{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Data Driven Modeling\n", "### (Theme of this semester: CODING AS LITERACY)\n", "
\n", "### PhD seminar series at Chair for Computer Aided Architectural Design (CAAD), ETH Zurich\n", "\n", "\n", "[Vahid Moosavi](https://vahidmoosavi.com/)\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# 18th Session \n", "
\n", "09 May 2017\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Reinforcement Learning (Learning by Interaction)\n", "### To be discussed\n", "* **Supervised, Unsupervised and Reinforcement Learning**\n", "* ** Main Problem of RL**\n", "* **Markov Decision Process (MDP)**\n", "* **Main approaches and architectures**\n", "* ****\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", "import datetime\n", "import pandas as pd\n", "# import pandas.io.data\n", "import numpy as np\n", "import matplotlib\n", "from matplotlib import pyplot as plt\n", "import sys\n", "import sompylib.sompy as SOM# from pandas import Series, DataFrame\n", "\n", "from ipywidgets import interact, HTML, FloatSlider\n", "import tensorflow as tf\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Three main classes of Machine Learning Problems\n", "- **Supervised Learning**\n", " - Target based and no direct effect on the environment\n", "- ** Unsupervised Learning**\n", " - No Target to predict and more on exploring the state space and learning the topology\n", "- ** Reinforcement Learning**\n", " - Learning to how to act where our actions change the state of the environment\n", "
\n", "\n", "- [On of the Best Source to start](http://people.inf.elte.hu/lorincz/Files/RL_2006/SuttonBook.pdf)\n", "- **According to Sutton: Reinforcement learning is learning... ** \n", " - ... what to do—how to map situations to actions—\n", " - ... So as to maximize a numerical reward signal. \n", " - ... The learner is not told which actions to take, as in most forms of machine learning, but instead must discover which actions yield the most reward by trying them. \n", " - ... actions may affect not only the immediate reward but also the next situation and, through that, all subsequent rewards. \n", "
\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Reinforcement Learning (RL) and Markov Decision Process (MDP)\n", "![](Images/MDP.png)\n", "# Key Terms\n", "\n", "- **State Space**\n", "- **Policy function (how to act)**\n", "- **State value (its reward and what to expect later on from this state)**\n", "- **Episodic vs. Continuous games**\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Real World Examples of RL\n", "- Game theory and RL as Dynamic Game Playing\n", " - Game theoretical problems can be modeled as model based RL problems, usually with known strategies (i.e. policy functions of the players)\n", "- Planning Vs. Learning \n", "- Dynamic Resource Allocation\n", " - Banks and economic polocies (e.g. interest rates)\n", " - Supply chain and Inventory management (e.g. VMI)\n", " - CPU\n", " - Cloud computing\n", " - Manufacturing: Job-Shop Scheduling\n", " - Smart Home (e.g. how to make home comfortable for its user. Think about this in comparison to classical optimization)\n", " - Urban Traffic planning: Dynamic tolls, Dynamic light control\n", "- Simulation Based Optimization\n", " - Water flow modeling in relation to urban design\n", " - Dynamic pricing\n", "- Multi-Agent Learning " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "# Main approaches to RL\n", "\n", "## Value Iteration method\n", "\n", "### Discounted reward\n", "\n", "### we want to know the value of each state, then, we can take a greedy action, which is optimal.\n", "## $$V^\\pi(s) = E \\{ r_t + \\gamma r_{t+1} + \\gamma^2 r_{t+2} + \\ldots \\mid s_t = s \\}$$\n", "\n", "\n", "## $$V^\\pi(s) = \\sum_{a} \\pi(s,a) \\sum_{s'} \\mathcal{P}_{ss'}^{a} \\left[ \\mathcal{R}_{ss'}^{a} + \\gamma V^\\pi(s') \\right]$$\n", "\n", "\n", "# Think about the \"Relational\" nature of this equation!\n", "#### This equation says, we need to calculate how much reward we expect by moving from the current state to all possible states and then continue the same way from all of them to all the other states in (in)finite manner. \n", "#### This equation is based on [Bellman_equation](https://en.wikipedia.org/wiki/Bellman_equation), which is the fundation of dynamic programming and optimal control theory. \n", "\n", "\n", "## Policy Iteration method\n", "### In the same manner, but when we adpat both values and policy functions sequentially\n", "
