{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Discrete State Dynamic Programming" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Discrete State Dynamic Programming](#Discrete-State-Dynamic-Programming) \n", " - [Overview](#Overview) \n", " - [Discrete DPs](#Discrete-DPs) \n", " - [Solving Discrete DPs](#Solving-Discrete-DPs) \n", " - [Example: A Growth Model](#Example:-A-Growth-Model) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) \n", " - [Appendix: Algorithms](#Appendix:-Algorithms) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "In this lecture we discuss a family of dynamic programming problems with the following features:\n", "\n", "1. a discrete state space and discrete choices (actions) \n", "1. an infinite horizon \n", "1. discounted rewards \n", "1. Markov state transitions \n", "\n", "\n", "We call such problems discrete dynamic programs, or discrete DPs.\n", "\n", "Discrete DPs are the workhorses in much of modern quantitative economics, including\n", "\n", "- monetary economics \n", "- search and labor economics \n", "- household savings and consumption theory \n", "- investment theory \n", "- asset pricing \n", "- industrial organization, etc. \n", "\n", "\n", "When a given model is not inherently discrete, it is common to replace it with a discretized version in order to use discrete DP techniques.\n", "\n", "This lecture covers\n", "\n", "- the theory of dynamic programming in a discrete setting, plus examples and\n", " applications \n", "- a powerful set of routines for solving discrete DPs from the [QuantEcon code libary](http://quantecon.org/quantecon-jl) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How to Read this Lecture\n", "\n", "We use dynamic programming many applied lectures, such as\n", "\n", "- The [shortest path lecture](short_path.html) \n", "- The [McCall search model lecture](mccall_model.html) \n", "- The [optimal growth lecture](optgrowth.html) \n", "\n", "\n", "The objective of this lecture is to provide a more systematic and theoretical treatment, including algorithms and implementation, while focusing on the discrete case." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### References\n", "\n", "For background reading on dynamic programming and additional applications, see, for example,\n", "\n", "- [[LS18]](../zreferences.html#ljungqvist2012) \n", "- [[HLL96]](../zreferences.html#hernandezlermalasserre1996), section 3.5 \n", "- [[Put05]](../zreferences.html#puterman2005) \n", "- [[SLP89]](../zreferences.html#stokeylucas1989) \n", "- [[Rus96]](../zreferences.html#rust1996) \n", "- [[MF02]](../zreferences.html#mirandafackler2002) \n", "- [EDTC](http://johnstachurski.net/edtc.html), chapter 5 \n", "\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete DPs\n", "\n", "Loosely speaking, a discrete DP is a maximization problem with an objective\n", "function of the form\n", "\n", "\n", "\n", "$$\n", "\\mathbb{E}\n", "\\sum_{t = 0}^{\\infty} \\beta^t r(s_t, a_t) \\tag{1}\n", "$$\n", "\n", "where\n", "\n", "- $ s_t $ is the state variable \n", "- $ a_t $ is the action \n", "- $ \\beta $ is a discount factor \n", "- $ r(s_t, a_t) $ is interpreted as a current reward when the state is $ s_t $ and the action chosen is $ a_t $ \n", "\n", "\n", "Each pair $ (s_t, a_t) $ pins down transition probabilities $ Q(s_t, a_t, s_{t+1}) $ for the next period state $ s_{t+1} $.\n", "\n", "Thus, actions influence not only current rewards but also the future time path of the state.