diff --git a/rl.ipynb b/rl.ipynb index 98b887f64..103c32e9e 100644 --- a/rl.ipynb +++ b/rl.ipynb @@ -98,7 +98,7 @@ { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 4, @@ -218,7 +218,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "{(0, 1): 0.40645681855595944, (1, 2): 0.7159329142704773, (3, 2): 1, (0, 0): 0.2886341019228155, (2, 0): 0.0, (3, 0): 0.0, (1, 0): 0.20553303981983, (3, 1): -1, (2, 2): 0.8560486321875528, (2, 1): 0.606857283945162, (0, 2): 0.5612793239398001}\n" + "{(0, 1): 0.4496668011879283, (1, 2): 0.619085803445832, (3, 2): 1, (0, 0): 0.32062531035042224, (2, 0): 0.0, (3, 0): 0.0, (1, 0): 0.235638474671875, (3, 1): -1, (2, 2): 0.7597530664991547, (2, 1): 0.4275522091676434, (0, 2): 0.5333144285450669}\n" ] } ], @@ -277,9 +277,9 @@ "outputs": [ { "data": { - "image/png": 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DiO2kw/U51K4d34bh3DQnN9f+f/x4O2egvHDYty/2HfJnn8VevvI4O8h0Cgfn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\negCNQp5LyLpI5ZpDNCfRVSu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LZOLFweMtB+cSt2XCgAF2PRIHUWyEQhzi3UolJel7aZSVmesnWQsx6Faqr7ff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\nrFq1Kq9pyq0khChKSkpK0HO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hLNenXLJwuqLp2KZEEHgy4iQvx17mg6Mf5OiNozPdJ+uOreMt39zCrSe3ev2eYeuHMaB3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\nw/8DGqwOkNBaudkAAAAASUVORK5CYII=\n", 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -320,6 +320,242 @@ "graph_utility_estimates(agent, sequential_decision_environment, 500, [(2,2), (3,2)])" ] }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Active Reinforcement Learning\n", + "\n", + "Unlike Passive Reinforcement Learning in Active Reinforcement Learning we are not bound by a policy pi and we need to select our actions. In other words the agent needs to learn an optimal policy. The fundamental tradeoff the agent needs to face is that of exploration vs. exploitation. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### QLearning Agent\n", + "\n", + "The QLearningAgent class in the rl module implements the Agent Program described in **Fig 21.8** of the AIMA Book. In Q-Learning the agent learns an action-value function Q which gives the utility of taking a given action in a particular state. Q-Learning does not required a transition model and hence is a model free method. Let us look into the source before we see some usage examples." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "%psource QLearningAgent" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Agent Program can be obtained by creating the instance of the class by passing the appropriate parameters. Because of the __ call __ method the object that is created behaves like a callable and returns an appropriate action as most Agent Programs do. To instantiate the object we need a mdp similar to the PassiveTDAgent.\n", + "\n", + " Let us use the same GridMDP object we used above. **Figure 17.1 (sequential_decision_environment)** is similar to **Figure 21.1** but has some discounting as **gamma = 0.9**. The class also implements an exploration function **f** which returns fixed **Rplus** untill agent has visited state, action **Ne** number of times. This is the same as the one defined on page **842** of the book. The method **actions_in_state** returns actions possible in given state. It is useful when applying max and argmax operations." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us create our object now. We also use the **same alpha** as given in the footnote of the book on **page 837**. We use **Rplus = 2** and **Ne = 5** as defined on page 843. **Fig 21.7** " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "q_agent = QLearningAgent(sequential_decision_environment, Ne=5, Rplus=2, \n", + " alpha=lambda n: 60./(59+n))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now to try out the q_agent we make use of the **run_single_trial** function in rl.py (which was also used above). Let us use **200** iterations." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "for i in range(200):\n", + " run_single_trial(q_agent,sequential_decision_environment)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let us see the Q Values. The keys are state-action pairs. Where differnt actions correspond according to:\n", + "\n", + "north = (0, 1)\n", + "south = (0,-1)\n", + "west = (-1, 0)\n", + "east = (1, 0)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "defaultdict(float,\n", + " {((0, 0), (-1, 0)): -0.07323076923076924,\n", + " ((0, 0), (0, -1)): -0.0759999433406361,\n", + " ((0, 0), (0, 1)): 0.2244371077466747,\n", + " ((0, 0), (1, 0)): -0.07085714285714287,\n", + " ((0, 1), (-1, 0)): -0.04883916667786259,\n", + " ((0, 1), (0, -1)): -0.05252175603090532,\n", + " ((0, 1), (0, 1)): 0.3396752416362625,\n", + " ((0, 1), (1, 0)): -0.07323076923076924,\n", + " ((0, 2), (-1, 0)): -0.05158410382845185,\n", + " ((0, 2), (0, -1)): -0.04733337973118637,\n", + " ((0, 2), (0, 1)): -0.048398095611170026,\n", + " ((0, 2), (1, 0)): 0.4729172313717893,\n", + " ((1, 0), (-1, 0)): 0.14857758363326573,\n", + " ((1, 0), (0, -1)): -0.0759999433406361,\n", + " ((1, 0), (0, 1)): -0.07695450531425811,\n", + " ((1, 0), (1, 0)): -0.09719395035017139,\n", + " ((1, 2), (-1, 0)): 0.21593724199115555,\n", + " ((1, 2), (0, -1)): 0.26570820298073916,\n", + " ((1, 2), (0, 1)): 0.19612684250448048,\n", + " ((1, 2), (1, 0)): 0.6105607273543103,\n", + " ((2, 0), (-1, 0)): 0.06795076480003,\n", + " ((2, 0), (0, -1)): -0.11306695825372484,\n", + " ((2, 0), (0, 1)): -0.105596446586541,\n", + " ((2, 0), (1, 0)): -0.10409381636745853,\n", + " ((2, 1), (-1, 0)): -0.0383184014263534,\n", + " ((2, 1), (0, -1)): -0.7913059177862865,\n", + " ((2, 1), (0, 1)): -0.7672970392961057,\n", + " ((2, 1), (1, 0)): -0.8402721538112866,\n", + " ((2, 2), (-1, 0)): 0.2351847866756862,\n", + " ((2, 2), (0, -1)): 0.24909509983624728,\n", + " ((2, 2), (0, 1)): 0.25112211666264095,\n", + " ((2, 2), (1, 0)): 0.7743960998734626,\n", + " ((3, 0), (-1, 0)): -0.1037923159515085,\n", + " ((3, 0), (0, -1)): -0.07807333741195537,\n", + " ((3, 0), (0, 1)): -0.9374064176172849,\n", + " ((3, 0), (1, 0)): -0.07323076923076924,\n", + " ((3, 1), None): -1,\n", + " ((3, 2), None): 1})" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "q_agent.Q" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Utility **U** of each state is related to **Q** by the following equation.\n", + "\n", + "**U (s) = max a Q(s, a)**\n", + "\n", + "Let us convert the Q Values above into U estimates.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "U = defaultdict(lambda: -1000.) # Very Large Negative Value for Comparison see below.\n", + "for state_action, value in q_agent.Q.items():\n", + " state, action = state_action\n", + " if U[state] < value:\n", + " U[state] = value" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "defaultdict(>,\n", + " {(0, 0): 0.2244371077466747,\n", + " (0, 1): 0.3396752416362625,\n", + " (0, 2): 0.4729172313717893,\n", + " (1, 0): 0.14857758363326573,\n", + " (1, 2): 0.6105607273543103,\n", + " (2, 0): 0.06795076480003,\n", + " (2, 1): -0.0383184014263534,\n", + " (2, 2): 0.7743960998734626,\n", + " (3, 0): -0.07323076923076924,\n", + " (3, 1): -1,\n", + " (3, 2): 1})" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "U" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us finally compare these estimates to value_iteration results." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{(0, 1): 0.3984432178350045, (1, 2): 0.649585681261095, (3, 2): 1.0, (0, 0): 0.2962883154554812, (3, 0): 0.12987274656746342, (3, 1): -1.0, (2, 1): 0.48644001739269643, (2, 0): 0.3447542300124158, (2, 2): 0.7953620878466678, (1, 0): 0.25386699846479516, (0, 2): 0.5093943765842497}\n" + ] + } + ], + "source": [ + "print(value_iteration(sequential_decision_environment))" + ] + }, { "cell_type": "code", "execution_count": null, @@ -346,7 +582,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.1" + "version": "3.4.3" } }, "nbformat": 4,