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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Optimisers · Flux</title><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
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</script><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link href="../../assets/flux.css" rel="stylesheet" type="text/css"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit">Flux</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><span class="tocitem">Building Models</span><ul><li><a class="tocitem" href="../../models/basics/">Basics</a></li><li><a class="tocitem" href="../../models/recurrence/">Recurrence</a></li><li><a class="tocitem" href="../../models/regularisation/">Regularisation</a></li><li><a class="tocitem" href="../../models/layers/">Model Reference</a></li><li><a class="tocitem" href="../../models/advanced/">Advanced Model Building</a></li><li><a class="tocitem" href="../../models/nnlib/">NNlib</a></li></ul></li><li><span class="tocitem">Handling Data</span><ul><li><a class="tocitem" href="../../data/onehot/">One-Hot Encoding</a></li><li><a class="tocitem" href="../../data/dataloader/">DataLoader</a></li></ul></li><li><span class="tocitem">Training Models</span><ul><li class="is-active"><a class="tocitem" href>Optimisers</a><ul class="internal"><li><a class="tocitem" href="#Optimiser-Reference-1"><span>Optimiser Reference</span></a></li><li><a class="tocitem" href="#Optimiser-Interface-1"><span>Optimiser Interface</span></a></li><li><a class="tocitem" href="#Composing-Optimisers-1"><span>Composing Optimisers</span></a></li><li><a class="tocitem" href="#Decays-1"><span>Decays</span></a></li></ul></li><li><a class="tocitem" href="../training/">Training</a></li></ul></li><li><a class="tocitem" href="../../gpu/">GPU Support</a></li><li><a class="tocitem" href="../../saving/">Saving &amp; Loading</a></li><li><a class="tocitem" href="../../ecosystem/">The Julia Ecosystem</a></li><li><a class="tocitem" href="../../performance/">Performance Tips</a></li><li><a class="tocitem" href="../../community/">Community</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Training Models</a></li><li class="is-active"><a href>Optimisers</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Optimisers</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/FluxML/Flux.jl/blob/master/docs/src/training/optimisers.md" title="Edit on GitHub"><span class="docs-icon fab">
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W = rand(2, 5)
b = rand(2)
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predict(x) = (W * x) .+ b
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loss(x, y) = sum((predict(x) .- y).^2)
x, y = rand(5), rand(2) # Dummy data
l = loss(x, y) # ~ 3
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θ = Params([W, b])
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grads = gradient(() -&gt; loss(x, y), θ)</code></pre><p>We want to update each parameter, using the gradient, in order to improve (reduce) the loss. Here&#39;s one way to do that:</p><pre><code class="language-julia">using Flux.Optimise: update!
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η = 0.1 # Learning Rate
for p in (W, b)
update!(p, -η * grads[p])
end</code></pre><p>Running this will alter the parameters <code>W</code> and <code>b</code> and our loss should go down. Flux provides a more general way to do optimiser updates like this.</p><pre><code class="language-julia">opt = Descent(0.1) # Gradient descent with learning rate 0.1
for p in (W, b)
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update!(opt, p, grads[p])
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end</code></pre><p>An optimiser <code>update!</code> accepts a parameter and a gradient, and updates the parameter according to the chosen rule. We can also pass <code>opt</code> to our <a href="../training/">training loop</a>, which will update all parameters of the model in a loop. However, we can now easily replace <code>Descent</code> with a more advanced optimiser such as <code>ADAM</code>.</p><h2 id="Optimiser-Reference-1"><a class="docs-heading-anchor" href="#Optimiser-Reference-1">Optimiser Reference</a><a class="docs-heading-anchor-permalink" href="#Optimiser-Reference-1" title="Permalink"></a></h2><p>All optimisers return an object that, when passed to <code>train!</code>, will update the parameters passed to it.</p><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.update!" href="#Flux.Optimise.update!"><code>Flux.Optimise.update!</code></a><span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">update!(opt, p, g)
