Direct, Stochastic Analogues to Deterministic Optimization Methods Using Statistical Filters
نویسنده
چکیده
Stochastic optimization—those problems that involve random variables—is a fundamental challenge in many disciplines. Unfortunately, current solvers for stochastic optimization restrictively require finiteness by either replacing the original problem with a sample average surrogate, or by having complete knowledge of a finite population. To help alleviate this restriction, we state a general, novel framework that generates practical, robust numerical methods to solve the actual stochastic optimization problem iteratively. Our key insight is to treat the objective and its gradient as a sequential estimation problem that is solved by integrating statistical filters and deterministic optimizers. We demonstrate the framework by generating a Kalman Filtering-based gradient descent method with line search or trust region to solve a challenging stochastic optimization problem in statistics.
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