This paper presents a comprehensive theoretical analysis of convergence properties for progressive selection algorithms across discrete and continuous domains, establishing a unified mathematical framework that characterizes the convergence behavior of multi-stage selection procedures.
Key findings
Unified mathematical framework for analyzing progressive selection algorithms.
Sufficient conditions for almost sure convergence to stationary points.
Non-asymptotic convergence rates O(1/√T) for convex objectives and linear convergence for strongly convex problems.
Characterization of convergence behavior across stages and insights into optimal stage transition policies.
Limitations & open questions
Analysis assumes mild regularity conditions including Lipschitz continuity and bounded variance.
Empirical validation is through synthetic experiments and may not fully capture real-world complexities.