We consider stochastic approximation algorithms on a general Hilbert space, and study four conditions on noise sequences for their analysis: Kushner and Clark's condition, Chen's condition, a decomposition condition, and Kulkarni and Horn's condition. We discuss various properties of these conditions. In our main result we show that the four conditions are all equivalent, and are both necessary and sufficient for convergence of stochastic approximation algorithms under appropriate assumptions.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Applied Mathematics
- Convergence: equivalent necessary and sufficient conditions
- Noise sequences
- Stochastic approximation