\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "# One important note related to the learning part of RL:\n", "# Plannign Vs. Learning\n", "## Learning the values is just enough. We don't need to teach the exact movements in a global view! \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# An example: Grid World\n", "### With value iteration\n", "## [From Sutton](http://people.inf.elte.hu/lorincz/Files/RL_2006/SuttonBook.pdf)\n", "### By the learning the values of each grid cell, we would like to learn to move from anywhere to the final state." ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# The agent has four actions (except in the corners)\n", "#Left, Right, Up, Down\n", "def action_LRUD(N):\n", " Action = np.zeros((N*N,N*N))\n", " # We have four actions everywhere\n", "\n", " #Top left corner\n", " i=0\n", " j=0\n", " state = i*N + j\n", " right = state + 1\n", " # left = state -1\n", " # up = (i-1)*N + j\n", " down = (i+1)*N +j\n", " Action[state,right] = 1/2.\n", " # Action[state,left] = 1/4.\n", " # Action[state,up] = 1/4.\n", " Action[state,down] = 1/2.\n", " \n", " #Top right corner\n", " i=0\n", " j=N-1\n", " state = i*N + j\n", " # right = state + 1\n", " left = state -1\n", " # up = (i-1)*N + j\n", " down = (i+1)*N +j\n", " # Action[state,right] = 1/4.\n", " Action[state,left] = 1/2.\n", " # Action[state,up] = 1/4.\n", " Action[state,down] = 1/2.\n", " \n", " \n", " #Lower left\n", " i=N-1\n", " j=0\n", " state = i*N + j\n", " right = state + 1\n", " # left = state -1\n", " up = (i-1)*N + j\n", " # down = (i+1)*N +j\n", " Action[state,right] = 1/2.\n", " # Action[state,left] = 1/2.\n", " Action[state,up] = 1/2.\n", " # Action[state,down] = 1/2.\n", "\n", " # Lower right\n", " i=N-1\n", " j=N-1\n", " state = i*N + j\n", " # right = state + 1\n", " left = state -1\n", " up = (i-1)*N + j\n", " # down = (i+1)*N +j\n", " # Action[state,right] = 1/4.\n", " Action[state,left] = 1/2.\n", " Action[state,up] = 1/2.\n", " # Action[state,down] = 1/2.\n", "\n", "\n", "\n", "\n", " #Top row\n", " i=0\n", " for j in range(1,N-1):\n", " state = i*N + j\n", " right = state + 1\n", " left = state -1\n", " # up = (i-1)*N + j\n", " down = (i+1)*N +j\n", " Action[state,right] = 1/3.\n", " Action[state,left] = 1/3.\n", " # Action[state,up] = 1/3.\n", " Action[state,down] = 1/3.\n", "\n", " #Last row\n", " i=N-1\n", " for j in range(1,N-1):\n", " state = i*N + j\n", " right = state + 1\n", " left = state -1\n", " up = (i-1)*N + j\n", " # down = (i+1)*N +j\n", " Action[state,right] = 1/3.\n", " Action[state,left] = 1/3.\n", " Action[state,up] = 1/3.\n", " # Action[state,down] = 1/3.\n", "\n", " #Left col\n", " j=0\n", " for i in range(1,N-1):\n", " state = i*N + j\n", " right = state + 1\n", " # left = state -1\n", " up = (i-1)*N + j\n", " down = (i+1)*N +j\n", " Action[state,right] = 1/3.\n", " # Action[state,left] = 1/3.\n", " Action[state,up] = 1/3.\n", " Action[state,down] = 1/3.\n", "\n", "\n", " #Right col\n", " j=N-1\n", " for i in range(1,N-1):\n", " state = i*N + j\n", " # right = state + 1\n", " left = state -1\n", " up = (i-1)*N + j\n", " down = (i+1)*N +j\n", " # Action[state,right] = 1/3.\n", " Action[state,left] = 1/3.\n", " Action[state,up] = 1/3.\n", " Action[state,down] = 1/3.\n", "\n", "\n", " for i in range(1,N-1):\n", " for j in range(1,N-1):\n", " state = i*N + j\n", " right = state + 1\n", " left = state -1\n", " up = (i-1)*N + j\n", " down = (i+1)*N +j\n", " Action[state,right] = 1/4.\n", " Action[state,left] = 1/4.\n", " Action[state,up] = 1/4.\n", " Action[state,down] = 1/4.\n", " return Action" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rewards we get in each state" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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oiHfxHmvECOngQekHP0im/bT86Edmv0aMSKb94mLzuHz4YfvHzDfHvix99tnm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\nq67irUUdIav2yKqdAs2qf4V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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 6\n", "Action = action_LRUD(N)\n", "\n", "#Reward\n", "#Everywhere negative\n", "state_reward = -1*np.ones((N*N))\n", "\n", "#Except the terminating state with positive reward\n", "terminating_state= np.random.randint(0,N)*N +np.random.randint(0,N)\n", "# middle = int(N/2)*N + int(N/2)\n", "state_reward[terminating_state] = +20\n", "\n", "\n", "fig = plt.figure(figsize=(5,5));\n", "ax = fig.add_subplot(1,1,1)\n", "ax.xaxis.set_ticks([i for i in range(1,N+1)])\n", "ax.yaxis.set_ticks([i for i in range(1,N+1)])\n", "ax.xaxis.set_ticklabels([])\n", "ax.yaxis.set_ticklabels([])\n", "ax.grid(True,linestyle='-', linewidth=.5)\n", "vals = np.around(state_reward.reshape(N,N)).astype(int)\n", "for i in range(0,N,1):\n", " for j in range(0,N,1):\n", " ax.annotate(vals[i,j], (i+.1,j+.1),size=10, va=\"center\")\n", " for i in range(0,N):\n", " for j in range(0,N):\n", " state = i*N+j\n", " valid_actions = Action[state]>0\n", " next_greedy_state = np.where(valid_actions)[0]\n", " for d in next_greedy_state:\n", " i1 = d/N \n", " j1 = d%N \n", " plt.arrow(i+.5,j+.5,.3*(i1-i),.3*(j1-j),head_width=.15, head_length=.13, fc='r', ec='r');\n", " plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": true }, "outputs": [], "source": [ "N = 10\n", "Action = action_LRUD(N)\n", "\n", "#Reward\n", "#Everywhere negative\n", "state_reward = -1*np.ones((N*N))\n", "\n", "#Except the terminating state with positive reward\n", "terminating_state= np.random.randint(0,N)*N +np.random.randint(0,N)\n", "# middle = int(N/2)*N + int(N/2)\n", "state_reward[terminating_state] = +20" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Value Iteration" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Gamma = .5\n", "# Value Iteration\n", "#initialize State_Value\n", "state_value = np.zeros((N*N))\n", "delta = 0\n", "deltas = []\n", "for i in range(40):\n", " temp = state_value.copy()\n", " #Update Values\n", " for j in