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update!(opt, ps::Params, gs)</code></pre><p>Perform an update step of the parameters <code>ps</code> (or the single parameter <code>p</code>) according to optimizer <code>opt</code> and the gradients <code>gs</code> (the gradient <code>g</code>).</p><p>As a result, the parameters are mutated and the optimizer&#39;s internal state may change. </p><p>update!(x, x̄)</p><p>Update the array <code>x</code> according to <code>x .-= x̄</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/train.jl#L5-L17">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Descent" href="#Flux.Optimise.Descent"><code>Flux.Optimise.Descent</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Descent(η)</code></pre><p>Classic gradient descent optimiser with learning rate <code>η</code>. For each parameter <code>p</code> and its gradient <code>δp</code>, this runs <code>p -= η*δp</code></p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): The amount by which the gradients are discounted before updating the weights. Defaults to <code>0.1</code>.</li></ul><p><strong>Example</strong></p><pre><code class="language-julia-repl">opt = Descent() # uses default η (0.1)
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opt = Descent(0.3) # use provided η
ps = params(model)
gs = gradient(ps) do
loss(x, y)
end
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Flux.Optimise.update!(opt, ps, gs)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L8-L31">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Momentum" href="#Flux.Optimise.Momentum"><code>Flux.Optimise.Momentum</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Momentum(η, ρ)</code></pre><p>Gradient descent with learning rate <code>η</code> and momentum <code>ρ</code>.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (<code>η</code>): Amount by which gradients are discounted before updating the weights. Defaults to <code>0.01</code>.</li><li>Momentum (<code>ρ</code>): Parameter that accelerates descent in the relevant direction and dampens oscillations. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = Momentum() # uses defaults of η = 0.01 and ρ = 0.9
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opt = Momentum(0.01, 0.99)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L42-L57">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.Nesterov" href="#Flux.Optimise.Nesterov"><code>Flux.Optimise.Nesterov</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">Nesterov(η, ρ)</code></pre><p>Gradient descent with learning rate <code>η</code> and Nesterov momentum <code>ρ</code>.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Amount by which the gradients are dicsounted berfore updating the weights. Defaults to <code>0.001</code>.</li><li>Nesterov Momentum (ρ): Parameters controlling the amount of nesterov momentum to be applied. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = Nesterov() # uses defaults η = 0.001 and ρ = 0.9
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opt = Nesterov(0.003, 0.95)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L73-L88">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.RMSProp" href="#Flux.Optimise.RMSProp"><code>Flux.Optimise.RMSProp</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">RMSProp(η, ρ)</code></pre><p>Implements the RMSProp algortihm. Often a good choice for recurrent networks. Parameters other than learning rate generally don&#39;t need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Rho (ρ): Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = RMSProp() # uses default η = 0.001 and ρ = 0.9
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opt = RMSProp(0.002, 0.95)</code></pre><p><strong>References</strong></p><p><a href="https://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf">RMSProp</a></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L105-L123">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAM" href="#Flux.Optimise.ADAM"><code>Flux.Optimise.ADAM</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADAM(η, β::Tuple)</code></pre><p>Implements the ADAM optimiser.</p><p><strong>Paramters</strong></p><ul><li>Learning Rate (<code>η</code>): Defaults to <code>0.001</code>.</li><li>Beta (<code>β::Tuple</code>): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAM() # uses the default η = 0.001 and β = (0.9, 0.999)
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opt = ADAM(0.001, (0.9, 0.8))</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1412.6980v8">ADAM</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L139-L157">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.AdaMax" href="#Flux.Optimise.AdaMax"><code>Flux.Optimise.AdaMax</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">AdaMax(η, β::Tuple)</code></pre><p>Variant of ADAM based on ∞-norm.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code></li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = AdaMax() # uses default η and β
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opt = AdaMax(0.001, (0.9, 0.995))</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1412.6980v9">AdaMax</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L221-L238">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAGrad" href="#Flux.Optimise.ADAGrad"><code>Flux.Optimise.ADAGrad</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADAGrad(η)</code></pre><p>Implements AdaGrad. It has parameter specific learning rates based on how frequently it is updated.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.1</code></li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAGrad() # uses default η = 0.1
