ipynb/spencer_lyon-career_rl.ipynb

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                "# Reinforcement Learning -- Economic Example\n",
                "\n",
                "**Prerequisites**\n",
                "\n",
                "- Dynamic Programming\n",
                "- Reinforcement Learning Introduction\n",
                "- Reinforcement Learning Sarsa algorithm\n",
                "- Reinforcement Learning Q-learning algorithm\n",
                "\n",
                "**Outcomes**\n",
                "\n",
                "- Understand the main points of the career choice model of Derek Neal\n",
                "- See how career choice model can be cast as a RL problem\n",
                "- Use Sarsa and QLearning to \"solve\" career choice model\n",
                "\n",
                "**References**\n",
                "\n",
                "- Barto & Sutton book (online by authors [here](http://incompleteideas.net/book/the-book.html)) chapters 4-6\n",
                "- [QuantEcon lecture](https://python.quantecon.org/career.html) on career choice model "
            ]
        },
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            "source": [
                "## Disclaimer: Julia\n",
                "\n",
                "- The code for this notebook is written in the [Julia](https://julialang.org) programming language\n",
                "- Julia is a newer language created specificly for doing numerical computing\n",
                "- It is friendly like Python, but can run *much* faster\n",
                "- Most of the code for this example in in a file `neal.jl`, which we will not study directly\n",
                "- The examples that do appear in the notebook will be commented and should be similar enough to Python for us to follow\n",
                "- To learn more about Julia, we recommend the [QuantEcon Julia Lectures](https://julia.quantecon.org/)\n",
                "\n",
                "> Note: using Julia was necessary to have the code run quickly enough..."
            ]
        },
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            "source": [
                "## Career Model\n",
                "\n",
                "- We'll summarize the model here\n",
                "- See the [QuantEcon lecture](https://python.quantecon.org/career.html) for more details\n",
                "- Workers have a career and a job\n",
                "    - Career is general field\n",
                "    - Job is position within a firm -- many jobs per career\n",
                "- Wage has career and job component: $$w_t = \\underbrace{\\theta_t}_{\\text{career part}} + \\underbrace{\\epsilon_t}_{\\text{job part}}$$\n",
                "- Each period, worker has three mutually exclusive choices\n",
                "    1. Stay at job -- \"stay put\"\n",
                "    2. Switch jobs in same career -- \"new job\"\n",
                "    3. Swich careers (requires new job) -- \"new life\"\n",
                "- Draws of $\\theta$ and $\\epsilon$ are time-invariant:$$\\theta_t \\sim F, \\epsilon_t \\sim G \\quad \\forall t$$\n",
                "- New $\\epsilon$ and $\\theta$ are only drawn when a worker switches jobs or careers"
            ]
        },
        {
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            "source": [
                "### State Value Function\n",
                "\n",
                "- State of model is $s = (\\theta, \\epsilon)$\n",
                "- The state value function obeys\n",
                "$$\n",
                "\\begin{aligned}\n",
                "v(\\theta, \\epsilon) &= \\max\\{I, II, III\\}, \\text{ where} \\\\\n",
                "& I = \\theta + \\epsilon + \\beta v(\\theta, \\epsilon) \\\\\n",
                "& II = \\theta + E[ \\epsilon' + \\beta  v(\\theta, \\epsilon')  | \\epsilon' \\sim G] \\\\\n",
                "& III = E[\\theta' + \\epsilon' + \\beta v(\\theta', \\epsilon') |  \\epsilon' \\sim G, \\theta' \\sim F]\n",
                "\\end{aligned}\n",
                "$$\n",
                "- $I$, $II$, and $III$ correspond to value of \"stay put\", \"new job\", \"new life\"; respectively"
            ]
        },
        {
            "cell_type": "markdown",
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            "source": [
                "### Action Value Function\n",
                "\n",
                "\n",
                "- The action space is $\\mathcal{A} = \\{\\text{stay put}, \\text{ new job}, \\text{ new life} \\}$ for all states\n",
                "- The action value function $Q(s, a)$ is:\n",
                "$$\n",
                "\\begin{aligned}\n",
                "Q(\\theta, \\epsilon, \\text{ stay put}) &= \\theta + \\epsilon + \\beta \\max_{a'} Q(\\theta, \\epsilon, a') \\\\\n",
                "Q(\\theta, \\epsilon, \\text{ new job}) &= \\theta + E[ \\epsilon' + \\beta  \\max_{a'} Q(\\theta, \\epsilon', a')  | \\epsilon' \\sim G] \\\\\n",
                "Q(\\theta, \\epsilon, \\text{ new life}) &= E[\\theta' + \\epsilon' + \\beta  \\max_{a'} Q(\\theta', \\epsilon', a')  | \\epsilon' \\sim G, \\theta' \\sim F] \\\\\n",
                "\\end{aligned}\n",
                "$$"
            ]
        },
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            "source": [
                "### Discrete Distributions\n",
                "\n",
                "- In our examples today, we will use discrete distributions for $F$ and $G$\n",
