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657 lines
22 KiB
Plaintext
657 lines
22 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "religious-anaheim",
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"metadata": {},
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"outputs": [],
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"source": [
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"import torch\n",
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"from torch.autograd.functional import jacobian\n",
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"import itertools\n",
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"import math\n",
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"import abc"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "green-brunei",
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"metadata": {},
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"outputs": [],
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"source": [
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"class EconomicAgent(metaclass=abc.ABCMeta):\n",
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" @abc.abstractmethod\n",
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" def period_benefit(self,state,estimand_interface):\n",
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" pass\n",
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" @abc.abstractmethod\n",
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" def _period_benefit(self):\n",
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" pass\n",
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" @abc.abstractmethod\n",
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" def period_benefit_jacobian_wrt_states(self):\n",
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" pass\n",
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" @abc.abstractmethod\n",
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" def _period_benefit_jacobian_wrt_states(self):\n",
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" pass\n",
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" @abc.abstractmethod\n",
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" def period_benefit_jacobian_wrt_launches(self):\n",
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" pass\n",
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" @abc.abstractmethod\n",
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" def _period_benefit_jacobian_wrt_launches(self):\n",
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" pass\n",
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"\n",
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"class LinearProfit(EconomicAgent):\n",
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" \"\"\"\n",
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" The simplest type of profit function available.\n",
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" \"\"\"\n",
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" def __init__(self, constellation_number, discount_factor, benefit_weight, launch_cost, deorbit_cost=0):\n",
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" #track which constellation this is.\n",
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" self.constellation_number = constellation_number\n",
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"\n",
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" #parameters describing the agent's situation\n",
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" self.discount_factor = discount_factor\n",
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" self.benefit_weights = benefit_weight\n",
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" self.launch_cost = launch_cost\n",
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" self.deorbit_cost = deorbit_cost\n",
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"\n",
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" def __str__(self):\n",
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" return \"LinearProfit\\n Benefit weights:\\t{}\\n launch cost:\\t{}\\n Deorbit cost:\\t{}\".format(self.benefit_weights, self.launch_cost, self.deorbit_cost)\n",
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"\n",
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" def period_benefit(self,state,estimand_interface):\n",
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" return self._period_benefit(state.stocks, state.debris, estimand_interface.choices)\n",
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" \n",
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" def _period_benefit(self,stocks,debris,choice):\n",
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" profits = self.benefit_weights @ stocks \\\n",
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" - self.launch_cost * choice[self.constellation_number] #\\ \n",
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" #- deorbit_cost @ deorbits[self.constellation_number]\n",
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" return profits\n",
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"\n",
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" def period_benefit_jacobian_wrt_states(self, states, estimand_interface):\n",
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" return self._period_benefit_jacobian_wrt_states(states.stocks, states.debris, estimand_interface.choices)\n",
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"\n",
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" def _period_benefit_jacobian_wrt_states(self, stocks, debris, launches):\n",
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" jac = jacobian(self._period_benefit, (stocks,debris,launches))\n",
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" return torch.cat((jac[0], jac[1]))\n",
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" \n",
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" def period_benefit_jacobian_wrt_launches(self, states, estimand_interface):\n",
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" return self._period_benefit_jacobian_wrt_launches(states.stocks, states.debris, estimand_interface.choices)\n",
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"\n",
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" def _period_benefit_jacobian_wrt_launches(self,stocks,debris,launches):\n",
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" jac = jacobian(self._period_benefit, (stocks,debris,launches))\n",
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" return jac[2]\n",
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"\n",
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"class States():\n",
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" \"\"\"\n",
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" This is supposed to capture the state variables of the model, to create a common interface \n",
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" when passing between functions.\n",
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" \"\"\"\n",
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" def __init__(self, stocks,debris):\n",
