```python
from typing import Callable, Dict, Any, List

class JobQueue:
    def __init__(self):
        self.jobs: Dict[str, Any] = {}
        self.retry_counts: Dict[str, int] = {}
        self.backoff_history: Dict[str, List[float]] = {}

    def add_job(self, job_id: str, data: Any) -> None:
        self.jobs[job_id] = data
        self.retry_counts[job_id] = 0
        self.backoff_history[job_id] = []

    def process_job(self, job_id: str, processor: Callable) -> bool:
        if job_id not in self.jobs:
            return False

        data = self.jobs[job_id]
        
        while True:
            try:
                processor(data)
                return True
            except Exception:
                if self.retry_counts[job_id] < 3:
                    self.retry_counts[job_id] += 1
                    # Exponential backoff: 1s, 2s, 4s
                    delay = 2 ** (self.retry_counts[job_id] - 1)
                    self.backoff_history[job_id].append(delay)
                    # Backoff delays are tracked instead of sleeping
                else:
                    return False
```