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Merge pull request #53 from shayandavoodii/EGM
Add EGM 🆕
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,199 @@ | ||
| """ | ||
| wᵢᵗ⁺¹func( | ||
| model::EGE, | ||
| η::AbstractFloat, | ||
| vᵗ::AbstractVector, | ||
| _::AbstractVector, | ||
| wᵗ::AbstractVector, | ||
| xᵗ::AbstractVector | ||
| ) | ||
| wᵢᵗ⁺¹func( | ||
| model::EGR, | ||
| η::AbstractFloat, | ||
| _::AbstractVector, | ||
| mᵗ::AbstractVector, | ||
| wᵗ::AbstractVector, | ||
| xᵗ::AbstractVector | ||
| ) | ||
| wᵢᵗ⁺¹func( | ||
| model::EGA, | ||
| η::AbstractFloat, | ||
| vᵗ::AbstractVector, | ||
| mᵗ::AbstractVector, | ||
| wᵗ::AbstractVector, | ||
| xᵗ::AbstractVector | ||
| ) | ||
| Calculate the weights for the next period using the EGM framework. | ||
| # Method 1: EGE | ||
| ## Arguments | ||
| - `model::EGE`: EGM framework with `gamma1` parameter. See [`EGE`](@ref) type. | ||
| - `η::AbstractFloat`: learning rate. | ||
| - `vᵗ::AbstractVector`: vector of size `n_assets`. | ||
| - `_::AbstractVector`: dummy vector of size `n_assets`. | ||
| - `wᵗ::AbstractVector`: vector of size `n_assets` containing the weights for the current period. | ||
| - `xᵗ::AbstractVector`: vector of size `n_assets` containing the relative prices for the current period. | ||
| ## Returns | ||
| - `::AbstractVector`: vector of size `n_assets` containing the weights for the next period. | ||
| # Method 2: EGR | ||
| ## Arguments | ||
| - `model::EGR`: EGM framework with `gamma2` parameter. See [`EGR`](@ref) type. | ||
| - `η::AbstractFloat`: learning rate. | ||
| - `_::AbstractVector`: dummy vector of size `n_assets`. | ||
| - `mᵗ::AbstractVector`: vector of size `n_assets`. | ||
| - `wᵗ::AbstractVector`: vector of size `n_assets` containing the weights for the current period. | ||
| - `xᵗ::AbstractVector`: vector of size `n_assets` containing the relative prices for the current period. | ||
| ## Returns | ||
| - `::AbstractVector`: vector of size `n_assets` containing the weights for the next period. | ||
| # Method 3: EGA | ||
| ## Arguments | ||
| - `model::EGA`: EGM framework with `gamma1` and `gamma2` parameters. See [`EGA`](@ref) type. | ||
| - `η::AbstractFloat`: learning rate. | ||
| - `vᵗ::AbstractVector`: vector of size `n_assets`. | ||
| - `mᵗ::AbstractVector`: vector of size `n_assets`. | ||
| - `wᵗ::AbstractVector`: vector of size `n_assets` containing the weights for the current period. | ||
| - `xᵗ::AbstractVector`: vector of size `n_assets` containing the relative prices for the current period. | ||
| ## Returns | ||
| - `::AbstractVector`: vector of size `n_assets` containing the weights for the next period. | ||
| """ | ||
| function wᵢᵗ⁺¹func( | ||
| model::EGE, | ||
| η::AbstractFloat, | ||
| vᵗ::AbstractVector, | ||
| _::AbstractVector, | ||
| wᵗ::AbstractVector, | ||
| xᵗ::AbstractVector | ||
| ) | ||
| γ₁ = model.gamma1 | ||
| gᵗ = xᵗ./sum(xᵗ.*wᵗ) | ||
| vᵗ⁺¹ = vᵗ .= γ₁*vᵗ.+(1-γ₁).*gᵗ | ||
| numerator_ = wᵗ.*exp.(η.*vᵗ⁺¹) | ||
| return numerator_/sum(numerator_) | ||
| end | ||
|
|
||
| function wᵢᵗ⁺¹func( | ||
| model::EGR, | ||
| η::AbstractFloat, | ||
| _::AbstractVector, | ||
| mᵗ::AbstractVector, | ||
| wᵗ::AbstractVector, | ||
| xᵗ::AbstractVector | ||
| ) | ||
| γ₂ = model.gamma2 | ||
| gᵗ = xᵗ./sum(xᵗ.*wᵗ) | ||
| mᵗ⁺¹ = mᵗ .= γ₂*mᵗ.+(1-γ₂).*(gᵗ.^2) | ||
| numerator_ = ((wᵗ.*exp.(η.*gᵗ))./(sqrt.(mᵗ⁺¹).+1e-8)) | ||
| return numerator_/sum(numerator_) | ||
| end | ||
|
|
||
| algname(::EGE) = "EGE" | ||
| algname(::EGR) = "EGR" | ||