                "- There will be a finite number of possible $\\epsilon$ and $\\theta$ -- each with a fixed probability of being drawn from their repsective distributions"
            ]
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            "source": [
                "# set up all dependencies for this code\n",
                "using Pkg\n",
                "Pkg.activate(\".\")\n",
                "Pkg.resolve()\n",
                "\n",
                "# load up example code\n",
                "include(\"src/Career.jl\")\n",
                "using .Career"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "id": "8134e6e4",
            "metadata": {},
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                            "data: [\n",
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                    },
                    "execution_count": 7,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "m = NealDSDC(N=15);\n",
                "plot_distributions(m)"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "099c5b9c",
            "metadata": {},
            "source": [
                "Notes: \n",
                "\n",
                "- Both $\\theta$ and $\\epsilon$ live in [0, 5]\n",
                "- $\\theta$ is uniformly distributed\n",
                "- $\\epsilon$ looks to be nearly Gaussian on that range"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "426e5e2b",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "source": [
                "### Optimal solution via Dynamic Programming\n",
                "\n",
                "- We can apply dynamic programming methods to solve this model numerically\n",
                "- We have code that can solve model this via value function iteration\n",
                "- Here's the state value function $v^*$ for this model:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "id": "fdd5ce65",
            "metadata": {},
            "outputs": [
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                                    }
                                },
                                "yaxis": {
                                    "title": {
                                        "text": "epsilon"
                                    }
                                }
                            }
                        },
                        "image/png": 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                    "execution_count": 8,
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            "source": [
                "plot_vf(m)"
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            "metadata": {
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            "source": [
                "#### Policy function $a^*(s)$\n",
                "\n",
                "- Optimal policy function is easier to read/understand\n",
                "- We'll look more at it"
            ]
        },
        {
            "cell_type": "code",
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            "id": "addb0aa1",
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                    },
                    "execution_count": 9,
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            ],
            "source": [
                "plot_policy(m)"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "27927809",
            "metadata": {},
            "source": [
                "Notes\n",
                "\n",
                "- If both job and career are good, worker stays put\n",
                "- If career is good, worker explores new jobs until $\\epsilon$ is sufficiently high\n",
                "- If neither is very good, worker re-draws both career and job"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "808f857b",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
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                "tags": []
            },
            "source": [
                "#### Comment on model knowledge\n",
                "\n",
                "- See code for `bellman_operator!` repeated below\n",
                "- Note in doing VFI and leveraging this operator, we let algorithm (VFI) know the model for $\\theta$ and $\\epsilon$ (we use $F$ and $G$ to take expectations)\n",
                "\n",
                "```julia\n",
                "function bellman_operator!(m::NealDSDC, v::Array, out::Array;\n",
                "                           ret_policy=false)\n",
                "    # new life. This is a function of the distribution parameters and is\n",
                "    # always constant. No need to recompute it in the loop\n",
                "    v3 = (m.G_mean + m.F_mean + m.beta .* (m.F_probs' * v * m.G_probs))\n",
                "\n",
                "    for j=1:m.N\n",
                "        for i=1:m.N\n",
                "            # stay put\n",
                "            v1 = m.θ[i] + m.ϵ[j] + m.beta * v[i, j]\n",
                "\n",
                "            # new job\n",
                "            v2 = m.θ[i] + m.G_mean + m.beta * dot(v[i, :], m.G_probs)\n",
                "\n",
                "            if ret_policy\n",
                "                if v1 >= max(v2, v3)\n",
                "                    action = 1\n",
                "                elseif v2 >= max(v1, v3)\n",
                "                    action = 2\n",
                "                else\n",
                "                    action = 3\n",
                "                end\n",
                "                out[i, j] = action\n",
                "            else\n",