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opt = ADAGrad(0.001)</code></pre><p><strong>References</strong></p><p><a href="http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf">ADAGrad</a> optimiser. Parameters don&#39;t need tuning.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L257-L275">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADADelta" href="#Flux.Optimise.ADADelta"><code>Flux.Optimise.ADADelta</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ADADelta(ρ)</code></pre><p>Version of ADAGrad that adapts learning rate based on a window of past gradient updates. Parameters don&#39;t need tuning.</p><p><strong>Parameters</strong></p><ul><li>Rho (ρ): Factor by which gradient is decayed at each time step. Defaults to <code>0.9</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADADelta() # uses default ρ = 0.9
opt = ADADelta(0.89)</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1212.5701">ADADelta</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L290-L306">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.AMSGrad" href="#Flux.Optimise.AMSGrad"><code>Flux.Optimise.AMSGrad</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">AMSGrad(η, β::Tuple)</code></pre><p>Implements AMSGrad version of the ADAM optimiser. Parameters don&#39;t need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = AMSGrad() # uses default η and β
opt = AMSGrad(0.001, (0.89, 0.995))</code></pre><p><strong>References</strong></p><p><a href="https://openreview.net/forum?id=ryQu7f-RZ">AMSGrad</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L323-L340">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.NADAM" href="#Flux.Optimise.NADAM"><code>Flux.Optimise.NADAM</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">NADAM(η, β::Tuple)</code></pre><p>Nesterov variant of ADAM. Parameters don&#39;t need tuning.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to <code>(0.9, 0.999)</code>.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = NADAM() # uses default η and β
opt = NADAM(0.002, (0.89, 0.995))</code></pre><p><strong>References</strong></p><p><a href="http://cs229.stanford.edu/proj2015/054_report.pdf">NADAM</a> optimiser.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L358-L375">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ADAMW" href="#Flux.Optimise.ADAMW"><code>Flux.Optimise.ADAMW</code></a><span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia">ADAMW(η, β::Tuple, decay)</code></pre><p>Variant of ADAM defined by fixing weight decay regularization.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (η): Defaults to <code>0.001</code>.</li><li>Beta (β::Tuple): The first element refers to β1 and the second to β2. Defaults to (0.9, 0.999).</li><li>decay: Decay applied to weights during optimisation. Defaults to 0.</li></ul><p><strong>Examples</strong></p><pre><code class="language-julia">opt = ADAMW() # uses default η, β and decay
opt = ADAMW(0.001, (0.89, 0.995), 0.1)</code></pre><p><strong>References</strong></p><p><a href="https://arxiv.org/abs/1711.05101">ADAMW</a></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L394-L412">source</a></section></article><h2 id="Optimiser-Interface-1"><a class="docs-heading-anchor" href="#Optimiser-Interface-1">Optimiser Interface</a><a class="docs-heading-anchor-permalink" href="#Optimiser-Interface-1" title="Permalink"></a></h2><p>Flux&#39;s optimisers are built around a <code>struct</code> that holds all the optimiser parameters along with a definition of how to apply the update rule associated with it. We do this via the <code>apply!</code> function which takes the optimiser as the first argument followed by the parameter and its corresponding gradient.</p><p>In this manner Flux also allows one to create custom optimisers to be used seamlessly. Let&#39;s work this with a simple example.</p><pre><code class="language-julia">mutable struct Momentum
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eta
rho
velocity
end
Momentum(eta::Real, rho::Real) = Momentum(eta, rho, IdDict())</code></pre><p>The <code>Momentum</code> type will act as our optimiser in this case. Notice that we have added all the parameters as fields, along with the velocity which we will use as our state dictionary. Each parameter in our models will get an entry in there. We can now define the rule applied when this optimiser is invoked.</p><pre><code class="language-julia">function apply!(o::Momentum, x, Δ)
η, ρ = o.eta, o.rho
v = get!(o.velocity, x, zero(x))::typeof(x)
@. v = ρ * v - η * Δ
@. Δ = -v
end</code></pre><p>This is the basic definition of a Momentum update rule given by:</p><div>\[v = ρ * v - η * Δ