range(Action.shape[0]):\n", " state_value[j] = np.sum(np.multiply(Action[j],state_reward+Gamma*state_value))\n", " \n", " diff = np.sum(np.abs(temp-state_value))\n", " \n", " delta = np.maximum(delta,diff)\n", " deltas.append(diff)\n", "plt.plot(deltas);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Policy will be based on the Greedy Approach (i.e. we chose the action which leads us to the next state with the maximum state value)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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14ULgww+Bk08GGjXSPvtQrFsnLwXRrx+w3XZRV6NGCGDaNGC33WRXLqZPlz+X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rBBa/Hg2yTJmip+3ZcqHgtpOpn013Zr1uC0f/wDU2+4ASM++0zZV2yb81DFW7J0m6jPTZ4iJISg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\nPvoo8vffj3CHHfTpD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "fig = plt.figure(figsize=(7,7));\n", "plt.imshow(state_value.reshape(N,N),cmap=plt.cm.gray_r);\n", "i = terminating_state/N\n", "j = terminating_state%N\n", "plt.plot(j,i,'og',markersize=9)\n", "plt.axis('off')\n", "for i in range(0,N):\n", " for j in range(0,N):\n", " state = i*N+j\n", " valid_actions = Action[state]>0\n", " action_reward = np.around(np.multiply(Action[state],state_value),decimals=3)\n", " try:\n", " max_val = np.max(action_reward[valid_actions])\n", " next_greedy_state = np.where(action_reward==max_val)[0]\n", " for d in next_greedy_state:\n", " i1 = d/N\n", " j1 = d%N\n", " plt.arrow(j,i,.3*(j1-j),.3*(i1-i),head_width=.15, head_length=.13, fc='r', ec='r');\n", " except:\n", " continue\n", "\n", "\n", "plt.grid()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Now Let's play with Gamma and iteration times (as meta-parameters)\n", "### Larger Gamma means we care more about future steps\n", "### $$V^\\pi(s) = E \\{ r_t + \\gamma r_{t+1} + \\gamma^2 r_{t+2} + \\ldots \\mid s_t = s \\}$$" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def value_iteration(Itern=50,Gamma=.4):\n", " # Value Iteration\n", " #initialize State_Value\n", " state_value = np.zeros((N*N))\n", " delta = 0\n", " deltas = []\n", " for i in range(Itern):\n", " temp = state_value.copy()\n", " #Update Values\n", " for j in range(Action.shape[0]):\n", " state_value[j] = np.sum(np.multiply(Action[j],state_reward+Gamma*state_value))\n", " \n", " diff = np.sum(np.abs(temp-state_value))\n", " \n", " delta = np.maximum(delta,diff)\n", " deltas.append(diff)\n", " \n", " state_value = np.around(state_value,decimals=1)\n", " fig = plt.figure(figsize=(14,7));\n", " plt.subplot(1,2,1)\n", " plt.plot(deltas);\n", " plt.subplot(1,2,2)\n", " plt.imshow(state_value.reshape(N,N),cmap=plt.cm.gray_r);\n", " i = terminating_state/N\n", " j = terminating_state%N\n", " plt.plot(j,i,'og',markersize=9)\n", " plt.axis('off')\n", " for i in range(0,N):\n", " for j in range(0,N):\n", " state = i*N+j\n", " valid_actions = Action[state]>0\n", " action_reward = np.around(np.multiply(Action[state],state_value),decimals=2)\n", " try:\n", " max_val = np.max(action_reward[valid_actions])\n", " next_greedy_state = np.where(action_reward==max_val)[0]\n", " for d in next_greedy_state:\n", " i1 = d/N\n", " j1 = d%N\n", " plt.arrow(j,i,.3*(j1-j),.3*(i1-i),head_width=.15, head_length=.13, fc='r', ec='r');\n", " except:\n", " continue\n", " plt.grid()\n", " plt.tight_layout()\n", " \n", " \n", " " ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Wzdbs2bP9PQsAAACEZtWqVVq1atWAbW+88UZE1QBAeqQ5yC0+tzSdV7UIb8uL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GtvGhPVpkxxUfWmfbjIl6QvQkatuN1228b7woXAfvsVOxZCCCGEEEJI8bgUpTbtXPQbldt/qcZo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\nIYSQ5kX3D/ErV67Ecccd16AeEaKXq6b0MoRuVlHrs+LW1LeUiSB+Q1bcq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XQFCm6raNAg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33UXzkiWdAnZwAsEhzz1Hv5dfrjhsDdImjj7GGPrPncsG06d3CjjB+aW4Zdkytpg61fN8lb7K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\nREREpMb8f98kkS1FUs4GAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interact(value_iteration,Itern=(20,100,10),Gamma=(.0,1,.05));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Blocking some cells" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [], "source": [ "N = 10\n", "Action = action_LRUD(N)\n", "\n", "#Reward\n", "state_reward = -1*np.ones((N*N))\n", "\n", "terminating_state= np.random.randint(0,N)*N +np.random.randint(0,N)\n", "# middle = int(N/2)*N + int(N/2)\n", "state_reward[terminating_state] = +20\n", "\n", "\n", "blocking_state= np.random.randint(1,N-1)*N +np.random.randint(1,N-1)\n", "Action[blocking_state] = 0\n", "Action[:,blocking_state] = 0\n", "state_reward[blocking_state] = -20\n", "\n", "blocking_state= np.random.randint(1,N-1)*N +np.random.randint(1,N-1)\n", "Action[blocking_state] = 0\n", "Action[:,blocking_state] = 