```python
import os
from typing import Any
import pyautogui as pag
from openai import OpenAI, APIError

class PragmaticProgrammerAGIAgent:
    """
    A PragmaticProgrammerAGIAgent operates by strategizing a step-by-step decomposition of problems,
    the creation of solutions, error detection, and performance improvement tasks.
    """

    def __init__(self) -> None:
        self.api_key = os.getenv("OPENAI_API_KEY")
        self.client = OpenAI(api_key=self.api_key)

    def decompose_problem(self, problem: str) -> Any:
        """
        Decompose any given problem into sub-problems that are simpler and easier to handle.
        """

        decomposition_prompt = f"Given problem: {problem}. Break this down into simpler sub-problems."
        api_call = self.client.Completion.create(
            engine="text-davinci-002",
            prompt=decomposition_prompt,
            temperature=0.7,
            max_tokens=300
        )

        return api_call.choices[0].text.strip()

    def generate_solution(self, sub_problem: str) -> Any:
        """
        Generate a solution for the given sub-problem using the OpenAI API.
        """

        generation_prompt = f"Subproblem: {sub_problem}. Write a python function that might solve this."

        api_call = self.client.Completion.create(
            engine="text-davinci-002",
            prompt=generation_prompt,
            temperature=0.7,
            max_tokens=300
        )

        return api_call.choices[0].text.strip()

    def error_detection(self, script: str) -> Any:
        """
        Perform a real-time error detection on the generated script.
        """

        error_detection_prompt = f"Python script:\n{script}\nDetect any potential errors and propose corrections."

        api_call = self.client.Completion.create(
            engine="text-davinci-002",
            prompt=error_detection_prompt,
            temperature=0.5,
            max_tokens=300
        )

        return api_call.choices[0].text.strip()

    def performance_improvement(self, script: str) -> str:
        """
        Perform a performance improvement on the generated script.
        """

        improvement_prompt = f"Python script:\n{script}\nPropose improvements to optimize performance."

        api_call = self.client.Completion.create(
            engine="text-davinci-002",
            prompt=improvement_prompt,
            temperature=0.7,
            max_tokens=300
        )

        return api_call.choices[0].text.strip()

    def __str__(self) -> str:
        return "PragmaticProgrammerAGIAgent"

if __name__ == "__main__":
    pp_agent = PragmaticProgrammerAGIAgent()
    complex_problem = "Implement an object detection method using deep learning."
    decomposed_problem = pp_agent.decompose_problem(complex_problem)
    solution = pp_agent.generate_solution(decomposed_problem)
    error_check = pp_agent.error_detection(solution)
    improved_solution = pp_agent.performance_improvement(solution)

    print(f"Decomposed problem: {decomposed_problem}\n\nGenerated solution: {solution}\n\nErrors detected: {error_check}\n\nImproved solution: {improved_solution}")
```
In the code above, the `PragmaticProgrammerAGIAgent` starts by decomposing complex problem to simpler sub-problems using openai gpt-3. Then, it generates a solution for the sub-problem, performs real-time error detection and optimize the initial solution for better performance. Following this process, we can ensure the delivery of comprehensive and top quality solutions.