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" self.stocks = stocks\n",
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" self.debris = debris\n",
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" \n",
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"\n",
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" def __str__(self):\n",
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" return \"stocks\\t{} \\ndebris\\t {}\".format(self.stocks,self.debris)\n",
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"\n",
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" @property\n",
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" def number_constellations(self):\n",
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" return len(self.stocks)\n",
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" @property\n",
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" def number_debris_trackers(self):\n",
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" return len(self.debris)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "sweet-injection",
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"metadata": {},
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"outputs": [],
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"source": [
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" \n",
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"class EstimandInterface():\n",
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" \"\"\"\n",
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" This defines a clean interface for working with the estimand (i.e. thing we are trying to estimate).\n",
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" In general, we are trying to estimate the choice variables and the partial derivatives of the value functions.\n",
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" This \n",
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"\n",
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" This class wraps output for the neural network (or other estimand), allowing me to \n",
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" - easily substitute various types of launch functions by having a common interface\n",
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" - this eases testing\n",
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" - check dimensionality etc without dealing with randomness\n",
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" - again, easing testing\n",
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" - reason more cleanly about the component pieces\n",
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" - easing programming\n",
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" - provide a clean interface to find constellation level launch decisions etc.\n",
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"\n",
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" It takes inputs of two general categories:\n",
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" - the choice function results\n",
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" - the partial derivatives of the value function\n",
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" \"\"\"\n",
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" def __init__(self, partials, choices, deorbits=None):\n",
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" self.partials = partials\n",
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" self.choices = choices\n",
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" \n",
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" @property\n",
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" def number_constellations(self):\n",
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" pass #fix this\n",
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" return self.choices.shape[-1]\n",
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" @property\n",
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" def number_states(self):\n",
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" pass #fix this\n",
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" return self.partials.shape[-1] #This depends on the debris trackers technically.\n",
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"\n",
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" def choice_single(self, constellation):\n",
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" #returns the launch decision for the constellation of interest\n",
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" \n",
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" filter_tensor = torch.zeros(self.number_constellations)\n",
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" filter_tensor[constellation] = 1.0\n",
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" \n",
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" return self.choices @ filter_tensor\n",
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" \n",
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" def choice_vector(self, constellation):\n",
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" #returns the launch decision for the constellation of interest as a vector\n",
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" \n",
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" filter_tensor = torch.zeros(self.number_constellations)\n",
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" filter_tensor[constellation] = 1.0\n",
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" \n",
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" return self.choices * filter_tensor\n",
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" \n",
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" def partial_vector(self, constellation):\n",
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" #returns the partials of the value function corresponding to the constellation of interest\n",
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" \n",
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" filter_tensor = torch.zeros(self.number_states)\n",
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" filter_tensor[constellation] = 1.0\n",
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" \n",
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" return self.partials @ filter_tensor\n",
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" \n",
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" def partial_matrix(self, constellation):\n",
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" #returns the partials of the value function corresponding to \n",
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" #the constellation of interest as a matrix\n",
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" \n",
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" filter_tensor = torch.zeros(self.number_states)\n",
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" filter_tensor[constellation] = 1.0\n",
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" \n",
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" return self.partials * filter_tensor\n",
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" \n",
