rm Adam for now
This commit is contained in:
Steven G. Johnson committed
1 parent
9ed7e009b2
commit
e4ff01607e
1 file changed
+30
-147
@@ -145,7 +145,7 @@
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{
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"data": {
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"text/plain": [
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"(100001, 2.1898661935779876e-7)"
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"(100001, 8.283307337600646e-6)"
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]
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},
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"execution_count": 3,
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@@ -162,12 +162,12 @@
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"image/png": 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truncated
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"image/png": 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truncated
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"text/plain": [
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"Figure(PyObject <Figure size 1000x400 with 2 Axes>)"
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]
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@@ -178,10 +178,10 @@
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{
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"data": {
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"text/plain": [
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"(0.0, 9.264876845621783e-5)"
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"(0.0, 0.0013784058155002347)"
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]
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},
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"execution_count": 19,
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -223,7 +223,7 @@
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{
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"data": {
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"text/plain": [
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"6.650888617809801e-7"
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"8.995093126267436e-5"
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]
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},
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"execution_count": 5,
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@@ -410,7 +410,7 @@
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{
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"data": {
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"text/plain": [
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"(100001, 2.2419170480036973e-7)"
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"(100001, 2.594316141650972e-5)"
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]
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},
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"execution_count": 8,
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@@ -430,12 +430,12 @@
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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"data": {
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||||
"image/png": 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truncated
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"Figure(PyObject <Figure size 640x480 with 1 Axes>)"
|
||||
]
|
||||
@@ -446,10 +446,10 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"PyObject <matplotlib.legend.Legend object at 0x7fc6b5565810>"
|
||||
"PyObject <matplotlib.legend.Legend object at 0x7ff4b23d1cd0>"
|
||||
]
|
||||
},
|
||||
"execution_count": 18,
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -656,16 +656,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 23,
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(1388, 9.925971497572407e-9)"
|
||||
"(1869, 9.892793280828157e-9)"
|
||||
]
|
||||
},
|
||||
"execution_count": 23,
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -687,12 +687,12 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 29,
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"Figure(PyObject <Figure size 640x480 with 1 Axes>)"
|
||||
]
|
||||
@@ -706,7 +706,7 @@
|
||||
"(0.0, 2000.0)"
|
||||
]
|
||||
},
|
||||
"execution_count": 29,
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -730,7 +730,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 30,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -749,7 +749,7 @@
|
||||
"PyObject Text(0.5, 1.0, 'convergence of 2x2 steepest-descent + momentum')"
|
||||
]
|
||||
},
|
||||
"execution_count": 30,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -792,7 +792,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -801,7 +801,7 @@
|
||||
"CG (generic function with 2 methods)"
|
||||
]
|
||||
},
|
||||
"execution_count": 14,
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -828,16 +828,16 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"execution_count": 16,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(100001, 2.1898661935779876e-7)"
|
||||
"(100001, 8.283307337600646e-6)"
|
||||
]
|
||||
},
|
||||
"execution_count": 15,
|
||||
"execution_count": 16,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -856,12 +856,12 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 16,
|
||||
"execution_count": 17,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": 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truncated
|
||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"Figure(PyObject <Figure size 640x480 with 1 Axes>)"
|
||||
]
|
||||
@@ -872,10 +872,10 @@
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"PyObject <matplotlib.legend.Legend object at 0x7fc6b32cae10>"
|
||||
"PyObject <matplotlib.legend.Legend object at 0x7ff4b622f290>"
|
||||
]
|
||||
},
|
||||
"execution_count": 16,
|
||||
"execution_count": 17,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -899,7 +899,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 17,
|
||||
"execution_count": 18,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
@@ -918,7 +918,7 @@
|
||||
"PyObject Text(0.5, 1.0, 'convergence of 2x2 conjugate-gradient: 2 steps')"
|
||||
]
|
||||
},
|
||||
"execution_count": 17,
|
||||
"execution_count": 18,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
@@ -938,123 +938,6 @@
|
||||
"title(\"convergence of 2x2 conjugate-gradient: 2 steps\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## The Adam algorithm\n",
|
||||
"\n",
|
||||
"A popular algorithm for machine learning is [*Adam* (Kingma & Ba, 2015)](https://arxiv.org/pdf/1412.6980.pdf), which is a momentum-like algorithm with some additional twists that make it easier to apply to arbitrary functions (without knowing eigenvalues of the Hessian).\n",
|
||||
"\n",
|
||||
"* It has a \"momentum\" or \"memory\" term, where the gradient is estimated by a weighted average of the current mini-batch gradient and the previous gradient estimate.\n",
|
||||
"* It also estimates the variance of the gradient components in the same way, and essentially uses this as rough diagonal estimate of the Hessian: it takes a \"crude Newton\"-like step where the gradient components are weighed inversely by the square roots of their variances.\n",
|
||||
"\n",
|
||||
"It's quite simple to implement directly from the description in the paper linked above. Let's try it out on our quadratic optimization problem:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 81,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"adam (generic function with 2 methods)"
|
||||
]
|
||||
},
|
||||
"execution_count": 81,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"function adam(A, b, x=zero(b); tol=1e-8, maxiters=1000,\n",
|
||||
" α = 0.001, ϵ = 1e-8, β₁ = 0.9, β₂ = 0.999) # hyper-parameters from the paper\n",
|
||||
" bnorm = norm(b)\n",
|
||||
" var, mom, r = zero(x), zero(x), b - A*x # pre-allocate\n",
|
||||
" rnorm = Float64[norm(r)] # return the array of residual norms\n",
|
||||
" for i = 1:maxiters\n",
|
||||
" # Adam update\n",
|
||||
" @. mom = β₁*mom - (1-β₁)*r\n",
|
||||
" @. var = β₂*var + (1-β₂)*r^2\n",
|
||||
" # m̂ = mom / (1 - β₁^i) # normalize by total weights\n",
|
||||
" # v̂ = var / (1 - β₂^i) # normalize by total weights\n",
|
||||
" # x = @. x - α * m̂ / (√v̂ + ϵ)\n",
|
||||
" @. x -= α * (mom / $(1 - β₁^i)) / (√(var / $(1 - β₂^i)) + ϵ)\n",
|
||||
" r .= b .- mul!(r, A, x) # b - Ax, in-place\n",
|
||||
" push!(rnorm, norm(r))\n",
|
||||
" rnorm[end] ≤ tol*bnorm && break # converged\n",
|
||||
" end\n",
|
||||
" return x, rnorm\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 82,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(100001, 0.004111429305032976)"
|
||||
]
|
||||
},
|
||||
"execution_count": 82,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"x_adam, rnorm_adam = adam(A, b, maxiters=100000)\n",
|
||||
"length(rnorm_adam), rnorm_adam[end]/norm(b)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 83,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"Figure(PyObject <Figure size 640x480 with 1 Axes>)"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"PyObject <matplotlib.legend.Legend object at 0x7fc6af71ad90>"
|
||||
]
|
||||
},
|
||||
"execution_count": 83,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"semilogy(rnorm_fixed, \"b-\")\n",
|
||||
"semilogy(rnorm_asd, \"r-\")\n",
|
||||
"semilogy(rnorm_adam, \"g-\")\n",
|
||||
"title(\"convergence of Adam\")\n",
|
||||
"ylabel(\"residual norm\")\n",
|
||||
"xlabel(\"iterations\")\n",
|
||||
"legend([\"steepest descent\", \"+ momentum\", \"Adam\"])\n",
|
||||
"#xlim(0, 2000)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Hmm, either Adam sucks for this problem or I have a bug?"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
|
||||
Reference in new issue
Block a user