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"""
Collection of various reward signal for the arithmetic problem.
"""
import logging
import re
from src.utils.string_helper import (
extract_answers_from_completions,
extract_response_from_completions,
)
logging.basicConfig(level=logging.INFO)
logger = logging.getLogger("rewards")
def _is_valid_arithmetic_expression(expression: str) -> bool:
"""
Check if a string is a valid arithmetic expression containing only:
- Numbers (integers only)
- Arithmetic operators: +, -, x, /
- Whitespace
Args:
expression: The expression to validate
Returns:
bool: True if valid arithmetic expression, False otherwise
"""
if not expression or not expression.strip():
return False
# Pattern that matches valid arithmetic expressions
# Allows: integers, operators (+, -, x, /), and whitespace (no decimal points)
pattern = r"^[\d\s\+\-x\/]+$"
# First check: contains only allowed characters
if not re.match(pattern, expression):
return False
# Second check: must contain at least one number and one operator
has_number = re.search(r"\d", expression)
has_operator = re.search(r"[\+\-x\/]", expression)
if not (has_number and has_operator):
return False
# Third check: basic structure validation (no consecutive operators)
try:
# Replace x with * for evaluation
normalized = expression.replace("x", "*")
# Remove whitespace for easier validation
normalized = "".join(normalized.split())
# Check for consecutive operators
if re.search(r"[\+\-\*\/]{2,}", normalized):
return False
# Try to evaluate the expression to ensure it's syntactically correct
# This will catch issues like "1 + + 2" or "3 * / 4"
eval(normalized)
return True
except (SyntaxError, ValueError):
# If eval fails due to syntax errors, it's not a valid expression
return False
except ZeroDivisionError:
# ZeroDivisionError is okay (the expression is valid, just results in division by zero)
return True
except:
# Any other error means invalid expression
return False
def _calculate_distance_based_reward(answer: str, correct_answer: int) -> float:
"""
Calculate reward based on distance from the correct answer.
Uses linear scaling: reward = max(0, max_reward - (distance * penalty_per_unit))
Args:
answer: The arithmetic expression to evaluate
correct_answer: The expected result
Returns:
float: Reward between 0.0 and 2.0 based on distance from correct answer
"""
if not answer or not answer.strip():
return 0.0
# First check if it's a valid arithmetic expression
if not _is_valid_arithmetic_expression(answer):
return 0.0
try:
# Replace x with * for evaluation
normalized = answer.replace("x", "*")
# Evaluate the expression
result = eval(normalized)
# Calculate distance from correct answer
if isinstance(result, (int, float)):
distance = abs(result - correct_answer)
# Perfect match gets full reward
if distance < 0.0001:
return 2.0
# Linear scaling reward function
# Parameters can be tuned:
# - max_reward: maximum possible reward (2.0)
# - penalty_per_unit: how much reward decreases per unit of distance
max_reward = 2.0
penalty_per_unit = 0.2 # Lose 0.2 points per unit of distance
reward = max_reward - (distance * penalty_per_unit)
# Ensure minimum reward is 0.0
return max(0.0, reward)
return 0.0
except (SyntaxError, ValueError, ZeroDivisionError, OverflowError):
# If evaluation fails, no reward
return 0.0
except:
# Any other error means no reward
return 0.0
def format_reward_functiondef(
completions: list[list[dict[str, str]]], **kwargs: dict[str, any]
) -> list[float]:
"""
Reward function that checks if a completion contains <think>...</think> and
<answer>...</answer> sections.
Args:
completions: List of completions of the format:
[
[
{"role": "user", "content": "..."},
{"role": "assistant", "content": "..."},
]
]
Returns:
List of rewards.
"""
pattern = re.compile(r"<think>.*?</think>.*?<answer>.*?</answer>", re.DOTALL)
responses = extract_response_from_completions(completions)
matches = [bool(pattern.search(response)) for response in responses]
return [1.0 if match else 0.0 for match in matches]
def arithmetic_format_reward_function(
completions: list[list[dict[str, str]]],
**kwargs: dict[str, any],
) -> list[float]:
"""
Reward function that checks if the content of the answer tag is a valid arithmetic expression.
The answer should contain only numbers, arithmetic operators (+, -, x, /),
and spaces. Examples of valid formats:
- "1 + 2 x 6 / 3"
- "2 x 1 + 3 - 1"
- "4 + 5 x 2 - 1"
Args:
completions: List of completions of the format:
[
[
{"role": "user", "content": "..."},
{"role": "assistant", "content": "..."},
]
]
Returns:
List of rewards (1.0 for valid arithmetic expressions, 0.0 otherwise).
"""
# Extract responses from the completions
answers = extract_answers_from_completions(completions)
return [
1.0 if _is_valid_arithmetic_expression(answer) else 0.0 for answer in answers
]
def correctness_reward_function(
completions: list[list[dict[str, str]]], **kwargs: dict[str, any]
) -> list[float]:
"""
Reward function that provides rewards based on how close the arithmetic answer is to the correct result.
The reward is calculated using linear scaling:
- Perfect match (distance = 0): reward = 2.0
- Each unit of distance reduces reward by 0.2 points
- Minimum reward is 0.0
- Invalid expressions get 0.0
Args:
completions: List of completions of the format:
[
[
{"role": "user", "content": "..."},
{"role": "assistant", "content": "..."},
]
]
**kwargs: Must contain 'correct_answer' key with the expected result
Returns:
List of rewards (0.0 to 2.0 based on distance from correct answer).
Raises:
ValueError: If the correct answer is not provided in the kwargs.