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" def __str__(self):\n",
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" #just a human readable descriptor\n",
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" return \"Launch Decisions and Partial Derivativs of value function with\\n\\tlaunches\\n\\t\\t {}\\n\\tPartials\\n\\t\\t{}\".format(self.choices,self.partials)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "right-dinner",
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"metadata": {},
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"outputs": [],
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"source": [
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"class ChoiceFunction(torch.nn.Module):\n",
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" \"\"\"\n",
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" This is used to estimate the launch function\n",
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" \"\"\"\n",
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" def __init__(self\n",
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" ,batch_size\n",
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" ,number_states\n",
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" ,number_choices\n",
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" ,number_constellations\n",
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" ,layer_size=12\n",
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" ):\n",
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" super().__init__()\n",
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" \n",
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" #preprocess\n",
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" self.preprocess = torch.nn.Linear(in_features=number_states, out_features=layer_size)\n",
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" \n",
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" #upsample\n",
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" self.upsample = lambda x: torch.nn.Upsample(scale_factor=number_constellations)(x).view(batch_size\n",
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" ,number_constellations\n",
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" ,layer_size)\n",
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" \n",
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" self.relu = torch.nn.ReLU() #used for coersion to the state space we care about.\n",
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" \n",
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" \n",
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" #sequential steps\n",
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" self.sequential = torch.nn.Sequential(\n",
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" torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
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" #who knows if a convolution might help here.\n",
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" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
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" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
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" )\n",
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"\n",
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" #reduce the feature axis to match expected results\n",
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" self.feature_reduction = torch.nn.Linear(in_features=layer_size, out_features=number_choices)\n",
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"\n",
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" \n",
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" def forward(self, input_values):\n",
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" \n",
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" intermediate_values = self.relu(input_values) #states should be positive anyway.\n",
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" \n",
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" intermediate_values = self.preprocess(intermediate_values)\n",
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" intermediate_values = self.upsample(intermediate_values)\n",
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" intermediate_values = self.sequential(intermediate_values)\n",
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" intermediate_values = self.feature_reduction(intermediate_values)\n",
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" \n",
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" intermediate_values = self.relu(intermediate_values) #launches are always positive, this may need removed for other types of choices.\n",
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" \n",
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" return intermediate_values"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "global-wallet",
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"metadata": {},
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"outputs": [],
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"source": [
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"class PartialDerivativesOfValueEstimand(torch.nn.Module):\n",
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" \"\"\"\n",
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" This is used to estimate the partial derivatives of the value functions\n",
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" \"\"\"\n",
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" def __init__(self\n",
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" ,batch_size\n",
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" , number_constellations\n",
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" , number_states\n",
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" , layer_size=12):\n",
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" super().__init__()\n",
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" self.batch_size = batch_size #used for upscaling\n",
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" self.number_constellations = number_constellations\n",
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" self.number_states = number_states\n",
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" self.layer_size = layer_size\n",
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" \n",
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" \n",
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" #preprocess (single linear layer in case there is anything that needs to happen to all states)\n",
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" self.preprocess = torch.nn.Sequential(\n",
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" torch.nn.ReLU() #cleanup as states must be positive\n",
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" ,torch.nn.Linear(in_features = self.number_states, out_features=self.number_states)\n",
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" )\n",
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" \n",