                "                out[i, j] = max(v1, v2, v3)\n",
                "            end\n",
                "        end\n",
                "    end\n",
                "end\n",
                "```"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "44dcdba7",
            "metadata": {
                "slideshow": {
                    "slide_type": "slide"
                },
                "tags": []
            },
            "source": [
                "## Model-free learning\n",
                "\n",
                "- RL algorithms like Sarsa and Q-learning are model-free algorithms\n",
                "- They do not take into account any specialized structure about the environment\n",
                "- Sarsa and Q-learning learn entirely from trial and error\n",
                "- Benefits: can learn in situations where we don't know dynamics\n",
                "- Downfalls: don't leverage model structure to accelerate learning ==> takes longer!"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "4b5a2b0b",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "source": [
                "### Sarsa for career model\n",
                "\n",
                "- Inside the `src/neal.jl` file you see the following code for the Sarsa algorithm\n",
                "\n",
                "```julia\n",
                "# Barto & Sutton Algorithm in figure 6.5\n",
                "mutable struct Sarsa <: AbstractQAlgorithm\n",
                "    Q::QFunction  # wrapper around 3d array (a, θ, ϵ)\n",
                "    α::Float64\n",
                "    \n",
                "    # store (s, a) to use in updates\n",
                "    s::State\n",
                "    a::Action\n",
                "end\n",
                "\n",
                "function update!(wp::NealDSDC, actor::AbstractActor, algo::Sarsa)\n",
                "    # use current state and action to do transition\n",
                "    sp, r = step(wp, algo.s, algo.a)\n",
                "\n",
                "    # get next action using actor's strategy\n",
                "    ap = get_action(wp, algo, actor, sp)[1]\n",
                "\n",
                "    # Apply TD update\n",
                "    algo.Q[algo.s, algo.a] = (1-algo.α)*algo.Q[algo.s, algo.a] +\n",
                "                             algo.α*(r + wp.beta * algo.Q[sp, ap])\n",
                "\n",
                "    # step forward in time\n",
                "    algo.s = sp\n",
                "    algo.a = ap\n",
                "end\n",
                "```"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "242ead07",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "source": [
                "- Below we'll set up a Sarsa model and plot the initial policy function"
            ]
        },
        {
            "cell_type": "code",
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                            "        {\"editable\":false,\"responsive\":true,\"staticPlot\":false,\"scrollZoom\":true},\n",
                            "    )\n",
                            "}\n",
                            "\n",
                            "        });\n",
                            "    </script>\n",
                            "</div>\n",
                            "\n",
                            "</body>\n",
                            "</html>"
                        ],
                        "text/plain": [
                            "data: [\n",
                            "  \"heatmap with fields colorbar, colorscale, showscale, type, x, y, and z\"\n",
                            "]\n",
                            "\n",
                            "layout: \"layout with fields annotations, height, margin, width, xaxis, and yaxis\"\n",
                            "\n"
                        ]
                    },
                    "execution_count": 10,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "# set random seed\n",
                "using Random  \n",
                "Random.seed!(56)\n",
                "sarsa = Sarsa(m, 0.01);\n",
                "\n",
                "# plot initial policy\n",
                "plot_policy(m, get_greedy(m, sarsa.Q))"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "ebf22d4b",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "source": [
                "- Now we will have Sarsa learn a policy by taking 150,000,000 steps"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 11,
            "id": "5c62b967",
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "  6.712036 seconds (1.79 M allocations: 106.000 MiB, 0.31% gc time, 6.59% compilation time)\n"
                    ]
                },
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",
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                        "text/plain": [
                            "data: [\n",
                            "  \"heatmap with fields colorbar, colorscale, showscale, type, x, y, and z\"\n",
                            "]\n",
                            "\n",
                            "layout: \"layout with fields annotations, height, margin, width, xaxis, and yaxis\"\n",
                            "\n"
                        ]
                    },
                    "execution_count": 11,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "# epsilson is prob of random action\n",
                "actor = EpsilonGreedy(1.0, 0.1, 10_000_000)\n",
                "@time learn(m, sarsa, actor; maxit=150_000_000,  should_plot=false);\n",
                "\n",