0\n", "state_reward[blocking_state] = -20\n", "\n" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2jn7kg7b77pM23lg6/3xp4UJvfa11/TbZRBo1Kr4q73Leest9ILLv\nvtKMGXHPJhJm0SKZc86R2XRT6S9/Cf6hSI34CUcLZe66S82bbaaGyy6TDXAdVTuul3lValNtn9eQ\nsRahr5+q2yjC27BBbfHxg/SDNwn5r6Z3zc3xfegHAAAAoAdrbw/2lct1Bmft7W5ZgKuucpWL11/v\nnpfz1lvSsGFuWYI334x2TmH6F845P9ZTT0lbbimdfHLlSuAvvpAuvNBVtf7pT25b4XjZbPB5SS7k\nCtq/MDDI5aTZs6VDDnFLXbS2ln9N1roK6I02ki64wP1Smp9PfqwwrymK9zo/xrJl0pgx7vq79dau\n+4u99pq0557S/vtL777bPUBM0vX30EOu+nbkyPg+3AjzPhe+15KMtdJ77ylz4IEye+3V+eFGvQX4\nebLLlpW8/kw2K7N0qRp/8Qs1b7mlMvfcs/yaiiKUrf5SSvfxGsIG7RcmEI6iUrfanGr9uBTC2eiY\nNJxMY8wQSdOnT5+uyy8foo8+im75HgAAACRPa2urWlpaJKnFWlshTUEPN1PSejU/ysCB0vz5tRv/\nllukI48svW/99aWZM2t37FrZbz9XKVjKWWdJV1xR3/lEIZMpH7I/84wLd41JXHVkVVOnumC2lFpf\n+7Vy5JHu56qerHVV8a++Gv3QkjRggOy8eT6nFP5aNOPGKXPuuaHHKWaNkbFWSx95RLlvfCN0cOun\nurbfmWeq+eabNX/uXNmC7V4qWKNs62ccr32lzqUsjDEVHxc+L7fdb5uoH6++xhpqHzxYnz35ZLf3\nt0b2W2211abV62BRaIx7An6xVAIAAACASOWDK/dhgX/Tp7vQr7CyMR/wbbmltP325fsef7w0enRn\nJV+xQYOkVVf1P6f33pM++cT92fyKK/rv/9pr0uLF3bc3NEgrrSQdfnj5vvvt55Yf+PDD8iFnmHPd\nt6+rvAzav1hjowtsf/KT8v022MDdhOyxx7q/13lhXlPY/sWBcv75Dju4sLGcE06Qxo1z7Utdf5tt\n5s63X//9r6uK3XJLqanJf/9S75Pkzv3Age7GffVmjDRmjOzo0cH6t7XJvPxyt822sdG9V8cfH2BK\nJnR4aw87TLmHHpIpqmL2OmqmRKW6zWRkcjlld95ZuUGDSvYrnrvf55UsHjdOS487ruwHLYVj5QPE\nwufljlupbdhx8s+97MtvrxaKFvYvt91vm6gfz3vhBfczjbJSV3H7m98M0T//Wf7fcQAAAKQfFbfo\nMFP1qLjN/yIZ9HejE06Qbr7Z/Ym65MKlVVZxgdhRR7mws5KZM92ff999t2tbWPX53nvSV77if05n\nnCFdeaX07LPuBlp+/fWv7mZreY2NLqw87TS3DEK1MHnxYmn8eOmXv3TnJf+aMhlp4kQ3ThDGuLVY\nX389WP+mps6AMh/A7rSTNGmSCxkrsdZVGZ9+untfCq+XXXZxNykLIuz194MfSH/8Y2f/TEZaYw1X\n9XzIIZ3jl/Of/7g1mf/61+6h9Oefu6Der2HDXKXvnDluLn797nddPxzIryE9cqR03nnB5hSRwBnK\nokUyBR+i5MNNu/fesldc4T5kqfecKozh9XnT3nsrU3DtW2Nk11lH7ePHK7vvvl2uvzBVtEGeR1Ut\nW6ld0H5hxqxVFWzhtnLba3XMOkpdxW3q1rjt25eKWwAAAAAJk826cKmx0S0V8M470jHHVA9tJemr\nX3XB2+OPu1AySfI3E9t1V+nll13o6qUCuF8/txbsm2+68FBy5yIphUPGSGut5cLyJ56oHtrm+xxw\ngAs6x4xxr9HL+1sP1rprr08f6Wc/cxWvhx5aPbSVXGB4//0uuB00yFufeslff/vuK73xhnTppbGG\ntlGwcuGm1l9fufvuk502LVRoK9U9+Cp5TNvQINuvn9ovvlhtL7+s3P77d7uWivt4mXe1PpWee93n\ntdK0Ur9qY1RqVyo0LbdkQbX9fh4Xz9VLtW6YCttS5zGOazdtUhfcslQCAAAAgERZbTVXpbj33m6J\ngbFjpZVX9j/OLrtI//639JvfuHC0Xz/3C1AcBgxwodl660n33eduDLXppv7HWWcd6fbb3RqxW23l\nAsbVVot+vl6tsoqrBvrlL12o/N3v+g8qm5ulUaOkt992a60aI/3f/9Vmvl7kz+d3v+te0+jRUv/+\n/sfJX78TJrjlNVZcMb5gOv/hwNe+Jj3yiHTvvW65ijTLZGTz53X8eHeu99knsuGjDsC8hqy248/c\nc4cdpqWvvabsWWct/3cryJyiCnP9hLZe23kNKqMIc/20iyKo9RPChukH/1K3VMK99w7Rb3/r/jIF\nAAAAPRNLJaDDTKVhqQRrXTXg4MHRzWnBAmnRIlcVGkTYpRIkV7W57rquijMKuZw0Y0a4qmITcqmE\nsOe1lBkzXKVqY8BbyIS9/qI4r8U+/dSNG2SZAyn8UglS+PNaI6EylE8+cd9XXz38WCWEGS/IsgWS\nZJctk3nnHdmNNvLep05tolrKoN5jVdpXapmBassQ1Gp/lG3raL+BAwemaqmEZP0L6EFzs7RkSdyz\nAAAAAIAOxkQb2kquMnSVVaId068NN4x2vEwm/qUganFev/a1aMfzqxbnNc4K4ry4z2stdAS2ecaE\nv7lYVON56VuyTWPj8tC2VJtSfby08XJsv8cqd5x8cFju5mB+H5cay8/jYsX7oghgg/SpVr1bvK34\ncaVtKI+lEgAAAAAAAHqAKEMxL2MFbVO8rdTzam2qjeN1+QEvbeJ8XOqrcL5BAlgvfSqdxyDhbbVt\nKI3gFgAAAAAAIAa1CK7iDsOCVllGGQKXG8trsFurx7UKdUvtL7eteH+5bWH6Fj+utM1P27Db4v7Z\nCCK1wW0KluYFAAAAAACou1oFVEFD2aBjhQnqvOwr3l/rQDbseOXGrMW2UnOKYlu5fZXC6Ki2pVHq\ngtu+fd33ZcvinQcAAAAAAEBY9QxZ6zWPKALXKMbyEpB6bVvcz+sYXkPdaoFqqWDSa99K28qdk1oH\ntfAmdcFtc7P7znIJAAAAAACgJ0hKeOulf5ShbC2PGWVoWy2orRbCem1brmq01P4ogtww+8ptC7sP\nXRHcAgAAAAAA9FBJCseiDoLLbfMSylba7zd8rbY/SDWtn2rbSmOECW1Lva6o96Gyxrgn4BfBLQAA\nAAAAgHfGGFkPNwsq1S6N20opbJd/7HWblz6Suuwv3lbIT59Sx6wWttazTfE5LrevuE255+gqtRW3\nS5bEOw8AAAAAAICo1DrAKq5ErdUx4trmNUgMchwv1aRBt3mpxi18HFUgW25+fsLXqMZDeakNbqm4\nBQAAAAAAiFaYALVexyl3bD8BbZRhrJcANsw2L6Gtn2C30nHDjl8KYW5wBLcAAAAAepfWVqmhQTLG\nfeXlnxsj/eY38c0viLY2af31O+d/5ZVu+9e/3rnt29+Od45BnHxy1/dFkt54o/P5gAHSp5/GO0e/\nHnus+2uSum67++745hfEwoXSmmt2zn/qVLf9S1/q3PbDH8Y7x5SoR5AVZeVtlEFrkG1e2vqtxA0S\n0Ppt72eb169yx680ptc+1c5fmDAXlfkObo0xOxljphpjPjDG5IwxB5Roc5Ex5kNjzCJjzMPGmA2L\n9q9qjLnDGPOZMWa+MeZGY0x/L8cnuAUAAAAQyqJFUi5XvU2atLdXX09uyRLJwzqQiVLtNbW1pe+X\nw4ULo2mTJMuWebv+4EmUwWq149SqvZ/w1k//sEFvqe9etwUNdMMGtV7n5TXw9TqG13PgZ17l+tXz\nK22CVNz2l/QvSadI6vZffWPMTyWdKukESdtL+kLSg8aYPgXNfidpsKQ9JO0raWdJ13s5eN++7nva\n/tsMAAAAICF23FH6/velxhL3as5kpA03lE45pf7zCmOFFaQrrii/3xjp6qu7Vnimwa9+5V5bKcZI\n558vrb12fecU1n77Sd/6Vunrr6FBGjJE+tGP6j+vMFZd1b1X5TQ2Vr4+EZtyQVbYkNVPW79zCDKG\n38pPvyFvkH5eAtVS7SuNEWU46yd49SuNAWpcfAe31toHrLU/t9beK6nUmR4u6WJr7V+sta9IOlLS\nWpIOlCRjzGBJe0k61lr7grX2GUmnSTrEGLNmteNTcQsAAAAgtHHjXEhbLJeTrrpKamqq/5zCOuQQ\naYcdXPhXqKFBOu44aeut45lXGGuuKV14YffAOZOR1lpLOuuseOYVhjFuKYtSVd/ZrDRpUulrM+mO\nP17aZJPu118m496nDTaIZ14pVq9wq54hbbnttQhvowhWvbTxEph6CUO9hrJxhLRJCn17m0j/a2CM\nWV/SmpIezW+z1n4u6TlJX+/YNFTSfGvtiwVdH5Gr3t2h2jEIbgEAAACEtt560k9/2jUga2yU9t5b\n2mef+OYVhjEu9Mtmu27v10/65S/jmVMUhg+X1l2363uVy0kTJrjXlkabbuqqugtDzoYG6dBD3brE\nadTY2P36M0YaONBVRiN1ahXSltse1RjlwkEvVbdBqmm9hr9eA95Kbb3MI23fUVnUH+OtKRfAzina\nPqdjX77Nx4U7rbVZSfMK2pSVD25ZHgcAAABAKD/9qbT66p3VnNZKEyfGO6ewtt1WOvrozkDQGOmi\ni9zrTKvmZlcFna9QbWyUvvlN6eCD451XWKNHSyuu2Pm8qUkaOza26URijz2kAw7oXAbCWlfdvtJK\n8c4rxZIYbkURsJbbHvXYQQLYoCGp37Zhwlw/X35fR5DvYUTxGv2ejzSp199fGJVYDzdAGypuAQAA\nAESjf39p/HgXLhkjnX66tPHGcc8qvEsvlfp03GJk/fXTt15vKfvvL+22m3uczaZzvd5iAwd2VkIb\nI517rrTOOvHOKQqFa9lus4105JHxzaWHqEfY5PcYtQ5vo9he6jjVgsegoW3xPIL2rRa61mrcMN/D\n9kVlJVZDD2W2XAD7JXWtul1D0osFbdYo7GSMaZC0qrpX6nYxYsQIrbzyAEnS5ZdLf/iDdOihh+rQ\nQw+NZvYAAACouylTpmjKlCldtn322WcxzQa9zmGHSddcI735pvTzn8c9m2isuaar5jz/fFep2qdP\n1S6JZ4wLa4cMkY46ygWCPcEJJ0i//rX0+efSyJFxzyYaG2zgXsvll7v3LI3r9SZQPuiytmq9W+TH\njeqYfscq197rdj/HK9fX7/cwfUt9l1RyW1ShaRRBaxR9UZ4J8wNojMlJOtBaO7Vg24eSxllrJ3Q8\nX1kukD3SWnuXMWYTSa9K2ja/zq0xZk9J90tax1o7u8RxhkiaPn36dA0ZMkRNTW4t95NPDjx1AAAA\nJFhra6taWlokqcVa2xr3fBCbmZLWi3sSAJBX7+C0nnMoN26l4/ntU4+xCrfnH0f5vXh8r8+j+h5F\nIOulTZg+ftvW0X4rr7zytDgOHJTviltjTH9JG8pV1krSIGPMVpLmWWtnSZoo6QJjzH/l/kfrYknv\nS/qzJFlr3zDGPCjpBmPMSZL6SLpa0pRSoW0pffuyVAIAAAAAAEBU/Fa4BukT9VhS9wC3XKVq0Ara\n4jkUj59XXCXrpW2lSttS7QrHLHxc6xDXa5tqbUuh6rayIEslbCvpMbn1aK2k8R3bb5F0jLV2rDFm\nBUnXS1pF0pOS9rHWthWMcZikSZIekZST9EdJw71OoLmZ4BYAAAAAAPQ+fpYAiPOY9Qhvg87Nq2oB\nrtfgtdzzcqq18xOsVtpXr/6V5o3KfAe31tonVOWmZtba0ZJGV9i/QNIRfo+dR3ALAAAAAAB6q+Iw\nMMpxowpoK+0rVy0bpk/xvrDVttWC2VqNXS0MLn7NUYWwUe6rNM9S+1BeKlcJJ7gFAAAAAACon6B/\n7h5kXy2OVam93+9RjlXpe+FX4XGq9fG7r9pr9Lsv6HHQXZClEmLX3CwtWRL3LAAAAAAAAOJVqRI1\n6HhRL0tQi6pcL/uqVbJWmk+9KnArKdfWayDqN0ANs83Pvmrb0ImKWwAAAAC924wZ0vTpcc8iWvPm\nSY89JrW1VW+bFtZKf/+79MEHcc8kWq+9Jv3733HPIloff+yuv2w27plEJ5dzr+njj+OeSVmBArCX\nXpJefTWy49ezKrfsMT/8UJknn3T/ZpQYx081rZ8+YSpp/fYp7ut1W/E5q7TN6+v0eg5Lbcu8+KLM\nm292249OBLcAAAAAeq+FC6WddpJ22EF6/fW4ZxOdESOk3XeXrr467plE589/lnbZRfr+97sFMqk1\nd6709a+76++99+KeTXSOPdZdf7fcEvdMonPLLe41HXts3DOpqFRgV9asWTJDh8p885vSp592G6fS\nMarNIei+cvs9h8LWqs+PfqTmvfZSw9SpnucTNpD1G8B6aVPuvaxXABs08PU6h8yMGVph993Vb889\n3X+LURLBLQAAAIDea8yYzsDi9NN7RiD4/PPSrbe6xxdeKM2ZE+98orBkiTR8uGSM9Oyz0h/+EPeM\nonHhhdIXX0jt7dKoUXHPJhoPPyzdd597fPbZ0uefxzufKHz+uXstksy0adKDD8Y8Ie8qhpbnnOOu\nvUWLZC68MLJxqx43ZN9K4W7DPfeo4dlnZY1R09lnL19nM0wwG0WbatWvYdqU2+Z1f7ltXl9n8eNS\n20r1af7pT922efPUZ/z4bv3hpDK47duX4BYAAABASDNnSmPHuj+BzmalRx6R7r8/7lmFY6106qlS\nQ4N7vmSJdP758c4pChMnSrNmuddnjHTmmdKiRXHPKpxXXpGuvdZde9msdOed0lNPxT2rcNrbu15/\nCxZIl1wS75yi8KtfSfPnS5JsJuM+5Fm2LOZJeVcy7HzmGZnf/14mm5XJZqXrr5defrlbv2rjhplT\n5PsXL1bT2WfLZjIy1sp8+KGaJk3yNUalYLZSmzDBbqV91QLZSuPUen/xtuLHlbY1PvSQGh991F1/\nuZyarrxSmXffLRtSR/mVNqkMbqm4BQAAABDaWWd1rbDNBzJpXhf2d7+T/vnPzrVFs1lp8mTpxRfj\nnVcYH30kXXRR53tlrTR7tnT55fHOKwxrpdNO6ww4Jff41FPdBwlpdd11bs3o/PWXy0kTJkhpXsPy\nrbek8eOXvy8ml3Ov57rrYp6Yf8uDq1xO5rTTZIuuPzN8uO+/OqgUhEURzlYbv3B/w5VXSrNnu/dI\nkrFWjZdeKvPRR12OVy2ILLevUkBbrn2lfqUqYSvtq1Y56yf09bLfy7kKEvpq2TI1dwTsy1mrPued\nJ3RHcAsAAACg93niCelPf3IVgnm5nPTOO1KFCq1EW7jQVaIWBxD5QDCty0Cce273MD2Xc1WQs2bF\nM6ewpk6VHn+86/WXzbqblKV1Xdi5c8tXd595Zn3nEqVyc7/ggm7rwqaFue02mX/9y1Xa5re1t8s8\n8bCNKWYAACAASURBVIRbS7qwbcgKRb/ha7k2VY/xwQdqHDNGpvjfuWXL1FSwDISfoNbrtkqBrpfA\ntHBbtfal+tcqnK1FqCtJfW64QWbmzOUBu+Suv8apU5V54gmhK4JbAAAAAL1LNiudckrXasc8a6Wf\n/zzRd44v67LLXJBUHFy0t0vPPCPddVc88wrjn/90QWZBwLRcNit1rJGYKkuXusruTIlfx41J77qw\no0e79XqLtbe7NW8feqjuUwrtkUdcyF4YsEsykluqw+e6sInQsV6vLRFc2kxGZsSI5evC5oUNVr2O\nESbgbTz//G7vkySZbFaNd9yhzAsvlJ2T36DW6za/oW2pbV5D2nJfXvqVm4OXx777ffqp+lx8cckP\nEm1Dg/qcdVbJ97E3S21wW/TvCAAAAAB4c/fd0quvlg4DJRc+jR1b3zmFtWCBC24r/Zn9qFHpq7qt\n9Kez7e3SlCnuvUyT3/5Weu+90u+Vta5yNW1V3x980LlebzlpDNnPOafsLpPNuuUS0lb1fe21MnPn\ndq9MlWRyOZn33pNuvrn7vpDBq5cxgh7HvPGGGu68s0sFcbGmn/+8pkFtVKFtudDVy1e58Wr5uPhc\nVHvc5+qrZb74QqXeZZPNquGNN9R4zz2+Xrffr7RpjHsCQVBxCwAAACCw3XaT9tmnM2TKVwLuuWdn\nm+99r/7zCmOVVaQTTnDri0qdr2mTTaR113WP99yz+zIKSXfMMV0rU4vfq4EDpY03rv+8wth7b2mv\nvTpD9FLX3wEH1H9eYay1lnT00dL777vn+de0005Sv37u8UEHxTK1UE44QfrjH93jtja3vIUk7bmn\nrCR9+cvS2mvHNLmA9t9fNv86JJmO98oWXn977x14eGOMbIUPiPLBWbU2lfYXj2M33FDZH/xAZt48\nSVLmkUckSdk99lj+b1728MPLHiP/2M+2/LFrPU65/cXnIS2P2/ffX5mXXlq+vfHRRyV1vFeSlMko\nu8suQidT7YchCYwxQyRNnz59uoYMGaIzzpAefjh9H6wCAADAm9bWVrW0tEhSi7W2Ne75IDYzJa1X\n86Pkf7lMwe9Gnp1xhnTlldKzz0pDh8Y9m+gY48Lo11+PeybR6YnX37BhbomBOXOkNdaIezbRmD9f\nGjhQdp99pGnT4p5NZEzHByM2l6salkqVA1e/7Wp1vKZtt1XmlVe0dPFi2RJtCttW2uZnf9jx/fTv\nVnEcUbga5Vhej9F/xRUlSYtKLbNSG/utsMIKqfoBTmXFbd++VNwCAAAAAADUk5dqWK/tvFbfVmvj\np13x3CpVxBbvz48fpG3xtnKPy+0v93pLPa9HSBt1H5SXyuCWpRIAAAAAAACiE2UoG3U7vwFuqbFr\nGc5W6hc2tC0X4IYNVZPSrtRzdErtzckIbgEAAAAAAKLjNUDz085LW7/t/AR9QSpDg/TLPy6cX6XH\nQfqVe15qn9d21c5F1NW0hLT+ENwCAAAAAAB41NODp6jDW79jRtW2FsFr2LG9Hsfr4+KvSu2K91Ua\n38u+QlEEuigttUslLFkS9ywAAAAAAEBvU/wn8T2R19eXD+KS0LZU+8LXEcXjwnnF8bjc6y5+Xmlf\nEtuivNQGt21t7qabvM8AAAAAAKCeenJoG4SfILtWAW6+faWYKOogt3iO9QptC1+P1+d+g9R6jYXK\nUhvcSi68zT8GAAAAAACoh55ecSv5f41BQlav7StV1XrpW9inFsFskD5+g9risQtfT1Kfew1sCXLL\nS+0atxLr3AIAAAAAANRKkEDNb5/i9VOjau91bdVy7bwGkl7Xgo2if9qeV0JY600qK2779nXfCW4B\nAAAAAEA95Ssr/VaYplWQ11mPPsXBX6l+XqpoK+3z2s7rGOUqa/0sj1DpHHipcK3FMgcslVA7VNwC\nAAAAQBgffSRNmCAtWBDdmH/7m3Tnne7GHnFoa5Ouu0565ZXoxnzvPWniRGnhwujG9OuRR6Q//CG6\n87pkiTRpkjRjRjTjBfHuu9GeV2ul++6Tpk6N7/pbvFi6+mrpzTejG/O//3VjLl4ceqjCm5N5Diat\nlf7yF3duUxr0lgzbZsxwPwNl7iDvt5q2sE9Ulbu+q2gXLlTDpEnKzJpVtp2fitlS+4pfo9d9lfaX\ney5JRlKfe+9V09//Xr6Nz+d+2lR6jsoIbgEAAAAgjNGjpTPPlAYNkn7zGymbDT7W229LBx4o7bGH\ndMgh0vvvRzZNXx59VDrpJGnLLaVTT5Xmzg0+1qJF7hxttJE0YoR0882RTdO3ffaRfvhDaccdpRdf\nDD6OtdLdd7vXdNpp0vHHRzdHv84+253XDTaQbrtNyuWCj/X669Kee0r77y8NGxZfyH7PPdLpp0ub\nbupe32efBR/r88+lUaOkwYPdmH/8YyRT9F1lu3ixzLBhMgcc4M7xa69FMo966xbCnXyyMsOHy2y8\nsfuZKHNeggSxYfqVGqfU41L7Gu+4Q31GjVLzlluq6ZJLpC++KDmXSksDhA13KwW6ldqVC3jNRx+p\n/zHHaMUDD1T/ww5T5p13qvYr97zSNr9tSs61xl9pQ3ALAAAAAGE1NEjz50snnCBttZX0+OP++v/v\nf9K550obbyxNm1aTKQZirau8HTTIVSsuW+av75QpLlC8+GJXxZuUX5qff15qaZGOO076+GN/fV96\nSdplF+ngg6UPP6zN/PwyRvrkE+nII6UddpCee85f//nzpTPOkDbf3P+1W0vt7dIVV7jr76ab/H0o\nkstJkydL668vjR/vxopQtcrOip54wn0oMny4O/cpUzIA+/BDZX7wA5nddpP+/W9/fX0c00//agFt\npTDXGiPT1qbGMWPUb4st1FhQqR80lC3X1k9o6yesLTeHxoce0orbbae+o0e7//Z47Od1W9CgF6Wl\nOrgtU4kPAAAAAPWVKfjV6o03pN12k773PWnmzMr9cjnplltcMDV2rAuXIg6YQstmXdXi6ae7YO/h\nh6v3eeEF6RvfkA47TJozp7MKNCm/qLe3uxDmt7915378eBcsV/LJJ9KJJ0pbby09+6zbFqa6NWr5\nSscXX5SGDpV+9KPqwXJ7u/TrX7tzMGmSez1Ju/5yORduHnectM020pNPVu/z1FPSkCHSsce6vjG+\nTyUD3vZ2mVxOuvZad+6vvTZ5592DLmFd/hw/+6xMS4vMSSe5n5kKfcMEd15DXC9VoZXmZKyVPv5Y\nfX78YzXvtpsyra2BxgrzvFrlqNdty/dlszLt7erz/+zdd5hTZfrG8e+bBBiwUAQUO64FxYIz6i6W\n3VVsuCiLHV117QWUpoKC0lwVFSnC2uuq+LNiF11XXQu6OqMu2BVZK6y6gFIGmOT9/fFOSGYmM5Ny\nkpOTuT/XNReZk5yT5yQn0bnz5DnTp7P+brvR6v7767xGsg1sUz0mmSyT1EwQhmgbY8qBysrKSsrL\ny5k/H3bZBd54A3r39rs6EREREfFaVVUVFRUVABXW2qrmbi8layGwVd7vJV9/QEYibtvPPutGH6Ry\n0EFu7qoxwZh7GQ67IHf4cBd2pjJzphsfEArlNjaikIxxnZlffJH6+o8/hr32cmMfgrJP4TC0auW6\nO/faK/Vt9tgDKisLW1cu4sffxIkwZkzq21x5JYwenbhtkbO4+aO2vBxT+1wkz9AF1l3Ox7J8vf/Z\ncBjatsW++aYbU5Hueh68D4b22QeTadd5Gmw4jIlGWXP99dScfXbd6+rVnWo/kpc1d32D32Mx2l5w\nAW3uuy+b0htljcFYS83vfkf1U081uD6XIDadZW3KygBYXbjOzH5t2rQpoq+1NC/QHbcalSAiIiIi\nIkXN2qbDo3iXZxBCW0jU2VR3arybNWia2qdi7ERtjjGu7qa6TdeuLZ4u6Ew09VxlMs6jCBiA2q/l\nr1vWyFfl87GMsWPztGe4974Mu5296MSMTZ+ObdUq5+00au3arMcFpHt9g9+txeQj3GzkPT3dDtv4\n8nSWpbL23ntZ+9prjXYV5+MnaAIZ3NYG8gpuRURERETEO9Zm93PWWa6zMS4+NuGQQ9wJiA4+uPH7\n/Mc/4OaboUOHuuMW4r76Kruahgxx68+dm936zzzTsBZjYMst4cknYfr0xvdpyBB4/XX3Ncn4esmP\nzfTp2T/WAD16ZL9+JFK31nDY/YE5cSJ8+mnj+7TTTq4b96STEusl+93vctsnyH79Y46p+xjHaxsw\nwO3Tb37T+H69846bIbv++g33CdyIjGxqOuIIt/7ixdmt31hX4bbbulEdEyY0vk9jx7ou9u22S339\nPfdkV9P//ufW79s3u/VrT3BVRzjsHvvJk/3rfB43DhuLZf+z//51Nmfjr7ETT8R+9hn07JlxSTmH\naxUVxFatombt2jo/a9esqfOzZvXqOj+rq6tZXV3N2qlTsUk1xC/bnj1Z/eKLRM8/P+06Mwpnm/o9\nHGblbbexdMmSdT/Lli5N+fPzsmUNfpZ//HGD2mw4DO3bUz1tGtXPPttoDZnsX6a3jR19NHbPPdPe\nRksUyOBWHbciIiIiIlJUkrvKfvUreO45eOqpxsOjuHDYBb9ffukCz3C4Ybjot3AY2rVzM3g/+QT6\n9Wu+S3PvvV0QdeedsNFGqUNpP8VDyoED4fPP3Vfr27Ztep1u3dz+xE9sBsXVrRqvZaed4J//hAcf\nhK22anqdVq3cSckWLHDzYI0pzuOvfXs3gmP+fDjwwObX6dMH5s1zs2Pbt08dSvspHHaP9emnu8d+\n2DBo3dq3crzoQlwXdO6+O7E338Teead7zRSxdOaz2lAIOnVi7c03s2buXOzee2e8jUzvN5e5senc\n1kYi2HCYteecw4p586g57bR1r5HG6s+kqzZfwW9LVWT/9UyPglsRERERESkq0ShssIHrJv3gA9dt\nm4kOHVznY7rBVKEYA3/+swuXLrwws3ApFEqse/HFLhAslpN5xU8w9re/wWabZbbunnvCm2+6rtCN\nN85PfZmy1h1Dt97qTk62336Zrd+li+v8fvfd4jqRTCgE553njqHzzsssVI5E4Nxz3bqDBhXXhwe9\ne0NVlXvMu3Txu5rcxIO3rl2x996LnTvXvUZy3qz3gV5GgaK12EiE6PDhrP7wQ6Inn5z2MZTvMDfX\nEDX629+y8q23WHP11dCxY8a1ZUMBbfaK7KO09Ci4FRERERGRojFmDGy9NZx5JnTunNu2evRwJzN7\n5hn48cfMQ0Wv7L8/TJkCv/0tlJfntq0NNoCrroIzzoCHH06MG/DD7NnuK+8nnphbkGcMnHAC9O8P\nN94Ihx7qXY2ZuvJK1wF8zjmuuzQXu+3mTmb26KPuw4j11/emxkz17w/XXuvGEmTxVfs6OnWCadPg\n7LPd62rAAG9qzFTbtvDQQ+7yUUcVVbd2TicEmzYN++yzLiRfbz13orVctpckHvZlu73kE7Jlsk5s\n4EBqli8nOmCA+wZFvW3U324695POOs3dJtMO1+TldpNNWHXzzdhOnYileL/KZdvpLJfsGa9eUPlk\njCkHKisrKykvLycWc13ct97q/tsvIiIiIqWlqqqKCvdV5AprbZXf9YhvFgLNfNfbA/E/NAPwt1Ha\nhg51YdXcuU3POA0aY1y4/dFHflfinVI8/vr3hyeecDNuu3b1uxpvLFniQuC+fVPPgA44r7MhL7eX\ny7bqr5tqW0G8TVymJwbz4vaZbqfIQt5+rVu3ftqPO85WEX1XIH2hkBvFo45bEREREREREZHsFXNo\nC94GfNmMLfDyNtnMr81lnq3Xt29qHcmPQAa34MYlKLgVEREREREREcme10Gc3/NpM12vkCGsF9v2\nc6xBQLpqS4qCWxERERERERERkVpeBsXZBryp1itEaFuIEFaBbvoCG9yWlSm4FRERERERERHJRT7O\nfZSvrlsvtpvPzthCb6upEQiFCm3VbZtfgQ1u1XErIiIiIiIiIpKboAVshao3l3DVqy7bxpZlszzb\n67LdnpfrtGQKbkVEREREREREWqh8dNxCfgO6TLadbVes17wKb/PRTVuoEFgyp+BWRERERERERKSF\nCmrIVoiTqhXbsmzD10IGswp0vRXo4La62u8qREREREREREQklXwHdblsv9hC2XSWpaKAtbQFOrhV\nx62IiIiIiIiISPbyNSohrhDhbTon8crH/RZimdddto3dVzrX5bKuwuDsRPwuIFsKbkVEREREJCs/\n/QRnnQWxWN3lAwYkLl96Key5Z2HrytXFF8Nnn7nLs2e7f885B7p3d5cPPBAGDfKntmw98gjce2/d\nZR9/nHiuOnaEW26BSID+tP36a7jggobLk4+/K6+EHXcsXE25shbOPx++/db9/sQT7t+TToJ27dzl\n/v3hz3/2pbys3XMPPPaYuxwPIJ59NvFcdesGM2dCwAMpY0xBwtug3Eeq7WSy7XTXb2wZNAzTk2+b\nr2A1n+tK9ky+XzheMMaUA5WVlZWUl5cDcPjh7r0x/t8DERERESkdVVVVVFRUAFRYa6v8rkd8sxDY\nyvOtPvAADBzY9G2GD4fJkz2/67xZuhS6dIGamsZvs+WWsHBhsEKmPn3gH/9o+jbz5sHOOxemHi/c\neCOcd17Tt7niChg9ujD1eOGbb9zx1VS+sNtu8N57havJC+Xl8O67jV9vjHtNbbllwUrKh0LlQsVw\nP6muS3dZIddvanljcg1W8xnaFlGo269169ZP+11EJgI7KqGsTB23IiIiIiKShaOPhh49IBxOfX3b\ntnDRRYWtKVcdOsCFF0KoiT/xrroqWKEtuACzMZGIey6DFNqC6zrdfPPGn6uOHYPXGb355nDmmY2/\npsAdf0Fz5ZWNXxcOwxlnBD60LaRChXde3E8m28hkPm2ut82kBi+vz0URhbaBFNjgVqMSREREREQk\nK5EIzJgB0WjD64yBsWNhk00KX1euLr0UOnVqGM6Gw7DXXs13GRej3r3hhBNSj0IIheDaawtfU67a\ntoUpUxqO6oi7+moXxAfNFVe4fasvEoFDDoG+fQtfU64OPdTVner4Kytr+oOFACnFYM2L0LOQgWxj\nM2nTCVyb65T1+/rmxLdRqJ+gUXArIiIiIiItT58+cMQRdQOZUMh1zw0d6l9dudhgAxdk1v96bTTq\nguoA/sEKwKRJDYOzUAhGjoStt/alpJwddRTsu2/dDtVwGHr2hNNP96+uXHTpAhMnNjzOrIWpU/2p\nyQtTpzZ8TRkDEyZA167+1OSxQo7Q9Ds4y2c3rhfdtF6ctMyL65uqMd3r0+H38RAEgQ5uq6v9rkJE\nRERERALr+uvr/h6LwbRp7o+NoDr5ZNh990QgGA7DKacE70R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n+3r6zz/DwQf7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interact(value_iteration,Itern=(20,160,10),Gamma=(.0,1,.05));\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Random Rewards" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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trRoaGlRfX+92lG4TdZGZMGFCx38PGzZM+fn5SktL0/PPP6+pU6dGu/rLkjFG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\nAAAAa1FkAACAtSgyAADAWhQZAABgLYo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10\n", "\n", "Action = action_LRUD(N)\n", "\n", "#Reward\n", "state_reward = np.random.randint(0,10,size=N*N)\n", "# state_reward = -1*np.ones((N*N))\n", "\n", "\n", "terminating_state= np.random.randint(0,N)*N +np.random.randint(0,N)\n", "# middle = int(N/2)*N + int(N/2)\n", "state_reward[terminating_state] = +20\n", "\n", "fig = plt.figure(figsize=(7,7))\n", "ax = fig.add_subplot(111)\n", "ax.xaxis.set_ticks([i for i in range(1,N+1)])\n", "ax.yaxis.set_ticks([i for i in