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" #upsample to get the basic dimensionality correct. From (batch,State) to (batch, constellation, state). Includes a reshape\n",
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" self.upsample = lambda x: torch.nn.Upsample(scale_factor=self.number_constellations)(x).view(self.batch_size\n",
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" ,self.number_constellations\n",
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" ,self.number_states)\n",
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" \n",
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" #sequential steps\n",
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" self.sequential = torch.nn.Sequential(\n",
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" torch.nn.Linear(in_features=number_states, out_features=layer_size)\n",
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" #who knows if a convolution or other layer type might help here.\n",
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" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
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" ,torch.nn.Linear(in_features=layer_size, out_features=layer_size)\n",
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" )\n",
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"\n",
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" #reduce the feature axis to match expected results\n",
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" self.feature_reduction = torch.nn.Linear(in_features=layer_size, out_features=number_states)\n",
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" \n",
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" def forward(self, states):\n",
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" #Note that the input values are just going to be the state variables\n",
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" #TODO:check that input values match the prepared dimension?\n",
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" \n",
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" #preprocess\n",
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" intermediate = self.preprocess(states)\n",
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" \n",
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" #upscale the input values\n",
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" intermediate = self.upsample(intermediate)\n",
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" \n",
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" #intermediate processing\n",
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" intermediate = self.sequential(intermediate)\n",
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" \n",
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" #reduce feature axis to match the expected number of partials\n",
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" intermediate = self.feature_reduction(intermediate)\n",
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" \n",
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" \n",
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" return intermediate\n",
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" "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "resident-cooper",
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"metadata": {},
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"outputs": [],
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"source": [
|
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"class EstimandNN(torch.nn.Module):\n",
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" \"\"\"\n",
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" This neural network takes the current states as input values and returns both\n",
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" the partial derivatives of the value function and the launch function.\n",
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" \"\"\"\n",
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" def __init__(self\n",
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" ,batch_size\n",
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" ,number_states\n",
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" ,number_choices\n",
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" ,number_constellations\n",
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" ,layer_size=12\n",
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" ):\n",
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" super().__init__()\n",
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" \n",
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"\n",
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" self.partials_estimator = PartialDerivativesOfValueEstimand(batch_size, number_constellations, number_states, layer_size)\n",
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" self.launch_estimator = ChoiceFunction(batch_size, number_states, number_choices, number_constellations, layer_size)\n",
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" \n",
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" def forward(self, input_values):\n",
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" pass\n",
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" partials = self.partials_estimator(input_values)\n",
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" launch = self.launch_estimator(input_values)\n",
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" \n",
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" return EstimandInterface(partials,launch)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "compatible-conviction",
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"metadata": {},
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"source": [
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"# Testing\n",
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"\n",
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"Test if states can handle the dimensionality needed."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "explicit-sponsorship",
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"metadata": {},
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"outputs": [],
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"source": [
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"batch_size,states,choices = 5,3,1\n",
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"constellations = states -1 #determined by debris tracking\n",
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"max_start_state = 100\n",
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"\n",
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"stocks_and_debris = torch.randint(max_start_state,(batch_size,1,states),dtype=torch.float32)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "desperate-color",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"tensor([[[88., 68., 13.]],\n",
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"\n",
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" [[23., 8., 62.]],\n",
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"\n",
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" [[96., 65., 89.]],\n",