                "# plot final policy\n",
                "plot_policy(m, get_greedy(m, sarsa.Q))"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "9b2ff9a3",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "source": [
                "Notes\n",
                "\n",
                "- This is not bad, but...\n",
                "    - Sarsa  under-estimates the Q-function systematically\n",
                "    - We'll see this by looking at \"true q*\" obtained via QFI"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 12,
            "id": "a0c43b6a",
            "metadata": {},
            "outputs": [],
            "source": [
                "opt_Q = Career.qfi(m);"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "58f11915",
            "metadata": {},
            "source": [
                "- We'll compare opt_Q to Sarsa's Q in the upper right corner of state space (where it seems to struggle most)"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 13,
            "id": "a8482200",
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "3×3×3 Array{Float64, 3}:\n",
                            "[:, :, 1] =\n",
                            "  9.9898   9.89119   9.90818\n",
                            " 10.0404  10.1329   10.0137\n",
                            " 11.0849  10.5908   10.4959\n",
                            "\n",
                            "[:, :, 2] =\n",
                            "  9.93097   9.94257  10.0245\n",
                            " 10.0652   10.0367    9.95953\n",
                            " 10.9327   10.1025   10.6261\n",
                            "\n",
                            "[:, :, 3] =\n",
                            " 10.1664  10.1106  10.1637\n",
                            " 10.111   10.0961  10.0616\n",
                            " 10.7898  10.5648  10.5708"
                        ]
                    },
                    "execution_count": 13,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "opt_Q[:, 8:10, 8:10] - sarsa.Q.q[:, 8:10, 8:10] "
            ]
        },
        {
            "cell_type": "markdown",
            "id": "16cb40f8",
            "metadata": {},
            "source": [
                "- $q^*$ higher everywhere \n",
                "- Part of issue is that $TD(0)$ is only accurate when Q is accurate and $\\epsilon$ is zero (greedy updates)\n",
                "- We don't set $\\epsilon$ to zero, so we make some sub-optimal transitions, which introduces downward bias in $Q$"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "4f2fc41d",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "source": [
                "### Q-learning for career model\n",
                "\n",
                "- We can use the off-policy Q-learning algorithm to overcome this problem\n",
                "- In Q-learning, $TD(0)$ is always computed using greedy policy derived from $Q$\n",
                "- This will remove large portion of downward bias we saw with Sarsa\n",
                "- My implementation of Q-learning for this model is found below\n",
                "\n",
                "```julia\n",
                "# Barto & Sutton Algorithm in figure 6.7\n",
                "mutable struct QLearning <: AbstractQAlgorithm\n",
                "    Q::QFunction\n",
                "    s::State\n",
                "    α::Float64\n",
                "end\n",
                "\n",
                "function update!(wp::NealDSDC, actor::AbstractActor, algo::QLearning)\n",
                "    # choose a\n",
                "    a = get_action(wp, algo, actor, algo.s)[1]\n",
                "\n",
                "    # use current state and action to do transition\n",
                "    sp, r = step(wp, algo.s, a)\n",
                "\n",
                "    # ap is greedy in Q\n",
                "    ap = get_greedy(algo, sp)\n",
                "\n",
                "    # Apply TD update\n",
                "    algo.Q[algo.s, a] = (1-algo.α)*algo.Q[algo.s, a] +\n",
                "                           algo.α*(r + wp.beta * algo.Q[sp, ap])\n",
                "\n",
                "    # step forward in time\n",
                "    algo.s = sp\n",
                "end\n",
                "```"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "0036d8c2",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "source": [
                "- We'll run same experiment with Q-learning"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 14,
            "id": "2c9b2120",
            "metadata": {},
            "outputs": [
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",
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                            "        [{\"colorbar\":{\"dtick\":1,\"tick0\":1,\"autotick\":false},\"y\":[0.0,0.35714285714285715,0.7142857142857143,1.0714285714285714,1.4285714285714286,1.7857142857142858,2.142857142857143,2.5,2.857142857142857,3.2142857142857144,3.5714285714285716,3.9285714285714284,4.285714285714286,4.642857142857143,5.0],\"type\":\"heatmap\",\"colorscale\":[[0,\"#FFB4CE\"],[0.3333333333333333,\"#FFB4CE\"],[0.3333333333333333,\"#FFE5B4\"],[0.6666666666666666,\"#FFE5B4\"],[0.6666666666666666,\"#B4FFE5\"],[1,\"#B4FFE5\"]],\"z\":[[3.0,3.0,3.0,3.0,3.0,3.0,3.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0],[3.0,3.0,3.0,3.0,3.0,3.0,3.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0],[3.0,3.0,3.0,3.0,3.0,3.0,3.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0],[3.0,3.0,3.0,3.0,3.0,3.0,3.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0],[3.0,3.0,3.0,3.0,3.0,3.0,3.