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AdaBelief bias correction #1963

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May 10, 2022
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AdaBelief bias correction #1963

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AdaBelief bias correction
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22 changes: 19 additions & 3 deletions src/optimise/optimisers.jl
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Expand Up @@ -532,10 +532,26 @@ AdaBelief(η::Real, β::Tuple, state::IdDict) = AdaBelief(η, β, EPS, state)

function apply!(o::AdaBelief, x, Δ)
η, β = o.eta, o.beta
mt, st = get!(() -> (zero(x), zero(x)), o.state, x)::NTuple{2,typeof(x)}

mt, st, βp = get!(o.state, x) do
(zero(x), zero(x), Float64[β[1], β[2]])
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🤮

I know this is what ADAM does, but it really is non-optimal. Not a blocker for this PR, but more impetus to move to Optimisers.jl ASAP.

end :: Tuple{typeof(x), typeof(x), Vector{Float64}}

#= st is a variance and can go to zero. This is in contrast to ADAM, which uses the
second moment which is usually far enough from zero. This is problematic, since st
can be slightly negative due to numerical error, and the square root below will fail.
Also, if we want to differentiate through the optimizer, √0 is not differentiable.
To protect against this, we add a small number, st -> st + eps2.
The original implementation (https://github.com/juntang-zhuang/Adabelief-Optimizer)
uses the square of Adam's epsilon, which we do here.
See also: https://github.com/juntang-zhuang/Adabelief-Optimizer/issues/61 =#
eps2 = o.epsilon^2 # TODO: make epsilon^2 the default in next breaking release

@. mt = β[1] * mt + (1 - β[1]) * Δ
@. st = β[2] * st + (1 - β[2]) * (Δ - mt) * conj(Δ - mt)
@. Δ = η * mt / (√(st) + o.epsilon)
@. st = β[2] * st + (1 - β[2]) * (Δ - mt) * conj(Δ - mt) + eps2
@. Δ = η * mt / (1 - βp[1]) / (√(st / (1 - βp[2])) + eps2)
βp .= βp .* β

return Δ
end

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