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An off-policy confidence sequence suitable for general purposes which supports oblivious data censorship.
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{
"cells": [
{
"cell_type": "markdown",
"id": "38cb8dc5",
"metadata": {},
"source": [
"# Reference OPE CS Impl"
]
},
{
"cell_type": "markdown",
"id": "376afba0",
"metadata": {},
"source": [
"An off-policy confidence sequence suitable for general purposes which supports oblivious data censorship."
]
},
{
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"source": [
"## API\n",
"\n",
"The public API is:\n",
" * `Constructor`$(r_\\min, r_\\max, \\text{adjust})$: takes an initial reward range and a boolean saying whether to adjust automatically.\n",
" * `addobs(w_t, r_t, p_drop=0, n_drop=None)`: Observe an importance weighted reward.\n",
" * `p_drop` and `n_drop` model an oblivious random data censorship process, e.g., a logging system randomly dropping events in response to queue backpressure.\n",
" * Oblivious means “conditionally independent of the reward given the context and action”: ${p_{\\text{drop}}}_t \\perp r_{a_t} | a_t, x_t$.\n",
" * `p_drop` is the probability of dropping an event, should be $\\in [0, 1)$.\n",
" * `n_drop` is the number of events that were dropped prior to this event being not-dropped. Should be `None` or non-negative.\n",
" * Since `addobs()` is being called, this event is presumed not-dropped.\n",
" * If `n_drop is None`, we will assume `ndrop` is the mean of a negative binomial process.\n",
" * If you know `n_drop`, it's better to use the actual value than this assumption.\n",
" * `getci`$(\\alpha)$: Return a CI at confidence level $(1 - \\alpha)$."
]
},
{
"cell_type": "markdown",
"id": "29e5928b",
"metadata": {},
"source": [
"## Coverage Guarantee"
]
},
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"source": [
"For the coverage guarantee you must certify the preconditions:\n",
" * $w_t = \\frac{d\\pi_t}{d \\mu_t}(a_t)$ is the correct importance weight:\n",
" * $\\mu_t$ is the logging policy (i.e., the distribution from which the action is drawn):\n",
" * $\\pi_t$ is the policy being evaluated (i.e., the policy whose mean is being estimated).\n",
" * $r_t \\in [ r_{\\min}, r_{\\max} ]$ with probability 1.\n",
" * $r_t = r_t(a_t)$ where $a_t \\sim \\mu_t$.\n",
" * `p_drop` is the actual probability of dropping this event (which, by virtue of being here, is not-dropped).\n",
" * `n_drop` is the actual number of dropped events prior to this event being not-dropped.\n",
" \n",
"Then you get the following guarantee $$\n",
"\\mathrm{Pr}\\left( \\forall t: \\frac{1}{t} \\sum_{s=1}^t \\mathbb{E}_{\\substack{t-1 \\\\ a \\sim \\pi_t}}\\left[r_t(a)\\right] \\in \\text{getci}(\\alpha) \\right) \\geq 1 - \\alpha.\n",
"$$\n",
"This guarantee is:\n",
" * time-uniform coverage (simultaneously valid for all sample sizes)\n",
" * of the running mean of the policy sequence (evaluated in an environment where `p_drop=0` and `n_drop=0` always)\n",
" * the environment can [adaptively](https://math.stackexchange.com/questions/1794875/what-is-the-difference-between-an-adapted-process-and-a-predictable-process) change each timestep\n",
" * this includes `p_drop` adaptively changing each timestep\n",
" * the policy being evaluated can [predictably](https://math.stackexchange.com/questions/1794875/what-is-the-difference-between-an-adapted-process-and-a-predictable-process) change with each timestep"
]
},
{
"cell_type": "markdown",
"id": "6da1e3b7",
"metadata": {},
"source": [
"### Reward Range Robustness"
]
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"id": "7d3e116e",
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"To facilitate unknown reward ranges we have two strategies:\n",
" * `adjust=False`: clips the realized reward to be in the constructor supplied range $[r_{\\min}, r_{\\max}]$ and provides the coverage guarantee on this modified random variable.\n",
" * `adjust=True`: expands the reward range if an observed value exceeds the constructor supplied range.\n",
" * in this case, the coverage guarantee is conditioned on observing the complete range (if initially incorrectly specified), which can cover a value very different than the running mean if extreme reward values are rare."
