For tracking time-varying systems, the step size is kept strictly away from zero¶

Claim · All claims
Evidence · 1 study · theoretical r3 · q2
Currency · newest study 2003 · not yet checked against its sources · not reviewed by a person · overdue for a recheck since 2006: tool and model accuracy changes quickly

Subclaims¶

q2 i? When the underlying processes are nonstationary and the optimal parameter value changes with time, the step size is kept strictly away from zero to allow tracking. → Harold J. Kushner and G. George Yin 2003

Evidence¶

Harold J. Kushner and G. George Yin 2003¶

Harold J. Kushner and G. George Yin. (2003). Stochastic Approximation and Recursive Algorithms and Applications, Second Edition. Springer-Verlag, New York. https://doi.org/10.1007/b97441

q2 · i? · theoretical · r3

Motivational statement from the Preface and Introduction describing practice in signal processing and communications applications, where step size is often a small constant or random. The text says "one keepsϵn strictly away from zero in order to allow “tracking.”"

"The underlying processes are often nonstationary and the optimal value of θ can change with time. Then one keepsϵn strictly away from zero in order to allow “tracking.”"

Discussion¶

Related Claims¶

• Iterate averaging with step sizes decreasing slower than O(1/n) converges at an optimal rate — related
• Diminishing step sizes in stochastic approximation induce implicit averaging that eliminates noise effects in the long run — related
• Many learning algorithms, including neural network training and Q-learning, have recursive forms of the stochastic approximation type — related