range(1,N+1)])\n", "ax.xaxis.set_ticklabels([])\n", "ax.yaxis.set_ticklabels([])\n", "ax.grid(True,linestyle='-', linewidth=.5)\n", "vals = np.around(state_reward.reshape(N,N)).astype(int)\n", "for i in range(0,N,1):\n", " for j in range(0,N,1):\n", " ax.annotate(vals[i,j], (i+.1,j+.1),size=10, va=\"center\")\n", " " ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def value_iteration1(Itern=100,Gamma=.5):\n", " # Value Iteration\n", " #initialize State_Value\n", " state_value = np.zeros((N*N))\n", " delta = 0\n", " deltas = []\n", " for i in range(Itern):\n", " temp = state_value.copy()\n", " #Update Values\n", " for j in range(Action.shape[0]):\n", " state_value[j] = np.sum(np.multiply(Action[j],state_reward+Gamma*state_value))\n", " \n", " diff = np.sum(np.abs(temp-state_value))\n", " \n", " delta = np.maximum(delta,diff)\n", " deltas.append(diff)\n", " \n", " \n", " state_value = np.around(state_value,decimals=2)\n", " \n", " fig = plt.figure(figsize=(14,7));\n", " plt.subplot(1,2,1)\n", " plt.plot(deltas);\n", "# plt.subplot(1,2,2)\n", " ax = fig.add_subplot(1,2,2)\n", " ax.xaxis.set_ticks([i for i in range(1,N+1)])\n", " ax.yaxis.set_ticks([i for i in range(1,N+1)])\n", " ax.xaxis.set_ticklabels([])\n", " ax.yaxis.set_ticklabels([])\n", " ax.grid(True,linestyle='-', linewidth=.5)\n", " vals = np.around(state_value.reshape(N,N)).astype(int)\n", " for i in range(0,N,1):\n", " for j in range(0,N,1):\n", " ax.annotate(vals[i,j], (i+.1,j+.1),size=10, va=\"center\")\n", " \n", "# plt.imshow(state_value.reshape(N,N),cmap=plt.cm.gray_r);\n", " i = terminating_state/N +.5\n", " j = terminating_state%N + .5\n", "# ax.plot(j,i,'og',markersize=9)\n", "# plt.axis('off')\n", " for i in range(0,N):\n", " for j in range(0,N):\n", " state = i*N+j\n", " valid_actions = Action[state]>0\n", " action_reward = np.around(np.multiply(Action[state],state_value),decimals=2)\n", " try:\n", " max_val = np.max(action_reward[valid_actions])\n", " next_greedy_state = np.where(action_reward==max_val)[0]\n", " for d in next_greedy_state:\n", " i1 = d/N \n", " j1 = d%N \n", " plt.arrow(i+.5,j+.5,.3*(i1-i),.3*(j1-j),head_width=.15, head_length=.13, fc='r', ec='r');\n", " except:\n", " continue\n", "# plt.grid()\n", " plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Scnh5SUFH777TfatGnD/PnzI+oQ2JJysG7d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\n9JHXEYmIiIiIiIiIiEhZqHEboZKT4dNPoXVrN4XCwIGwd6/XU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "interact(value_iteration1,Itern=(20,160,10),Gamma=(.0,1,.05));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "# In comparison to a Markov Chains\n", "### Here, we learn how to move in the underlying transition matrix, while we modify the transition probabilities\n", "\n", "![](Images/Deep_Mind_RL1-300x173.jpg)![](Images/Markov_Decision_Process_example-300x240.png)\n", "[image source](http://neuro.cs.ut.ee/demystifying-deep-reinforcement-learning/)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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G2mvXKg9emtjd4lxLgzskGVpUejd7SAxunWeUYNjBMyQJzQk6dUmrAu3y4F0M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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Graph of connectivity\n", "plt.imshow(Action)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# So far Value Iteration was similar to Dynamic Programming \n", "# This is called \"MODEL BASED RL\"\n", "## Which is based on:\n", "* **Deterministic state transition**\n", "* **Limited State Space**\n", "* **Limited Action Space**\n", "* **Deterministic Reward**\n", "\n", "
\n", "# In other words, so far we had no learning by experiments. \n", "
\n", "\n", "\n", "# Known limits of these approach\n", "- **State Space Explosion**\n", "- **Action Space Eplosion**\n", "- **Continuous Spaces**\n", "- **Unknown Behavior or the environment (e.g. imagine after every move, we don't know the exact reward!)**\n", "\n", "\n", "\n", "# However, in most of RL applications we need different approaches to learn value and policy Functions via interactions\n", "* **Temporal Difference Learning (TD-Learning)**\n", " * **Q-Learning**\n", " * **Actor-Critic Learning**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Q-Learning \n", "## We would like to learn Q values of state-action pairs as follows:\n", "\n", "\n", "# $$Q(s,a) = r + \\gamma (max(Q(s',a')))$$\n", "\n", "# We do thin by playing the game and sampling!\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "# Several games with Open AI: https://gym.openai.com/\n", "## Example [from](https://medium.com/emergent-future/simple-reinforcement-learning-with-tensorflow-part-0-q-learning-with-tables-and-neural-networks-d195264329d0)" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[2017-05-09 12:44:09,573] Making new env: FrozenLake-v0\n" ] } ], "source": [ "## Load the environment\n", "import gym\n", "env = gym.make('FrozenLake-v0')" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "env.action_space.sample()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implement Q-Table learning algorithm\n" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Initialize table with all zeros\n", "Q = np.zeros([env.observation_space.n,env.action_space.n])\n", "# Set learning parameters\n", "lr = .85\n", "y = .99\n", "num_episodes = 2000\n", "#create lists to contain total rewards and steps per episode\n", "#jList = []\n", "rList = []\n", "for i in range(num_episodes):\n", " #Reset environment and get first new observation\n", " s = env.reset()\n", " rAll = 0\n", " d = False\n", " j = 0\n", " #The Q-Table learning algorithm\n", " while j < 99:\n", " j+=1\n", " #Choose an action by greedily (with noise) picking from Q table\n", " a = np.argmax(Q[s,:] + np.random.randn(1,env.action_space.n)*(1./(i+1)))\n", " #Get new state and reward from environment\n", " s1,r,d,_ = env.step(a)\n", " #Update Q-Table with new knowledge\n", " Q[s,a] = Q[s,a] + lr*(r + y*np.max(Q[s1,:]) - Q[s,a])\n", " rAll += r\n", " s = s1\n", " if d == True:\n", " break\n", " #jList.append(j)\n", " rList.append(rAll)" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(0, 0.0, False, {'prob': 0.3333333333333333})" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = env.reset()\n", "a = np.argmax(Q[s,:] + np.random.randn(1,env.action_space.n)*(1./(i+1)))\n", "env.step(a)" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Score over time: 0.3775\n" ] } ], "source": [ "print \"Score over time: \" + str(sum(rList)/num_episodes)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final Q-Table Values\n", "[[ 2.41812747e-01 1.34668144e-02 1.37759130e-02 1.34745022e-02]\n", " [ 0.00000000e+00 1.54653562e-02 7.79397923e-05 3.28061161e-01]\n", " [ 2.95354171e-03 1.44168576e-02 3.38725506e-03 4.90887652e-01]\n", " [ 1.51910228e-03 1.80457987e-02 2.23516011e-03 3.57746406e-01]\n", " [ 2.50271470e-01 6.24764384e-04 0.00000000e+00 3.11052109e-04]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [ 6.24345458e-01 5.55418788e-09 1.72631494e-04 1.42910829e-04]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [ 1.64678842e-03 5.16343436e-05 2.41407774e-03 5.49872600e-01]\n", " [ 0.00000000e+00 8.43591681e-01 0.00000000e+00 0.00000000e+00]\n", " [ 6.12664778e-01 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]\n", " [ 0.00000000e+00 0.00000000e+00 8.25771751e-01 0.00000000e+00]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 9.35583578e-01]\n", " [ 0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]]\n" ] } ], "source": [ "print \"Final Q-Table Values\"\n", "print Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Excercise: Learn Q-tables for Grid World example above" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "\n", "
\n", "\n", "# Function Approximation for Q-values\n", "### Q-Tables are not scalable\n", "### So, what if we mixture learning of Q-values by supervised learning methods\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Deep Q-Networks\n", "### The right one, empirically works better\n", "![](Images/dqn.png)\n", "\n", "\n", "# [Deep Mind paper](https://www.nature.com/nature/journal/v518/n7540/full/nature14236.html)\n", "![](Images/atari.png)\n", "\n", "\n", "[A nice and simple tutorial](http://karpathy.github.io/2016/05/31/rl/)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/jpeg": 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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('V1eYniJ0Rnk',width=700, height=600)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# One important note!\n", "Comparing to classical computational modeling here we learn, but we don't say how. \n", "We don't hardcode the logics and strategies, we learn them" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "# Conclusions\n", "\n", "# RL in relation to Game theory and the notion of Planning and optimization\n", "- Game theory and RL as Dynamic Game Playing\n", "- Game theory is based on assumption of rational strategies and actions and min-max optimization\n", "- Planning Vs. Learning\n", "
\n", "\n", "# End of Model based Planning and Optimization!\n", "- **This can be a general statement in many fields**\n", "- ** We can think about it in terms of Black Swan too**\n", "\n", "\n", "
\n", "\n", "# One answer is learning with interaction\n", "- **We can think about it in relation to the success of social media, Google, ...**\n", "- ** We can think about it in relation to software architecture: MS. Windows vs. Android**\n", "
\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# But why only games? \n", "## Definitely, not because games are just cool!\n", "## One possible answer: Only via games we can experience the interactions faster than the reality. So, there is no problem with data collection!\n", "\n", "# Question: Can we use RL in other domains such as \n", "- Banks and economic polocies\n", "- Supply chain and Inventory management (VMI)\n", "\n", "- Dynamic Resource Allocation\n", " - CPU\n", " - Clouds\n", " - Manufacturing: Job-Shop Scheduling\n", " - **Smart Home**\n", " - Urban Traffic planning: Dynamic Tolls, Dynamic Light control\n", " \n", "- Simulation Based Optimization\n", " - Water flow \n" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" }, "widgets": { "state": { "30b756d59a1c416899d89bc3b75d3656": { "views": [ { "cell_index": 20 } ] }, "4c38dd9aa5974f899f25b6c7e6ca38e1": { "views": [ { "cell_index": 27 } ] }, "d44f6ecedb8e49ffafc68ff78fd62ad0": { "views": [ { "cell_index": 23 } ] } }, "version": "1.2.0" } }, "nbformat": 4, "nbformat_minor": 0 }