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The latest in OPE-CS. This can track the running mean of a predictable policy sequence in a nonstationary environment and does not require an explicit importance weight upper bound. For a fixed policy in a stationary environment the running intersection can be used to shrink the interval monotonically.
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"id": "a213a99d", | |
"metadata": {}, | |
"source": [ | |
"# Derivations " | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "aa11737c", | |
"metadata": {}, | |
"source": [ | |
"## Empirical Bernstein only bounded below (lower CS only)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "d6c5db8e", | |
"metadata": {}, | |
"source": [ | |
"Realizations $X_t \\geq 0$ bounded below with finite $\\mathbb{E}_{t-1}\\left[X_t\\right]$. We use a (predictable) predictor $\\hat{X}_t \\leq 1$. Then $$\n", | |
"\\begin{aligned}\n", | |
"Y_t &= X_t - \\mathbb{E}_{t-1}\\left[X_t\\right] \\\\\n", | |
"S_t &= \\sum_{s=1}^t Y_s \\\\\n", | |
"\\delta_t &= \\hat{X}_t - \\mathbb{E}_{t-1}\\left[X_t\\right] \\\\\n", | |
"Y_t - \\delta_t &= X_t - \\hat{X}_t \\geq -1 \\\\\n", | |
"\\text{Wealth}_t(\\lambda) &= \\exp\\left(\\lambda S_t - \\psi_E(\\lambda) \\sum_{s=1}^t (Y_s - \\delta_s)^2\\right) \\\\\n", | |
"&= \\prod_{s=1}^t \\exp\\left(\\lambda Y_s + \\left(\\lambda + \\log(1 - \\lambda)\\right) (Y_s - \\delta_s)^2\\right) \\\\\n", | |
"&= \\prod_{s=1}^t \\exp\\left(\\lambda \\delta_s \\right) \\exp\\left(\\lambda \\left(Y_s - \\delta_s\\right) + (Y_s - \\delta_s)^2 \\left(\\lambda + \\log(1 - \\lambda)\\right) \\right) \\\\\n", | |
"&\\leq \\prod_{s=1}^t \\exp\\left(\\lambda \\delta_s \\right) \\left(1 + \\lambda \\left(Y_s - \\delta_s\\right)\\right) & \\left(\\text{Fan 2015}\\right) \\\\\n", | |
"\\mathbb{E}_{t-1}\\left[\\text{Wealth}_t(\\lambda)\\right] &\\leq \\text{Wealth}_{t-1}(\\lambda) \\exp\\left(\\lambda \\delta_t \\right) \\left(1 - \\lambda \\delta_t\\right) & \\left(\\mathbb{E}_{t-1}[Y_t] = 0 \\land \\delta_t \\text{ predictable}\\right) \\\\\n", | |
"&\\leq \\text{Wealth}_{t-1}(\\lambda) & \\left( e^{x} (1 - x) \\leq 1 \\right)\n", | |
"\\end{aligned}\n", | |
"$$\n", | |
"Thus we can use an exponential CGF bound with $V_t = \\sum_{s=1}^t \\left(X_s - \\hat{X}_s\\right)^2$ with scale parameter 1 despite unbounded realization." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "63194734", | |
"metadata": {}, | |
"source": [ | |
"## OPE Specialization" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "0a1e52d1", | |
"metadata": {}, | |
"source": [ | |
"**Policy value** For an OPE-CS on the policy value , we have $x = w r$ with $E[w] = 1$, $w \\geq 0$ a.s., and $r \\in [0, 1]$ a.s. The yields a lower CS only. However an upper CS for $x$ can be derived from a lower CS for $x' = w (1 - r)$ via $E[x] = 1 - E[x']$.\n", | |
"\n", | |
