f'{word} with a score of {score} is found at index {i}')

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import argparse
from ai import AI
def main(args):
if args.n is None:
raise Exception('Need to specify n (i.e. n = 1 for wordle, n = 4 for quordle, n = 16 for sedecordle).')
ai = AI(args.vocab_file)
ai.solve()
if __name__ == '__main__':
parser = argparse.ArgumentParser()
parser.add_argument('--n', dest='n', type=int, default=None)
parser.add_argument('--vocab_file', dest='vocab_file', type=str, default='wordle_words.txt')
args = parser.parse_args()
main(args)

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import pandas
print('Loading in words dictionary; this may take a while...')
df = pandas.read_json('words_dictionary.json')
print('Done loading words dictionary.')
words = []
for word in df.axes[0].tolist():
if len(word) != 5:
continue
words.append(word)
words.sort()
with open('words.txt', 'w') as f:
for word in words:
f.write(word + '\n')

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letter_guess.py Normal file
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import gymnasium as gym
from gymnasium import spaces
import numpy as np
import random
import re
class LetterGuessingEnv(gym.Env):
"""
Custom Gymnasium environment for a letter guessing game with a focus on forming
valid prefixes and words from a list of valid Wordle words. The environment tracks
the current guess prefix and validates it against known valid words, ending the game
early with a negative reward for invalid prefixes.
"""
metadata = {'render_modes': ['human']}
def __init__(self, valid_words, seed=None):
self.action_space = spaces.Discrete(26)
self.observation_space = spaces.Box(low=0, high=1, shape=(26*2 + 26*4,), dtype=np.int32)
self.valid_words = valid_words # List of valid Wordle words
self.target_word = '' # Target word for the current episode
self.valid_words_str = ' '.join(self.valid_words) + ' '
self.letter_flags = None
self.letter_positions = None
self.guessed_letters = set()
self.guess_prefix = "" # Tracks the current guess prefix
self.reset()
def step(self, action):
letter_index = action % 26 # Assuming action is the letter index directly
position = len(self.guess_prefix) # The next position in the prefix is determined by its current length
letter = chr(ord('a') + letter_index)
reward = 0
done = False
# Check if the letter has already been used in the guess prefix
if letter in self.guessed_letters:
reward = -1 # Penalize for repeating letters in the prefix
else:
# Add the new letter to the prefix and update guessed letters set
self.guess_prefix += letter
self.guessed_letters.add(letter)
# Update letter flags based on whether the letter is in the target word
if self.target_word[position] == letter:
self.letter_flags[letter_index, :] = [1, 0] # Update flag for correct guess
elif letter in self.target_word:
self.letter_flags[letter_index, :] = [0, 1] # Update flag for correct guess wrong position
else:
self.letter_flags[letter_index, :] = [0, 0] # Update flag for incorrect guess
reward = 1 # Reward for adding new information by trying a new letter
# Update the letter_positions matrix to reflect the new guess
if position == 4:
self.letter_positions[:,:] = 1
else:
self.letter_positions[:, position] = 0
self.letter_positions[letter_index, position] = 1
# Use regex to check if the current prefix can lead to a valid word
if not re.search(r'\b' + self.guess_prefix, self.valid_words_str):
reward = -5 # Penalize for forming an invalid prefix
done = True # End the episode if the prefix is invalid
# guessed a full word so we reset our guess prefix to guess next round
if len(self.guess_prefix) == len(self.target_word):
self.guess_prefix = ''
self.round += 1
# end after 5 rounds of total guesses
if self.round == 2:
# reward = 5
done = True
obs = self._get_obs()
if reward < -50:
print(obs, reward, done)
return obs, reward, done, False, {}
def reset(self, seed=None):
self.target_word = random.choice(self.valid_words)
# self.target_word_encoded = self.encode_word(self.target_word)
self.letter_flags = np.ones((26, 2), dtype=np.int32)
self.letter_positions = np.ones((26, 4), dtype=np.int32)
self.guessed_letters = set()
self.guess_prefix = "" # Reset the guess prefix for the new episode
self.round = 1
return self._get_obs(), {}
def encode_word(self, word):
encoded = np.zeros((26,))
for char in word:
index = ord(char) - ord('a')
encoded[index] = 1
return encoded
def _get_obs(self):
return np.concatenate([self.letter_flags.flatten(), self.letter_positions.flatten()])
def render(self, mode='human'):
pass # Optional: Implement rendering logic if needed

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