RMSProp

Optimization · Formula · Appears in 1 lesson

st+1=ρst+(1−ρ)(∇θL)2,θt+1=θt−ηst+1+ϵ∇θLs_{t+1} = \rho s_t + (1-\rho)(\nabla_\theta L)^2, \qquad \theta_{t+1} = \theta_t - \frac{\eta}{\sqrt{s_{t+1}} + \epsilon} \nabla_\theta L

Gives every parameter its own learning rate by dividing by the recent size of its gradient. Parameters with consistently large gradients get smaller steps, which keeps badly scaled problems from stalling.

Symbols

ss
A running average of squared gradients.
ρ\rho
Its decay rate.
ϵ\epsilon
A small constant that prevents division by zero.
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