"""
# Get the correct answer from the kwargs
correct_answer = kwargs["correct_answer"]
# Get the answer from the completions
answers = extract_answers_from_completions(completions)
completions = [completion[-1]["content"] for completion in completions]
# Display first question and answer
logger.info("First question: %s", completions[0])
logger.info("First answer: %s", answers[0])
return [
_calculate_distance_based_reward(answer, correct_answer) for answer in answers
]
def mathematical_correctness_reward_function(
completions: list[str], **kwargs
) -> list[float]:
"""
Evaluates completions based on Mathematical correctness of the answer
Args:
completions: Generated outputs
target: Expected answers
**kwargs: Additional keyword arguments
Returns:
list[float]: Reward scores (1.0 for correct, 0.0 for incorrect)
"""
completions = [completion[-1]["content"] for completion in completions]
target = kwargs["correct_answer"]
first_nums = kwargs["num1"]
second_nums = kwargs["num2"]
third_nums = kwargs["num3"]
fourth_nums = kwargs["num4"]
rewards = []
# Display completions
logger.info("Completion:\n%s", completions[0])
for completion, gt, first_num, second_num, third_num, fourth_num in zip(
completions,
target,
first_nums,
second_nums,
third_nums,
fourth_nums,
strict=False,
):
reward = 0.0
try:
# Check if the format is correct
match = re.search(r"<answer>(.*?)<\/answer>", completion, re.DOTALL)
if match is None:
logger.info(
"┌─────────────────────────────────────────────────────────────────────┐"
)
logger.info(
"│ ❌ FORMAT ERROR: No <answer> tags found in completion │"
)
logger.info(
"├─────────────────────────────────────────────────────────────────────┤"
)
logger.info(
"│ Completion snippet: %-47s │",
completion[:47] + "..." if len(completion) > 47 else completion,
)
logger.info(
"└─────────────────────────────────────────────────────────────────────┘"
)
rewards.append(reward)
continue
# Add reward
reward += 1.0
# Extract the "answer" part from the completion
equation = match.group(1).strip()
if "=" in equation:
equation = equation.split("=")[0]
# Extract all numbers from the equation
used_numbers = [int(n) for n in re.findall(r"\d+", equation)]
# Check if all numbers are used exactly once
correct_numbers = [first_num, second_num, third_num, fourth_num]
if sorted(used_numbers) != sorted(correct_numbers):
logger.info(
"┌─────────────────────────────────────────────────────────────────────┐"
)
logger.info(
"│ ❌ NUMBER USAGE ERROR: Incorrect numbers used │"
)
logger.info(
"├─────────────────────────────────────────────────────────────────────┤"
)
logger.info("│ Equation: %-57s │", equation[:57])
logger.info("│ Expected numbers: %-51s │", str(correct_numbers))
logger.info("│ Used numbers: %-55s │", str(used_numbers))
logger.info(
"└─────────────────────────────────────────────────────────────────────┘"
)
rewards.append(reward)
continue
# Add reward
reward += 1.0
# Define a regex pattern that only allows numbers, operators, and whitespace
allowed_pattern = r"^[\d+\-*/.\s]+$"
if not re.match(allowed_pattern, equation):
logger.info(
"┌─────────────────────────────────────────────────────────────────────┐"
)
logger.info(
"│ ❌ INVALID CHARACTERS: Equation contains disallowed characters │"
)
logger.info(
"├─────────────────────────────────────────────────────────────────────┤"
)
logger.info("│ Equation: %-57s │", equation[:57])
logger.info(
"└─────────────────────────────────────────────────────────────────────┘"
)
rewards.append(reward)
continue
# Add reward
reward += 1.0
# Evaluate the equation with restricted globals and locals
result = eval(equation, {"__builtins__": None}, {})
# Check if the equation is correct and matches the ground truth
if abs(float(result) - float(gt)) < 1e-5:
logger.info(
"┌─────────────────────────────────────────────────────────────────────┐"
)
logger.info(
"│ ✅ CORRECT ANSWER: Perfect match! │"
)
logger.info(
"├─────────────────────────────────────────────────────────────────────┤"
)
logger.info(
"│ Equation: %-35s = %-20s │", equation[:35], str(result)[:20]
)
logger.info("│ Target: %-59s │", str(gt))
logger.info(
"└─────────────────────────────────────────────────────────────────────┘"
)
reward += 4.0
rewards.append(reward)
else:
logger.info(
"┌─────────────────────────────────────────────────────────────────────┐"
)
logger.info(
"│ ❌ WRONG RESULT: Equation evaluated to incorrect value │"
)
logger.info(
"├─────────────────────────────────────────────────────────────────────┤"
)
logger.info(
"│ Equation: %-35s = %-20s │", equation[:35], str(result)[:20]
)
logger.info("│ Expected: %-57s │", str(gt))
logger.info(
"│ Difference: %-55s │", str(abs(float(result) - float(gt)))
)
logger.info(
"└─────────────────────────────────────────────────────────────────────┘"
)
rewards.append(reward)
except Exception as e:
# If evaluation fails, reward is 0
logger.info(
"┌─────────────────────────────────────────────────────────────────────┐"
)
logger.info(
"│ ❌ EVALUATION ERROR: Exception occurred during processing │"
)
logger.info(
"├─────────────────────────────────────────────────────────────────────┤"
)
logger.info("│ Error: %-61s │", str(e)[:61])
logger.info(
"│ Equation: %-57s │",
(equation if "equation" in locals() else "N/A")[:57],
)
logger.info(
"└─────────────────────────────────────────────────────────────────────┘"
)
rewards.append(reward)
return rewards
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