"**Policy improvement** Similarly for an OPE-CS on (half the amount of the) policy improvement over the logging policy, we have $x = (w - 1) \\frac{r}{2}$ with $X \\geq -\\frac{1}{2}$ a.s., $E[w] = 1$, $w \\geq 0$ a.s. and $r \\in [0, 1]$ a.s. If we clip the predictor $\\hat{X}$ to be in $[-\\frac{1}{2}, \\frac{1}{2}]$ we again get a lower CS; and we can get an upper CS from a lower CS on $x' = (w - 1)(\\frac{1 - r}{2})$ via $E[x] = -E[x']$." | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "75e1c383", | |
"metadata": {}, | |
"source": [ | |
"## Gamma Mixture" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "18a84930", | |
"metadata": {}, | |
"source": [ | |
"Our wealth process for $c = 1$ and $\\lambda \\in [0, 1]$ is $$\n", | |
"\\begin{aligned}\n", | |
"\\text{Wealth}(\\lambda) &= \\exp\\left(\\lambda s + \\left(\\lambda + \\log\\left(1 - \\lambda\\right)\\right) v\\right) = \\left(1 - \\lambda\\right)^v \\exp\\left(\\lambda (s + v)\\right)\n", | |
"\\end{aligned}\n", | |
"$$ We will mix with the gamma distribution on $(1 - \\lambda)$ with $a = \\rho$, $b = 1/\\rho$, $$\n", | |
"\\begin{aligned}\n", | |
"f(\\lambda) &= \\frac{\\rho^{\\rho} e^{-\\rho \\left(1 - \\lambda\\right)} \\left(1 - \\lambda\\right)^{\\rho - 1}}{\\Gamma(\\rho)}\n", | |
"\\end{aligned}\n", | |
"$$ Yielding mixture $$\n", | |
"\\begin{aligned}\n", | |
"\\frac{\\int_0^1 d\\lambda\\ f(\\lambda) \\text{Wealth}(\\lambda)}{\\int_0^1 d\\lambda\\ f(\\lambda)} &= \\frac{\\rho^{\\rho} e^{s + v}}{\\left(s + v + \\rho\\right)^{v + \\rho}} \\frac{\\gamma\\left(v + \\rho, s + v + \\rho\\right)}{\\gamma\\left(\\rho, \\rho\\right)},\n", | |
"\\end{aligned}\n", | |
"$$ where $\\gamma(a, x) = \\int_0^x dt\\ t^{a-1} e^{-t}$." | |
] | |
}, | |
{ | |
"cell_type": "raw", | |
"id": "87862f6a", | |
"metadata": {}, | |
"source": [ | |
"Refine[PDF[GammaDistribution[\\[Rho],1/ \\[Rho]], 1 - \\[Lambda]], 1 - \\[Lambda] > 0]\n", | |
"Refine[Integrate[% (1 - \\[Lambda])^v Exp[\\[Lambda] (s + v)], { \\[Lambda], 0, 1 }], Re[v + \\[Rho]] > 0 && Re[\\[Rho]] > 0] / Refine[Integrate[%, { \\[Lambda], 0, 1 }], Re[\\[Rho]] > 0]" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"id": "fcd6b927", | |
"metadata": {}, | |
"source": [ | |
"## Code" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 67, | |
"id": "846c04f8", | |
"metadata": { | |
"code_folding": [ | |
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}, | |
"outputs": [ | |
{ | |
"data": { | |
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\n", | |
"text/plain": [ | |
"<Figure size 1152x432 with 2 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 1152x432 with 2 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"class EmpBernCS(object):\n", | |
" def __init__(self, rho=1):\n", | |
" super().__init__()\n", | |
" \n", | |
" self.rho = rho\n", | |
" self.sumXlow = 0\n", | |
" self.sumXhigh = 0\n", | |
" self.t = 0\n", | |
" self.sumvlow = 0\n", | |
" self.sumvhigh = 0\n", | |
" \n", | |
" def addobs(self, w, r):\n", | |
" assert w >= 0\n", | |