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0],[3.0,3.0,3.0,3.0,3.0,3.0,3.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0],[3.0,3.0,3.0,3.0,3.0,3.0,3.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0,2.0],[3.0,3.0,3.0,3.0,3.0,3.0,3.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],[3.0,3.0,3.0,3.0,3.0,3.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],[3.0,3.0,3.0,3.0,3.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],[3.0,3.0,3.0,3.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],[3.0,3.0,3.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],[3.0,3.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],[3.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0],[1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0]],\"showscale\":false,\"x\":[0.0,0.35714285714285715,0.7142857142857143,1.0714285714285714,1.4285714285714286,1.7857142857142858,2.142857142857143,2.5,2.857142857142857,3.2142857142857144,3.5714285714285716,3.9285714285714284,4.285714285714286,4.642857142857143,5.0]}],\n",
                            "        {\"xaxis\":{\"title\":\"theta\"},\"annotations\":[{\"y\":2.5,\"showarrow\":false,\"text\":\"new life\",\"x\":2.5},{\"y\":2.5,\"showarrow\":false,\"text\":\"new job\",\"textangle\":270,\"x\":4.5},{\"y\":4.5,\"showarrow\":false,\"text\":\"stay put\",\"x\":4.5}],\"height\":500,\"margin\":{\"l\":50,\"b\":50,\"r\":50,\"t\":60},\"yaxis\":{\"title\":\"epsilon\"},\"width\":500},\n",
                            "        {\"editable\":false,\"responsive\":true,\"staticPlot\":false,\"scrollZoom\":true},\n",
                            "    )\n",
                            "}\n",
                            "\n",
                            "        });\n",
                            "    </script>\n",
                            "</div>\n",
                            "\n",
                            "</body>\n",
                            "</html>"
                        ],
                        "text/plain": [
                            "data: [\n",
                            "  \"heatmap with fields colorbar, colorscale, showscale, type, x, y, and z\"\n",
                            "]\n",
                            "\n",
                            "layout: \"layout with fields annotations, height, margin, width, xaxis, and yaxis\"\n",
                            "\n"
                        ]
                    },
                    "execution_count": 14,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "# reset random seed\n",
                "Random.seed!(56)\n",
                "qlearning = QLearning(m, 0.01);\n",
                "\n",
                "# plot initial policy\n",
                "plot_policy(m, get_greedy(m, qlearning.Q))"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 15,
            "id": "52f4c613",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "  8.096814 seconds (98.02 k allocations: 6.062 MiB, 0.96% compilation time)\n"
                    ]
                },
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                        "text/plain": [
                            "data: [\n",
                            "  \"heatmap with fields colorbar, colorscale, showscale, type, x, y, and z\"\n",
                            "]\n",
                            "\n",
                            "layout: \"layout with fields annotations, height, margin, width, xaxis, and yaxis\"\n",
                            "\n"
                        ]
                    },
                    "execution_count": 15,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "actor = EpsilonGreedy(1.0, 0.1, 10_000_000)\n",
                "@time learn(m, qlearning, actor; maxit=150_000_000,  should_plot=false);\n",
                "\n",
                "# plot final policy\n",
                "plot_policy(m, get_greedy(m, qlearning.Q))"
            ]
        },
        {
            "cell_type": "markdown",
            "id": "bb495d6a",
            "metadata": {
                "slideshow": {
                    "slide_type": "subslide"
                },
                "tags": []
            },
            "source": [
                "- Check the Q-learning Q function against $q^*$ and see bias is smaller:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 16,
            "id": "d5fffb7c",
            "metadata": {
                "scrolled": true
            },
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "3×3×3 Array{Float64, 3}:\n",
                            "[:, :, 1] =\n",
                            " 0.166843   0.349435  0.0305733\n",
                            " 0.186209   0.106912  0.223948\n",
                            " 0.707085  -0.592787  0.402138\n",
                            "\n",
                            "[:, :, 2] =\n",
                            "  0.220097   0.197678  -0.0990846\n",
                            "  0.0473951  0.246321   0.0989512\n",
                            " -0.332978   0.690139   0.218061\n",
                            "\n",
                            "[:, :, 3] =\n",
                            "  0.260701   0.32411    0.603764\n",
                            "  0.0903624  0.101123  -0.0294898\n",
                            " -0.286058   0.529283   0.407503"
                        ]
                    },
                    "execution_count": 16,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "opt_Q[:, 8:10, 8:10] - qlearning.Q.q[:, 8:10, 8:10] "
            ]
        }
    ],
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