\n", "\n", "The essence of dynamic programming problems is to trade off current rewards\n", "vs favorable positioning of the future state (modulo randomness).\n", "\n", "Examples:\n", "\n", "- consuming today vs saving and accumulating assets \n", "- accepting a job offer today vs seeking a better one in the future \n", "- exercising an option now vs waiting " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Policies\n", "\n", "The most fruitful way to think about solutions to discrete DP problems is to compare *policies*.\n", "\n", "In general, a policy is a randomized map from past actions and states to\n", "current action.\n", "\n", "In the setting formalized below, it suffices to consider so-called *stationary Markov policies*, which consider only the current state.\n", "\n", "In particular, a stationary Markov policy is a map $ \\sigma $ from states to actions\n", "\n", "- $ a_t = \\sigma(s_t) $ indicates that $ a_t $ is the action to be taken in state $ s_t $ \n", "\n", "\n", "It is known that, for any arbitrary policy, there exists a stationary Markov policy that dominates it at least weakly.\n", "\n", "- See section 5.5 of [[Put05]](../zreferences.html#puterman2005) for discussion and proofs. \n", "\n", "\n", "In what follows, stationary Markov policies are referred to simply as policies.\n", "\n", "The aim is to find an optimal policy, in the sense of one that maximizes [(1)](#equation-dp-objective).\n", "\n", "Let’s now step through these ideas more carefully." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Formal definition\n", "\n", "Formally, a discrete dynamic program consists of the following components:\n", "\n", "1. A finite set of *states* $ S = \\{0, \\ldots, n-1\\} $ \n", "1. A finite set of *feasible actions* $ A(s) $ for each state $ s \\in S $, and a corresponding set of *feasible state-action pairs* \n", " \n", " $$\n", " \\mathit{SA} := \\{(s, a) \\mid s \\in S, \\; a \\in A(s)\\}\n", " $$\n", " \n", "1. A *reward function* $ r\\colon \\mathit{SA} \\to \\mathbb{R} $ \n", "1. A *transition probability function* $ Q\\colon \\mathit{SA} \\to \\Delta(S) $, where $ \\Delta(S) $ is the set of probability distributions over $ S $ \n", "1. A *discount factor* $ \\beta \\in [0, 1) $ \n", "\n", "\n", "We also use the notation $ A := \\bigcup_{s \\in S} A(s) = \\{0, \\ldots, m-1\\} $ and call this set the *action space*.\n", "\n", "A *policy* is a function $ \\sigma\\colon S \\to A $.\n", "\n", "A policy is called *feasible* if it satisfies $ \\sigma(s) \\in A(s) $ for all $ s \\in S $.\n", "\n", "Denote the set of all feasible policies by $ \\Sigma $.\n", "\n", "If a decision maker uses a policy $ \\sigma \\in \\Sigma $, then\n", "\n", "- the current reward at time $ t $ is $ r(s_t, \\sigma(s_t)) $ \n", "- the probability that $ s_{t+1} = s' $ is $ Q(s_t, \\sigma(s_t), s') $ \n", "\n", "\n", "For each $ \\sigma \\in \\Sigma $, define\n", "\n", "- $ r_{\\sigma} $ by $ r_{\\sigma}(s) := r(s, \\sigma(s)) $) \n", "- $ Q_{\\sigma} $ by $ Q_{\\sigma}(s, s') := Q(s, \\sigma(s), s') $ \n", "\n", "\n", "Notice that $ Q_\\sigma $ is a [stochastic matrix](../tools_and_techniques/finite_markov.html#finite-dp-stoch-mat) on $ S $.\n", "\n", "It gives transition probabilities of the *controlled chain* when we follow policy $ \\sigma $.