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7248ace | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 | import numpy as np
HORIZON = 400
FULL_TIME = 60
FEEDBACK_STEPS = 3
MAX_ANSWERS = (HORIZON + FEEDBACK_STEPS) // (FEEDBACK_STEPS + 1)
class BMathEnvironment:
score_cap = 57 * MAX_ANSWERS * (MAX_ANSWERS + 1) // 2
def __init__(self, sticky_action_prob: float = 0.1, horizon: int = HORIZON):
self.sticky_action_prob = sticky_action_prob
self.horizon = min(horizon, HORIZON)
self.seed(0)
self.reset()
def seed(self, seed: int) -> None:
self.random = np.random.default_rng(seed)
def reset(self) -> None:
self.steps = self.questions = self.feedback = self.last_action = 0
self.time = FULL_TIME
self.multiplier = 1
self.correct = False
self.selected = 0
self.terminal = False
self._question()
def _question(self) -> None:
self.operation = int(self.random.integers(min(4, 1 + self.questions // 5)))
if self.operation < 2:
total = int(self.random.integers(10, 100))
part = int(self.random.integers(1, total))
self.left, self.right, self.answer = (
(part, total - part, total) if self.operation == 0 else (total, part, total - part)
)
else:
factor = int(self.random.integers(2, 10))
quotient = int(self.random.integers(2, 99 // factor + 1))
product = factor * quotient
self.left, self.right, self.answer = (
(quotient, factor, product) if self.operation == 2 else (product, factor, quotient)
)
distractors = [value for value in range(max(1, self.answer - 7), min(99, self.answer + 7) + 1)
if value != self.answer]
choices = self.random.choice(distractors, size=4, replace=False)
self.options = self.random.permutation([self.answer, *choices]).tolist()
@classmethod
def normalize_score(cls, score: float) -> float:
return min(max(score, 0), cls.score_cap) / cls.score_cap
def act(self, action: int) -> tuple[float, bool]:
if self.terminal:
return 0.0, True
if self.random.random() < self.sticky_action_prob:
action = self.last_action
self.last_action = action
self.steps += 1
reward = 0
if self.feedback:
self.feedback -= 1
if not self.feedback:
self._question()
elif 1 <= action <= 5:
reward = (57 * self.time * self.multiplier + FULL_TIME - 1) // FULL_TIME
self.correct = self.options[action - 1] == self.answer
self.selected = action
if self.correct:
self.time += 30
if self.time >= FULL_TIME:
self.multiplier += 1
else:
self.time -= 15
self.multiplier = max(1, self.multiplier - 1)
self.time = min(FULL_TIME, self.time)
self.feedback = FEEDBACK_STEPS
self.questions += 1
self.time = max(0, self.time - 1)
self.terminal = self.time == 0 or self.steps >= self.horizon
return float(reward), self.terminal
def state(self) -> np.ndarray:
state = np.zeros((10, 10, 6), dtype=bool)
state[self.operation, 0, 0] = True
for row, value in enumerate((self.left, self.right, *self.options)):
for bit in range(8):
state[row, bit, 1] = bool(value & (1 << bit))
if self.feedback:
state[0, self.selected, 2] = True
state[int(self.correct), 0, 3] = True
for row, value in enumerate((self.time, self.multiplier, self.questions,
self.feedback, self.steps, self.last_action)):
for bit in range(9):
state[row, bit, 5] = bool(value & (1 << bit))
return state
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