| algname(::EGA) = "EGA" | ||
|
|
||
| function wᵢᵗ⁺¹func( | ||
| model::EGA, | ||
| η::AbstractFloat, | ||
| vᵗ::AbstractVector, | ||
| mᵗ::AbstractVector, | ||
| wᵗ::AbstractVector, | ||
| xᵗ::AbstractVector | ||
| ) | ||
| γ₁ = model.gamma1 | ||
| γ₂ = model.gamma2 | ||
| gᵗ = xᵗ./sum(xᵗ.*wᵗ) | ||
| vᵗ⁺¹ = vᵗ .= γ₁*vᵗ.+(1-γ₁).*gᵗ | ||
| mᵗ⁺¹ = mᵗ .= γ₂*mᵗ.+(1-γ₂).*(gᵗ.^2) | ||
| numerator_ = (wᵗ.*exp.(η.*vᵗ⁺¹))./(sqrt.(mᵗ⁺¹).+1e-8) | ||
| return numerator_/sum(numerator_) | ||
| end | ||
|
|
||
| """ | ||
| egm(rel_pr::AbstractMatrix, model::EGMFramework, η::AbstractFloat=0.05) | ||
| Run the Exponential Gradient with Momentum (EGM) algorithm. This framework contains three \ | ||
| variants: [`EGE`](@ref), [`EGR`](@ref) and [`EGA`](@ref). | ||
| # Arguments | ||
| - `rel_pr::AbstractMatrix`: matrix of size `n_assets` by `n_periods` containing the \ | ||
| relative prices. | ||
| - `model::EGMFramework`: EGM framework. [`EGE`](@ref), [`EGR`](@ref) or [`EGA`](@ref) can \ | ||
| be used. | ||
| - `η::AbstractFloat=0.05`: learning rate. | ||
| # Returns | ||
| - `::OPSAlgorithm`: An [`OPSAlgorithm`](@ref) object. | ||
| # Example | ||
| ```julia | ||
| julia> using OnlinePortfolioSelection, YFinance | ||
| julia> tickers = ["AAPL", "MSFT", "GOOG"]; | ||
| julia> querry = [get_prices(ticker, startdt="2019-01-01", enddt="2019-01-12")["adjclose"] for ticker in tickers]; | ||
| julia> prices = stack(querry) |> permutedims; | ||
| julia> rel_pr = prices[:, 2:end]./prices[:, 1:end-1] | ||
| 3×7 Matrix{Float64}: | ||
| 0.900393 1.04269 0.997774 1.01906 1.01698 1.0032 0.990182 | ||
| 0.963212 1.04651 1.00128 1.00725 1.0143 0.993574 0.992278 | ||
| 0.971516 1.05379 0.997833 1.00738 0.998495 0.995971 0.987723 | ||
| julia> # EGE variant | ||
| julia> variant = EGE(0.5) | ||
| julia> model = egm(rel_pr, variant); | ||
| julia> model.b | ||
| 3×7 Matrix{Float64}: | ||
| 0.333333 0.33294 0.332704 0.332576 0.332576 0.332634 0.332711 | ||
| 0.333333 0.333493 0.333564 0.333619 0.333614 0.333647 0.33363 | ||
| 0.333333 0.333567 0.333732 0.333805 0.33381 0.333719 0.333659 | ||
| julia> # EGR variant | ||
| julia> variant = EGR(0.) | ||
| julia> model = egm(rel_pr, variant); | ||
| julia> model.b | ||
| 3×7 Matrix{Float64}: | ||
| 0.333333 0.348653 0.350187 0.350575 0.348072 0.345816 0.344006 | ||
| 0.333333 0.327 0.327299 0.326573 0.327852 0.326546 0.327824 | ||
| 0.333333 0.324347 0.322514 0.322853 0.324077 0.327638 0.328169 | ||
| julia> # EGA variant | ||
| julia> variant = EGA(0.5, 0.) | ||
| julia> model = egm(rel_pr, variant); | ||
| julia> model.b | ||
| 3×7 Matrix{Float64}: | ||
| 0.333333 0.349056 0.350429 0.350706 0.348071 0.345757 0.343929 | ||
| 0.333333 0.326833 0.327223 0.326516 0.327857 0.326514 0.327842 | ||
| 0.333333 0.324111 0.322348 0.322779 0.324072 0.327729 0.328229 | ||
| ``` | ||
| # References | ||
| > [Exponential Gradient with Momentum for Online Portfolio Selection](https://doi.org/10.1016/j.eswa.2021.115889) | ||
| """ | ||
| function egm(rel_pr::AbstractMatrix, variant::EGMFramework, η::AbstractFloat=0.05) | ||
| η>0 || ArgumentError("η must be positive") |> throw | ||
| n_assets, n_periods = size(rel_pr) | ||
| b = ones(n_assets, n_periods)/n_assets | ||
| vₜ = zeros(n_assets) | ||
| mₜ = zeros(n_assets) | ||
|
|
||
| for t ∈ 1:n_periods-1 | ||
| b[:, t+1] = wᵢᵗ⁺¹func(variant, η, vₜ, mₜ, b[:, t], rel_pr[:, t]) | ||
| end | ||
|
|
||
| return OPSAlgorithm(n_assets, b, algname(variant)) | ||
| end |
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