" assert 0 <= r <= 1\n", | |
" \n", | |
" Xhatlow = (self.sumXlow + 1/2) / (self.t + 1)\n", | |
" Xhathigh = (self.sumXhigh + 1/2) / (self.t + 1)\n", | |
" \n", | |
" self.sumvlow += (w * r - min(1, Xhatlow))**2\n", | |
" self.sumvhigh += (w * (1 - r) - min(1, Xhathigh))**2\n", | |
" \n", | |
" self.sumXlow += w * r\n", | |
" self.sumXhigh += w * (1 - r)\n", | |
" self.t += 1\n", | |
"\n", | |
" def logwealth(self, *, s, v, rho):\n", | |
" from math import log\n", | |
"\n", | |
" def loggammalowerinc(*, a, x):\n", | |
" import scipy.special as sc\n", | |
"\n", | |
" return log(sc.gammainc(a, x)) + sc.loggamma(a)\n", | |
" \n", | |
" assert s + v + rho > 0\n", | |
" assert rho > 0\n", | |
"\n", | |
" return (s + v\n", | |
" + rho * log(rho)\n", | |
" - (v + rho) * log(s + v + rho)\n", | |
" + loggammalowerinc(a = v + rho, x = s + v + rho)\n", | |
" - loggammalowerinc(a = rho, x = rho)\n", | |
" )\n", | |
"\n", | |
" def lblogwealth(self, *, t, sumXt, v, rho, alpha):\n", | |
" from math import log\n", | |
" import scipy.optimize as so\n", | |
"\n", | |
" assert 0 < alpha < 1, alpha\n", | |
" thres = -log(alpha)\n", | |
"\n", | |
" minmu = 0\n", | |
" logwealthminmu = self.logwealth(s=sumXt, v=v, rho=rho)\n", | |
"\n", | |
" if logwealthminmu <= thres:\n", | |
" return minmu\n", | |
" \n", | |
" maxmu = min(1, sumXt/t)\n", | |
" logwealthmaxmu = self.logwealth(s=sumXt - t * maxmu, v=v, rho=rho)\n", | |
"\n", | |
" assert logwealthmaxmu <= thres, (logwealthmaxmu, thres)\n", | |
"\n", | |
" res = so.root_scalar(f = lambda mu: self.logwealth(s=sumXt - t * mu, v=v, rho=rho) - thres,\n", | |
" method = 'brentq',\n", | |
" bracket = [ minmu, maxmu ])\n", | |
" assert res.converged, res\n", | |
" return res.root\n", | |
" \n", | |
" def getci(self, alpha):\n", | |
" if self.t == 0:\n", | |
" return 0, 1\n", | |
" \n", | |
" l = self.lblogwealth(t=self.t, sumXt=self.sumXlow, v=self.sumvlow, rho=self.rho, alpha=alpha/2)\n", | |
" u = 1 - self.lblogwealth(t=self.t, sumXt=self.sumXhigh, v=self.sumvhigh, rho=self.rho, alpha=alpha/2)\n", | |
" \n", | |
" return l, u\n", | |
"\n", | |
"class DataGen(object):\n", | |
" def __init__(self, *, wmax, expwsq, truemu, seed):\n", | |
" import numpy as np\n", | |
" import scipy.optimize as so\n", | |
" import random\n", | |
" \n", | |
" # { 0, 1, wmax } \\times { 0, 1 } -> 6 values -> we need 6 constraints\n", | |
" # 1 = sum_i p_i\n", | |
" # 1 = sum_i w_i p_i\n", | |
" # E[w^2] = sum_i w_i^2 p_i\n", | |
" # logging policy value = sum_i r_i p_i\n", | |
" # evaluated policy value = sum_i w_i r_i p_i\n", | |
" # we need 1 more constraint to be unique ...\n", | |
" # SURPRISE: just the above 5 constraints can be infeasible ...\n", | |
" # instead just minimize the logging policy value subject to other constraints\n", | |
" # this makes the distribution very difficult to lower bound\n", | |
" \n", | |
" self.gen = random.Random(seed)\n", | |
" self.wmax = wmax\n", | |