]
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"source": [
"class IncrementalFsum:\n",
" \"\"\" Incremental version of https://en.wikipedia.org/wiki/Kahan_summation_algorithm \"\"\"\n",
"\n",
" def __init__(self):\n",
" self.partials = []\n",
"\n",
" def __iadd__(self, x):\n",
" i = 0\n",
" for y in self.partials:\n",
" if abs(x) < abs(y):\n",
" x, y = y, x\n",
" hi = x + y\n",
" lo = y - (hi - x)\n",
" if lo:\n",
" self.partials[i] = lo\n",
" i += 1\n",
" x = hi\n",
" self.partials[i:] = [x]\n",
" return self\n",
"\n",
" def __add__(self, other):\n",
" result = IncrementalFsum()\n",
" result.partials = deepcopy(self.partials)\n",
" for y in other.partials:\n",
" result += y\n",
" return result\n",
"\n",
" def __float__(self):\n",
" return sum(self.partials, 0.0)\n",
"\n",
"class EmpBernDynDropCS(object):\n",
" def __init__(self, rmin=0, rmax=1, adjust=True):\n",
" super().__init__()\n",
" \n",
" assert rmin <= rmax, (rmin, rmax)\n",
" \n",
" self.rho = 1\n",
" self.rmin = rmin\n",
" self.rmax = rmax\n",
" self.adjust = adjust\n",
" \n",
" self.t = 0\n",
"\n",
" self.sumwsqrsq = IncrementalFsum()\n",
" self.sumwsqr = IncrementalFsum()\n",
" self.sumwsq = IncrementalFsum()\n",
" self.sumwr = IncrementalFsum()\n",
" self.sumw = IncrementalFsum()\n",
" self.sumwrxhatlow = IncrementalFsum()\n",
" self.sumwxhatlow = IncrementalFsum()\n",
" self.sumxhatlowsq = IncrementalFsum()\n",
" self.sumwrxhathigh = IncrementalFsum()\n",
" self.sumwxhathigh = IncrementalFsum()\n",
" self.sumxhathighsq = IncrementalFsum()\n",
" \n",
" def addobs(self, w, r, p_drop=0, n_drop=None):\n",
" assert w >= 0\n",
" assert 0 <= p_drop < 1\n",
" assert n_drop is None or n_drop >= 0\n",
" \n",
" if not self.adjust:\n",
" r = min(self.rmax, max(self.rmin, r))\n",
" else:\n",
" self.rmin = min(self.rmin, r)\n",
" self.rmax = max(self.rmax, r)\n",
" \n",
" if n_drop is None:\n",
" n_drop = p_drop / (1 - p_drop)\n",
" \n",
" if n_drop > 0:\n",
" import scipy.special as sc\n",
" \n",
" # we have to simulate presenting n_drop events with w=0 in a row, which we can do in closed form\n",
" # Sum[(a/(b + s))^2, { s, 0, n - 1 }] \n",
" # a^2 PolyGamma[1,b]-a^2 PolyGamma[1,b+n] \n",
" \n",
" sumXlow = (float(self.sumwr) - float(self.sumw) * self.rmin) / (self.rmax - self.rmin)\n",
" alow = sumXlow + 1/2\n",
" blow = self.t + 1\n",
" self.sumxhatlowsq += alow**2 * (sc.polygamma(1, blow).item() - sc.polygamma(1, blow + n_drop).item())\n",
" \n",
" sumXhigh = (float(self.sumw) * self.rmax - float(self.sumwr)) / (self.rmax - self.rmin)\n",
" ahigh = sumXhigh + 1/2\n",
" bhigh = self.t + 1\n",
" self.sumxhathighsq += ahigh**2 * (sc.polygamma(1, bhigh).item() - sc.polygamma(1, bhigh + n_drop).item())\n",
" \n",
" self.t += n_drop\n",
" \n",
" sumXlow = (float(self.sumwr) - float(self.sumw) * self.rmin) / (self.rmax - self.rmin)\n",
" Xhatlow = (sumXlow + 1/2) / (self.t + 1)\n",
" sumXhigh = (float(self.sumw) * self.rmax - float(self.sumwr)) / (self.rmax - self.rmin)\n",
" Xhathigh = (sumXhigh + 1/2) / (self.t + 1)\n",
" \n",
" w /= (1 - p_drop)\n",
" \n",
" self.sumwsqrsq += (w * r)**2\n",
" self.sumwsqr += w**2 * r\n",
" self.sumwsq += w**2\n",
" self.sumwr += w * r\n",
" self.sumw += w\n",
" self.sumwrxhatlow += w * r * Xhatlow\n",
" self.sumwxhatlow += w * Xhatlow\n",
" self.sumxhatlowsq += Xhatlow**2\n",
" self.sumwrxhathigh += w * r * Xhathigh\n",
" self.sumwxhathigh += w * Xhathigh\n",
" self.sumxhathighsq += Xhathigh**2\n",
" \n",
" self.t += 1\n",
" \n",
" def getci(self, alpha):\n",
" if self.t == 0 or self.rmin == self.rmax:\n",
" return [self.rmin, self.rmax]\n",
" \n",
" sumvlow = ( (float(self.sumwsqrsq) - 2 * self.rmin * float(self.sumwsqr) + self.rmin**2 * float(self.sumwsq)) / (self.rmax - self.rmin)**2\n",
" - 2 * (float(self.sumwrxhatlow) - self.rmin * float(self.sumwxhatlow)) / (self.rmax - self.rmin)\n",
" + float(self.sumxhatlowsq)\n",
" )\n",