\n", "\n", "If we think of $ r_\\sigma $ as a column vector, then so is $ Q_\\sigma^t r_\\sigma $, and the $ s $-th row of the latter has the interpretation\n", "\n", "\n", "\n", "$$\n", "(Q_\\sigma^t r_\\sigma)(s) = \\mathbb E [ r(s_t, \\sigma(s_t)) \\mid s_0 = s ]\n", "\\quad \\text{when } \\{s_t\\} \\sim Q_\\sigma \\tag{2}\n", "$$\n", "\n", "Comments\n", "\n", "- $ \\{s_t\\} \\sim Q_\\sigma $ means that the state is generated by stochastic matrix $ Q_\\sigma $ \n", "- See [this discussion](../tools_and_techniques/finite_markov.html#finite-mc-expec) on computing expectations of Markov chains for an explanation of the expression in [(2)](#equation-ddp-expec) \n", "\n", "\n", "Notice that we’re not really distinguishing between functions from $ S $ to $ \\mathbb R $ and vectors in $ \\mathbb R^n $.\n", "\n", "This is natural because they are in one to one correspondence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Value and Optimality\n", "\n", "Let $ v_{\\sigma}(s) $ denote the discounted sum of expected reward flows from policy $ \\sigma $\n", "when the initial state is $ s $.\n", "\n", "To calculate this quantity we pass the expectation through the sum in\n", "[(1)](#equation-dp-objective) and use [(2)](#equation-ddp-expec) to get\n", "\n", "$$\n", "v_{\\sigma}(s) = \\sum_{t=0}^{\\infty} \\beta^t (Q_{\\sigma}^t r_{\\sigma})(s)\n", "\\qquad (s \\in S)\n", "$$\n", "\n", "This function is called the *policy value function* for the policy $ \\sigma $.\n", "\n", "The *optimal value function*, or simply *value function*, is the function $ v^*\\colon S \\to \\mathbb{R} $ defined by\n", "\n", "$$\n", "v^*(s) = \\max_{\\sigma \\in \\Sigma} v_{\\sigma}(s)\n", "\\qquad (s \\in S)\n", "$$\n", "\n", "(We can use max rather than sup here because the domain is a finite set)\n", "\n", "A policy $ \\sigma \\in \\Sigma $ is called *optimal* if $ v_{\\sigma}(s) = v^*(s) $ for all $ s \\in S $.\n", "\n", "Given any $ w \\colon S \\to \\mathbb R $, a policy $ \\sigma \\in \\Sigma $ is called $ w $-greedy if\n", "\n", "$$\n", "\\sigma(s) \\in \\operatorname*{arg\\,max}_{a \\in A(s)}\n", "\\left\\{\n", " r(s, a) +\n", " \\beta \\sum_{s' \\in S} w(s') Q(s, a, s')\n", "\\right\\}\n", "\\qquad (s \\in S)\n", "$$\n", "\n", "As discussed in detail below, optimal policies are precisely those that are $ v^* $-greedy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Two Operators\n", "\n", "It is useful to define the following operators:\n", "\n", "- The *Bellman operator* $ T\\colon \\mathbb{R}^S \\to \\mathbb{R}^S $\n", " is defined by \n", "\n", "\n", "$$\n", "(T v)(s) = \\max_{a \\in A(s)}\n", "\\left\\{\n", " r(s, a) + \\beta \\sum_{s' \\in S} v(s') Q(s, a, s')\n", "\\right\\}\n", "\\qquad (s \\in S)\n", "$$\n", "\n", "- For any policy function $ \\sigma \\in \\Sigma $, the operator $ T_{\\sigma}\\colon \\mathbb{R}^S \\to \\mathbb{R}^S $ is defined by \n", "\n", "\n", "$$\n", "(T_{\\sigma} v)(s) = r(s, \\sigma(s)) +\n", " \\beta \\sum_{s' \\in S} v(s') Q(s, \\sigma(s), s')\n", "\\qquad (s \\in S)\n", "$$\n", "\n", "This can be written more succinctly in operator notation as\n", "\n", "$$\n", "T_{\\sigma} v = r_{\\sigma} + \\beta Q_{\\sigma} v\n", "$$\n", "\n", "The two operators are both monotone\n", "\n", "- $ v \\leq w $ implies $ Tv \\leq Tw $ pointwise on $ S $, and\n", " similarly for $ T_\\sigma $ \n", "\n", "\n", "They are also contraction mappings with modulus $ \\beta $\n", "\n", "- $ \\lVert Tv - Tw \\rVert \\leq \\beta \\lVert v - w \\rVert $ and similarly for $ T_\\sigma $, where $ \\lVert \\cdot\\rVert $ is the max norm \n", "\n", "\n", "For any policy $ \\sigma $, its value $ v_{\\sigma} $ is the unique fixed point of $ T_{\\sigma} $.\n", "\n", "For proofs of these results and those in the next section, see, for example, [EDTC](http://johnstachurski.net/edtc.html), chapter 10." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Bellman Equation and the Principle of Optimality\n", "\n", "The main principle of the theory of dynamic programming is that\n", "\n", "- the optimal value function $ v^* $ is a unique solution to the *Bellman equation*, \n", " \n", " $$\n", " v(s) = \\max_{a \\in A(s)} \\left\\{ r(s, a) + \\beta \\sum_{s' \\in S} v(s') Q(s, a, s') \\right\\} \\qquad (s \\in S),\n", " $$\n", " \n", " or in other words, $ v^* $ is the unique fixed point of $ T $, and \n", "- $ \\sigma^* $ is an optimal policy function if and only if it is $ v^* $-greedy \n", "\n", "\n", "By the definition of greedy policies given above, this means that\n", "\n", "$$\n", "\\sigma^*(s) \\in \\operatorname*{arg\\,max}_{a \\in A(s)}\n", " \\left\\{\n", " r(s, a) + \\beta \\sum_{s' \\in S} v^*(s') Q(s, \\sigma(s), s')\n", " \\right\\}\n", "\\qquad (s \\in S)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving Discrete DPs\n", "\n", "Now that the theory has been set out, let’s turn to solution methods.\n", "\n", "Code for solving discrete DPs is available in [ddp.jl](https://github.com/QuantEcon/QuantEcon.jl/blob/master/src/markov/ddp.jl) from the [QuantEcon.jl](http://quantecon.org/quantecon-jl) code library.\n", "\n", "It implements the three most important solution methods for discrete dynamic programs, namely\n", "\n", "- value function iteration \n", "- policy function iteration \n", "- modified policy function iteration \n", "\n", "\n", "Let’s briefly review these algorithms and their implementation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Value Function Iteration\n", "\n", "Perhaps the most familiar method for solving all manner of dynamic programs is value function iteration.\n", "\n", "This algorithm uses the fact that the Bellman operator $ T $ is a contraction mapping with fixed point $ v^* $.\n", "\n", "Hence, iterative application of $ T $ to any initial function $ v^0 \\colon S \\to \\mathbb R $ converges to $ v^* $.\n", "\n", "The details of the algorithm can be found in [the appendix](#ddp-algorithms)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Policy Function Iteration\n", "\n", "This routine, also known as Howard’s policy improvement algorithm, exploits more closely the particular structure of a discrete DP problem.\n", "\n", "Each iteration consists of\n", "\n", "1. A policy evaluation step that computes the value $ v_{\\sigma} $ of a policy $ \\sigma $ by solving the linear equation $ v = T_{\\sigma} v $. \n", "1. A policy improvement step that computes a $ v_{\\sigma} $-greedy policy. \n", "\n", "\n", "In the current setting policy iteration computes an exact optimal policy in finitely many iterations.\n", "\n", "- See theorem 10.2.6 of [EDTC](http://johnstachurski.net/edtc.html) for a proof \n", "\n", "\n", "The details of the algorithm can be found in [the appendix](#ddp-algorithms)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Modified Policy Function Iteration\n", "\n", "Modified policy iteration replaces the policy evaluation step in policy iteration with “partial policy evaluation”.\n", "\n", "The latter computes an approximation to the value of a policy $ \\sigma $ by iterating $ T_{\\sigma} $ for a specified number of times.\n", "\n", "This approach can be useful when the state space is very large and the linear system in the policy evaluation step of policy iteration is correspondingly difficult to solve.\n", "\n", "The details of the algorithm can be found in [the appendix](#ddp-algorithms).\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: A Growth Model\n", "\n", "Let’s consider a simple consumption-saving model.