{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# TD学習"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"TD (Temporal difference) learningにおいて,**報酬予測誤差**(reward prediction error, **RPE**) $\\delta_{i}$は次のように計算される. \n",
"\n",
"$$ \n",
"\\delta_{i}=r+\\gamma V_{j}\\left(x^{\\prime}\\right)-V_{i}(x) \n",
"$$ \n",
"\n",
"ただし,現在の状態を$x$, 次の状態を$x'$, 予測価値分布を$V(x)$, 報酬信号を$r$, 時間割引率(time discount)を$\\gamma$としました.\n",
"また,$V_{j}\\left(x^{\\prime}\\right)$は予測価値分布$V\\left(x^{\\prime}\\right)$からのサンプルです. このRPEは脳内において主に中脳の**VTA**(腹側被蓋野)や**SNc**(黒質緻密部)における**ドパミン(dopamine)ニューロン**の発火率として表現されています.\n",
"\n",
"ただし,VTAとSNcのドパミンニューロンの役割は同一ではありません.ドパミンニューロンへの入力が異なっています [(Watabe-Uchida et al., _Neuron._ 2012)](https://www.cell.com/neuron/fulltext/S0896-6273(12)00281-4). また,細かいですがドパミンニューロンの発火は報酬量に対して線形ではなく,やや飽和する非線形な応答関数 (Hill functionで近似可能)を持ちます([Eshel et al., _Nat. Neurosci._ 2016](https://www.nature.com/articles/nn.4239)).このため著者実装では報酬 $r$に非線形関数がかかっているものもあります.\n",
"\n",
"先ほどRPEはドパミンニューロンの発火率で表現されている,といいました.RPEが正の場合はドパミンニューロンの発火で表現できますが,単純に考えると負の発火率というものはないため,負のRPEは表現できないように思います.ではどうしているかというと,RPEが0(予想通りの報酬が得られた場合)でもドパミンニューロンは発火しており,RPEが正の場合にはベースラインよりも発火率が上がるようになっています.逆にRPEが負の場合にはベースラインよりも発火率が減少する(抑制される)ようになっています\n",
" ([Schultz et al., Science. 1997](https://science.sciencemag.org/content/275/5306/1593.long \"https://science.sciencemag.org/content/275/5306/1593.long\"); [Chang et al., Nat Neurosci. 2016](https://www.nature.com/articles/nn.4191 \"https://www.nature.com/articles/nn.4191\")).発火率というのを言い換えればISI (inter-spike interval, 発火間隔)の長さによってPREが符号化されている(ISIが短いと正のRPE, ISIが長いと負のRPEを表現)ともいえます ([Bayer et al., J.\n",
" Neurophysiol. 2007](https://www.physiology.org/doi/full/10.1152/jn.01140.2006 \"https://www.physiology.org/doi/full/10.1152/jn.01140.2006\")).\n",
"\n",
"予測価値(分布) $V(x)$ですが,これは線条体(striatum)のパッチ (SNcに抑制性の投射をする)やVTAのGABAニューロン (VTAのドパミンニューロンに投射して減算抑制をする, ([Eshel, et al., _Nature_. 2015](https://www.nature.com/articles/nature14855 \"https://www.nature.com/articles/nature14855\")))などにおいて表現されている. この予測価値は通常のTD learningでは次式により更新されます. \n",
"\n",
"$$ \n",
"V_{i}(x) \\leftarrow V_{i}(x)+\\alpha_{i} f\\left(\\delta_{i}\\right) \n",
"$$ \n",
"\n",
"ただし,$\\alpha_{i}$は学習率(learning rate), $f(\\cdot)$はRPEに対する応答関数である.生理学的には$f(\\delta)=\\delta$を使うのが妥当である."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"TD誤差\n",
"\n",
"$$\n",
"\\begin{align}\n",
"\\delta_{t} = r_{t+1} + \\gamma V(s_{t+1}) - V(s_{t})\n",
"\\end{align}\n",
"$$\n",
"\n",
"価値の更新\n",
"\n",
"$$\n",
"\\begin{align}\n",
"V(s_{t}) \\leftarrow V(s_{t}) + \\alpha \\delta_{t}\n",
"\\end{align}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"([Schultz, Dayan & Montague, Science, 1997](https://science.sciencemag.org/content/275/5306/1593))を参考にシミュレーションを行う.60試行する.0秒の時に条件刺激(光刺激)が入る.また,6試行目から40試行目まで条件刺激があってから1.2秒後に報酬が与えられるとする."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"using PyPlot\n",
"rc(\"axes.spines\", top=false, right=false)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"num_trial = 60 # 試行回数\n",
"T = 3.0f0 # s\n",
"dt = 0.1f0 # s\n",
"nt = UInt(T/dt) + 1 # number of timesteps\n",
"value = zeros(num_trial, nt) \n",
"delta = zeros(num_trial, nt) # TD error\n",
"\n",
"flash_time = UInt(1.1f0/dt)\n",
"delay = UInt(1.2f0/dt)\n",
"reward_trial = 6:40 # 報酬が貰える試行の区間を設定する\n",
"reward = zeros(num_trial, nt)\n",
"reward[reward_trial, flash_time+delay] .= 1.0\n",
"\n",
"α = 0.8 # 学習率\n",
"γ = 0.99 # 割引率\n",
"\n",
"# simulation\n",
"for i in 2:num_trial\n",
" for t in 1:nt-1\n",
" delta[i, t] = reward[i, t] + γ*value[i-1, t+1] - value[i-1, t]\n",
" if t > flash_time\n",
" value[i, t] = value[i-1, t] + α*delta[i, t]\n",
" end\n",
" end\n",
"end"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"結果を描画する."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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",
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"Figure(PyObject