The problem statement involves several key dimensions:
1. Cumulative Privacy Loss: Sequential execution of queries or analyses
introduces cumulative privacy loss, potentially compromising the overall
privacy guarantee. The problem is to devise strategies that manage and
quantify this cumulative loss while providing clear bounds on the
resultant privacy leakage.
2. Parallel Execution Challenges: Parallel execution of multiple queries
demands a method to reconcile diverse privacy parameters and combine
them in a manner that preserves the highest achievable privacy level.
The problem is to establish a comprehensive approach for parallel
composition that considers varying sensitivities and privacy
requirements.
3. Advanced Composition Bounds: Basic composition techniques might yield
conservative privacy bounds that limit the utility of analysis results.
The problem is to explore and implement advanced composition theorems
that offer more accurate and tighter privacy guarantees, allowing for
more informative analyses.
4. Adaptability to Dynamic Scenarios: In dynamic environments where
queries are adaptive and may depend on previous analysis outcomes,
traditional composition techniques might not suffice. The problem is to
develop adaptive composition strategies that dynamically adjust privacy
parameters while safeguarding against privacy erosion.
5. Scalability and Efficiency: As data sets grow in size and complexity,
composition algorithms must be scalable and efficient. The problem
involves creating composition techniques that are computationally
feasible, allowing for practical implementation across various
applications.