This paper presents a theoretical framework analyzing Online FISTA's convergence in non-stationary environments with pulse-driven variations. It introduces a novel problem formulation, provides theoretical convergence bounds, and proposes adaptive restart strategies for linear convergence under certain conditions.
Key findings
Novel problem formulation capturing pulse-driven non-stationarity.
Theoretical convergence bounds quantifying the trade-off between convergence rate and environmental non-stationarity.
Dynamic regret bounds scaling as O(√(T(1 + PT))) where PT is the path length of optimal solutions.
Tracking error bounds under strong convexity assumptions.
Adaptive restart strategies for linear convergence under quadratic functional growth conditions.
Limitations & open questions
Analysis assumes certain regularity conditions on pulse arrival patterns.
Theoretical results may not directly apply to environments with more complex variations.