" sumXlow = (float(self.sumwr) - float(self.sumw) * self.rmin) / (self.rmax - self.rmin)\n",
" l = self.__lblogwealth(t=self.t, sumXt=sumXlow, v=sumvlow, rho=self.rho, alpha=alpha/2)\n",
" \n",
" sumvhigh = ( (float(self.sumwsqrsq) - 2 * self.rmax * float(self.sumwsqr) + self.rmax**2 * float(self.sumwsq)) / (self.rmax - self.rmin)**2\n",
" + 2 * (float(self.sumwrxhathigh) - self.rmax * float(self.sumwxhathigh)) / (self.rmax - self.rmin)\n",
" + float(self.sumxhathighsq)\n",
" )\n",
" sumXhigh = (float(self.sumw) * self.rmax - float(self.sumwr)) / (self.rmax - self.rmin)\n",
" u = 1 - self.__lblogwealth(t=self.t, sumXt=sumXhigh, v=sumvhigh, rho=self.rho, alpha=alpha/2)\n",
" \n",
" return self.rmin + l * (self.rmax - self.rmin), self.rmin + u * (self.rmax - self.rmin)\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",
" if logwealthmaxmu >= thres:\n",
" return maxmu\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"
]
},
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"id": "74bb2b73",
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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"
},
{
"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 DataGen(object):\n",
" def __init__(self, *, wmax, expwsq, truemu, seed, rvals):\n",
" import numpy as np\n",
" import scipy.optimize as so\n",
" import random\n",
" \n",
" if False:\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",
" pass\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 rvals ]\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",
" self._expOp = lambda func: sum(p * func(w) for p, (w, _) in zip(self.probs, self.population))\n",
" self.clippedtruemu = sum(p * w * r for p, (w, r) in zip(self.probs, [ (w, r) for w in (0, 1, wmax) for r in (0, 1)]))\n",
"\n",
" def genobs(self):\n",
" w, r = self.gen.choices(population=self.population,\n",
" weights=self.probs,\n",
" )[0]\n",
" return w, r, self._expOp\n",
"\n",
"def megasim(*, T, datagen, wmax, adjust, seed, dt=1, alpha = 0.05):\n",
" import itertools\n",
" from matplotlib import pyplot as plt \n",
" import numpy as np\n",
" \n",
" cs = EmpBernDynDropCS(adjust=adjust)\n",
" gen = np.random.RandomState(seed)\n",
" pdroplow = 9/10\n",
" pdrophigh = 99/100\n",
" \n",
" wrz = []\n",
" lbz, ubz = [], []\n",
" n_drop = 0\n",
" \n",
" for t in range(T):\n",
" w, r, expOp = datagen.genobs()\n",
" p_drop = gen.uniform(low=pdroplow, high=pdrophigh)\n",
" should_drop = (gen.uniform(low=0, high=1) <= p_drop)\n",
" if should_drop:\n",
" n_drop += 1\n",
" else:\n",
" cs.addobs(w, r, p_drop, n_drop)\n",
" n_drop = 0\n",
" \n",
" if t % dt == 0:\n",
" wrz.append(w*r)\n",
" l, u = cs.getci(alpha=0.05)\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",
" color = next(ax[1]._get_lines.prop_cycler)['color']\n",
" ax[1].plot(lbz, label='CS', color=color)\n",
" ax[1].plot(ubz, color=color)\n",
" color = next(ax[1]._get_lines.prop_cycler)['color']\n",
" ax[1].plot([datagen.truemu if adjust else datagen.clippedtruemu]*len(lbz), linestyle='dashed', color=color, label=f'{datagen.truemu if adjust else datagen.clippedtruemu:.3g}')\n",
" ax[1].set_xlabel(f'examples (x {dt})')\n",
" ax[1].set_ylabel('raw bounds')\n",
" ax[1].set_xscale('log')\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} pdrop $\\in [{pdroplow, pdrophigh}]$')\n",
" \n",
" return None\n",
"\n",
"def flass(seed):\n",
" dg = DataGen(wmax=10, expwsq=2, truemu=1/2, rvals=(-2, 2), seed=seed)\n",
" megasim(T=100000, wmax=10, dt=10, datagen=dg, adjust=True, seed=seed+1)\n",
" megasim(T=100000, wmax=10, dt=10, datagen=dg, adjust=False, seed=seed+1)\n",
" dg = DataGen(wmax=10, expwsq=2, truemu=1/2, rvals=(0, 1), seed=seed)\n",
" megasim(T=100000, wmax=10, dt=10, datagen=dg, adjust=False, seed=seed+1)\n",
"\n",
"flass(4545)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "223a98ab",
"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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