" self.expwsq = expwsq\n", | |
" self.truemu = truemu\n", | |
" self.population = [ (w, r) for w in (0, 1, wmax,) for r in (0, 1,) ]\n", | |
" \n", | |
" c = [ r for (w, r) in self.population ] \n", | |
" A_eq = [\n", | |
" [ 1 for (w, r) in self.population ],\n", | |
" [ w for (w, r) in self.population ],\n", | |
" [ w**2 for (w, r) in self.population ],\n", | |
" [ w*r for (w, r) in self.population ],\n", | |
" ]\n", | |
" b_eq = [ 1, 1, expwsq, truemu, ]\n", | |
" \n", | |
" res = so.linprog(np.array(c), A_eq=A_eq, b_eq=b_eq)\n", | |
" assert res.success, res\n", | |
" self.probs = res.x\n", | |
" self.logmu = res.fun\n", | |
" \n", | |
" ewwm1r = self.probs.dot([ w * (w - 1) * r for (w, r) in self.population ])\n", | |
" ewm1sq = self.probs.dot([ (w - 1)**2 for (w, r) in self.population])\n", | |
" self.kappalowstar = -ewwm1r/ewm1sq if ewm1sq > 0 else 0\n", | |
" ewwm11mr = self.probs.dot([ w * (w - 1) * (1 - r) for (w, r) in self.population ])\n", | |
" self.kappahighstar = -ewwm11mr/ewm1sq if ewm1sq > 0 else 0\n", | |
" \n", | |
" def genobs(self):\n", | |
" return self.gen.choices(population=self.population,\n", | |
" weights=self.probs,\n", | |
" )[0]\n", | |
"\n", | |
"def megasim(*, T, datagen, dt=1, alpha = 0.05, seed=4545):\n", | |
" import itertools\n", | |
" from matplotlib import pyplot as plt \n", | |
" import numpy as np\n", | |
" \n", | |
" cs = EmpBernCS()\n", | |
" wrz = []\n", | |
" lbz = []\n", | |
" ubz = []\n", | |
" \n", | |
" for t in range(T):\n", | |
" w, r = datagen.genobs()\n", | |
" cs.addobs(w, r)\n", | |
" if t % dt == 0:\n", | |
" l, u = cs.getci(alpha=0.05)\n", | |
"\n", | |
" wrz.append(w*r)\n", | |
" lbz.append(l)\n", | |
" ubz.append(u)\n", | |
" \n", | |
" fig, ax = plt.subplots(1, 2)\n", | |
" fig.set_size_inches(16, 6)\n", | |
" ax[0].plot(list(itertools.accumulate(wrz)))\n", | |
" ax[0].set_ylabel('sum(wr)')\n", | |
" ax[1].plot(lbz, label='lb library (E[w]=1)')\n", | |
" ax[1].plot(ubz, label='ub library (E[w]=1)')\n", | |
" ax[1].set_ylabel('raw bounds')\n", | |
" ax[1].legend()\n", | |
" \n", | |
" pstr = ','.join([f'{v:.3g}' for v in datagen.probs])\n", | |
" fig.suptitle(f'expwsq = {datagen.expwsq} wmax={datagen.wmax} truemu={datagen.truemu} p={pstr}')\n", | |
" \n", | |
" return None\n", | |
"\n", | |
"def flass():\n", | |
" dg = DataGen(wmax=10, expwsq=2, truemu=1/2, seed=4545)\n", | |
" megasim(T=1000, dt=1, datagen=dg)\n", | |
" dg = DataGen(wmax=10, expwsq=10, truemu=1/2, seed=4545)\n", | |
" megasim(T=1000, dt=1, datagen=dg)\n", | |
"\n", | |
"flass()" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"id": "3c81e20a", | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3 (ipykernel)", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.8.13" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 5 | |
} |
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Convergence is more rapid when evaluating policies nearer to the logging policy.