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"\n",
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" [[16., 27., 62.]],\n",
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"\n",
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" [[40., 38., 20.]]])"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"stocks_and_debris"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "median-nurse",
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"metadata": {},
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"outputs": [],
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"source": [
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"enn = EstimandNN(batch_size\n",
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" ,states\n",
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" ,choices\n",
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" ,constellations\n",
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" ,12)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "under-monroe",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Launch Decisions and Partial Derivativs of value function with\n",
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"\tlaunches\n",
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"\t\t tensor([[[0.8138],\n",
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" [4.6481]],\n",
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"\n",
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" [[1.1540],\n",
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" [2.0568]],\n",
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"\n",
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" [[2.1170],\n",
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" [6.2769]],\n",
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"\n",
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" [[1.3752],\n",
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" [2.4555]],\n",
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"\n",
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" [[0.7025],\n",
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" [2.5947]]], grad_fn=<ReluBackward0>)\n",
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"\tPartials\n",
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"\t\ttensor([[[-1.7285, -1.5841, -1.0559],\n",
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" [ 2.9694, 4.2772, 3.6800]],\n",
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"\n",
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" [[-0.6313, -1.6874, -0.1176],\n",
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" [ 2.3680, 3.5758, 2.4247]],\n",
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"\n",
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" [[-2.1381, -3.2882, -0.9620],\n",
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" [ 5.2646, 7.8475, 5.8994]],\n",
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"\n",
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" [[-1.2167, -2.0969, -0.4998],\n",
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" [ 1.7140, 2.4235, 2.1813]],\n",
|
|
"\n",
|
|
" [[-1.1293, -1.2674, -0.6386],\n",
|
|
" [ 1.5440, 2.1548, 2.0289]]], grad_fn=<AddBackward0>)\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"print(a := enn.forward(stocks_and_debris))"
|
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]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
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"execution_count": 11,
|
|
"id": "nonprofit-castle",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def lossb(a):\n",
|
|
" #test loss function\n",
|
|
" return (a**2).sum()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"id": "crucial-homeless",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"b = ChoiceFunction(batch_size\n",
|
|
" ,states\n",
|
|
" ,choices\n",
|
|
" ,constellations\n",
|
|
" ,12)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"id": "practical-journalist",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"tensor(29.0569, grad_fn=<SumBackward0>)\n",
|
|
"tensor(23187.2695, grad_fn=<SumBackward0>)\n",
|
|
"tensor(0., grad_fn=<SumBackward0>)\n",
|
|
"tensor(0., grad_fn=<SumBackward0>)\n",
|
|
"tensor(0., grad_fn=<SumBackward0>)\n",
|
|
"tensor(0., grad_fn=<SumBackward0>)\n",
|
|
"tensor(0., grad_fn=<SumBackward0>)\n",
|
|
"tensor(0., grad_fn=<SumBackward0>)\n",
|
|
"tensor(0., grad_fn=<SumBackward0>)\n",
|
|
"tensor(0., grad_fn=<SumBackward0>)\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"tensor([[[0.],\n",
|
|
" [0.]],\n",
|
|
"\n",
|
|
" [[0.],\n",
|
|
" [0.]],\n",
|
|
"\n",
|
|
" [[0.],\n",
|
|
" [0.]],\n",
|
|
"\n",
|
|
" [[0.],\n",
|
|
" [0.]],\n",
|
|
"\n",
|
|
" [[0.],\n",
|
|
" [0.]]], grad_fn=<ReluBackward0>)"
|
|
]
|
|
},
|
|
"execution_count": 13,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"optimizer = torch.optim.SGD(b.parameters(),lr=0.01)\n",
|
|
"\n",
|
|
"for i in range(10):\n",
|
|
" #training loop\n",
|
|
" optimizer.zero_grad()\n",
|
|
"\n",
|
|
" output = b.forward(stocks_and_debris)\n",
|
|
"\n",
|
|
" l = lossb(output)\n",
|
|
"\n",
|
|
" l.backward()\n",
|
|
"\n",
|
|
" optimizer.step()\n",
|
|
"\n",
|
|
" print(l)\n",
|
|
" \n",
|
|
"\n",
|
|
"b.forward(stocks_and_debris)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
|
"id": "correct-complex",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"def lossa(a):\n",
|
|
" #test loss function\n",
|
|
" return (a.choices**2).sum() + (a.partials**2).sum()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 15,
|
|
"id": "pharmaceutical-brush",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"tensor(336.1971, grad_fn=<AddBackward0>)\n",
|
|
"tensor(67583.6484, grad_fn=<AddBackward0>)\n",
|
|
"tensor(1.5658e+26, grad_fn=<AddBackward0>)\n",
|
|
"tensor(nan, grad_fn=<AddBackward0>)\n",
|
|
"tensor(nan, grad_fn=<AddBackward0>)\n",
|
|
"tensor(nan, grad_fn=<AddBackward0>)\n",
|
|
"tensor(nan, grad_fn=<AddBackward0>)\n",
|
|
"tensor(nan, grad_fn=<AddBackward0>)\n",
|
|
"tensor(nan, grad_fn=<AddBackward0>)\n",
|
|
"tensor(nan, grad_fn=<AddBackward0>)\n"
|
|
]
|
|
},
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"tensor([[[0.],\n",
|
|
" [0.]],\n",
|
|
"\n",
|
|
" [[0.],\n",
|
|
" [0.]],\n",
|
|
"\n",
|
|
" [[0.],\n",
|
|
" [0.]],\n",
|
|
"\n",
|
|
" [[0.],\n",
|
|
" [0.]],\n",
|
|
"\n",
|
|
" [[0.],\n",
|
|
" [0.]]], grad_fn=<ReluBackward0>)"
|
|
]
|
|
},
|
|
"execution_count": 15,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"optimizer = torch.optim.SGD(enn.parameters(),lr=0.001) #note the use of enn in the optimizer\n",
|
|
"\n",
|
|
"for i in range(10):\n",
|
|
" #training loop\n",
|
|
" optimizer.zero_grad()\n",
|
|
"\n",
|
|
" output = enn.forward(stocks_and_debris)\n",
|
|
"\n",
|
|
" l = lossa(output)\n",
|
|
"\n",
|
|
" l.backward()\n",
|
|
"\n",
|
|
" optimizer.step()\n",
|
|
"\n",
|
|
" print(l)\n",
|
|
" \n",
|
|
"\n",
|
|
"b.forward(stocks_and_debris)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "other-subdivision",
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"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": "3.8.8"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|