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w = w - v\]</div><p>The <code>apply!</code> defines the update rules for an optimiser <code>opt</code>, given the parameters and gradients. It returns the updated gradients. Here, every parameter <code>x</code> is retrieved from the running state <code>v</code> and subsequently updates the state of the optimiser.</p><p>Flux internally calls on this function via the <code>update!</code> function. It shares the API with <code>apply!</code> but ensures that multiple parameters are handled gracefully.</p><h2 id="Composing-Optimisers-1"><a class="docs-heading-anchor" href="#Composing-Optimisers-1">Composing Optimisers</a><a class="docs-heading-anchor-permalink" href="#Composing-Optimisers-1" title="Permalink"></a></h2><p>Flux defines a special kind of optimiser simply called <code>Optimiser</code> which takes in arbitrary optimisers as input. Its behaviour is similar to the usual optimisers, but differs in that it acts by calling the optimisers listed in it sequentially. Each optimiser produces a modified gradient that will be fed into the next, and the resultant update will be applied to the parameter as usual. A classic use case is where adding decays is desirable. Flux defines some basic decays including <code>ExpDecay</code>, <code>InvDecay</code> etc.</p><pre><code class="language-julia">opt = Optimiser(ExpDecay(0.001, 0.1, 1000, 1e-4), Descent())</code></pre><p>Here we apply exponential decay to the <code>Descent</code> optimiser. The defaults of <code>ExpDecay</code> say that its learning rate will be decayed every 1000 steps. It is then applied like any optimiser.</p><pre><code class="language-julia">w = randn(10, 10)
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w1 = randn(10,10)
ps = Params([w, w1])
loss(x) = Flux.mse(w * x, w1 * x)
loss(rand(10)) # around 9
for t = 1:10^5
θ = Params([w, w1])
θ̄ = gradient(() -&gt; loss(rand(10)), θ)
Flux.Optimise.update!(opt, θ, θ̄)
end
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loss(rand(10)) # around 0.9</code></pre><p>In this manner it is possible to compose optimisers for some added flexibility.</p><h2 id="Decays-1"><a class="docs-heading-anchor" href="#Decays-1">Decays</a><a class="docs-heading-anchor-permalink" href="#Decays-1" title="Permalink"></a></h2><p>Similar to optimisers, Flux also defines some simple decays that can be used in conjunction with other optimisers, or standalone.</p><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.ExpDecay" href="#Flux.Optimise.ExpDecay"><code>Flux.Optimise.ExpDecay</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">ExpDecay(eta, decay, decay_step, clip)</code></pre><p>Discount the learning rate <code>eta</code> by a multiplicative factor <code>decay</code> every <code>decay_step</code> till a minimum of <code>clip</code>.</p><p><strong>Parameters</strong></p><ul><li>Learning Rate (eta): Defaults to <code>0.001</code>.</li><li>decay: Factor by which the learning rate is discounted. Defaults to <code>0.1</code>.</li><li>decay_step: Schedules decay operations by setting number of steps between two decay operations. Defaults to <code>1000</code>.</li><li>clip: Minimum value of learning rate. Defaults to <code>1e-4</code>.</li></ul><p><strong>Example</strong></p><p>To apply exponential decay to an optimiser:</p><pre><code class="language-julia">Optimiser(ExpDecay(..), Opt(..))
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opt = Optimiser(ExpDecay(), ADAM())</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L471-L488">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.InvDecay" href="#Flux.Optimise.InvDecay"><code>Flux.Optimise.InvDecay</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">InvDecay(γ)</code></pre><p>Applies inverse time decay to an optimiser, i.e., the effective step size at iteration <code>n</code> is <code>eta / (1 + γ * n)</code> where <code>eta</code> is the initial step size. The wrapped optimiser&#39;s step size is not modified.</p><p><strong>Parameters</strong></p><ul><li>gamma (γ): Defaults to <code>0.001</code></li></ul><p><strong>Example</strong></p><pre><code class="language-julia">Optimiser(InvDecay(..), Opt(..))</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L443-L455">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="Flux.Optimise.WeightDecay" href="#Flux.Optimise.WeightDecay"><code>Flux.Optimise.WeightDecay</code></a><span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia">WeightDecay(wd)</code></pre><p>Decays the weight by <code>wd</code></p><p><strong>Parameters</strong></p><ul><li>weight decay (wd): 0</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/FluxML/Flux.jl/blob/a874bef6f9d8eb1ab2fe376cb8ad068eb36baf33/src/optimise/optimisers.jl#L509-L516">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../data/dataloader/">« DataLoader</a><a class="docs-footer-nextpage" href="../training/">Training »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Tuesday 10 March 2020 10:11">Tuesday 10 March 2020</span>. Using Julia version 1.3.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>