\n", "\n", "A single household either consumes or stores its own output of a single consumption good.\n", "\n", "The household starts each period with current stock $ s $.\n", "\n", "Next, the household chooses a quantity $ a $ to store and consumes $ c = s - a $\n", "\n", "- Storage is limited by a global upper bound $ M $ \n", "- Flow utility is $ u(c) = c^{\\alpha} $ \n", "\n", "\n", "Output is drawn from a discrete uniform distribution on $ \\{0, \\ldots, B\\} $.\n", "\n", "The next period stock is therefore\n", "\n", "$$\n", "s' = a + U\n", "\\quad \\text{where} \\quad\n", "U \\sim U[0, \\ldots, B]\n", "$$\n", "\n", "The discount factor is $ \\beta \\in [0, 1) $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discrete DP Representation\n", "\n", "We want to represent this model in the format of a discrete dynamic program.\n", "\n", "To this end, we take\n", "\n", "- the state variable to be the stock $ s $ \n", "- the state space to be $ S = \\{0, \\ldots, M + B\\} $ \n", " \n", " - hence $ n = M + B + 1 $ \n", " \n", "- the action to be the storage quantity $ a $ \n", "- the set of feasible actions at $ s $ to be $ A(s) = \\{0, \\ldots, \\min\\{s, M\\}\\} $ \n", " \n", " - hence $ A = \\{0, \\ldots, M\\} $ and $ m = M + 1 $ \n", " \n", "- the reward function to be $ r(s, a) = u(s - a) $ \n", "- the transition probabilities to be \n", "\n", "\n", "\n", "\n", "$$\n", "Q(s, a, s')\n", ":=\n", "\\begin{cases}\n", " \\frac{1}{B + 1} & \\text{if } a \\leq s' \\leq a + B\n", " \\\\\n", " 0 & \\text{ otherwise}\n", "\\end{cases} \\tag{3}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining a DiscreteDP Instance\n", "\n", "This information will be used to create an instance of DiscreteDP by passing\n", "the following information\n", "\n", "1. An $ n \\times m $ reward array $ R $ \n", "1. An $ n \\times m \\times n $ transition probability array $ Q $ \n", "1. A discount factor $ \\beta $ \n", "\n", "\n", "For $ R $ we set $ R[s, a] = u(s - a) $ if $ a \\leq s $ and $ -\\infty $ otherwise.\n", "\n", "For $ Q $ we follow the rule in [(3)](#equation-ddp-def-ogq).\n", "\n", "Note:\n", "\n", "- The feasibility constraint is embedded into $ R $ by setting $ R[s, a] = -\\infty $ for $ a \\notin A(s) $. \n", "- Probability distributions for $ (s, a) $ with $ a \\notin A(s) $ can be arbitrary. \n", "\n", "\n", "The following code sets up these objects for us." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using InstantiateFromURL\n", "# optionally add arguments to force installation: instantiate = true, precompile = true\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using LinearAlgebra, Statistics, BenchmarkTools, Plots, QuantEcon\n", "using SparseArrays" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using BenchmarkTools, Plots, QuantEcon, Parameters\n", "gr(fmt = :png);" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "transition_matrices (generic function with 1 method)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "SimpleOG = @with_kw (B = 10, M = 5, α = 0.5, β = 0.9)\n", "\n", "function transition_matrices(g)\n", " @unpack B, M, α, β = g\n", " u(c) = c^α\n", " n = B + M + 1\n", " m = M + 1\n", "\n", " R = zeros(n, m)\n", " Q = zeros(n, m, n)\n", "\n", " for a in 0:M\n", " Q[:, a + 1, (a:(a + B)) .+ 1] .= 1 / (B + 1)\n", " for s in 0:(B + M)\n", " R[s + 1, a + 1] = (a≤s ? u(s - a) : -Inf)\n", " end\n", " end\n", "\n", " return (Q = Q, R = R)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let’s run this code and create an instance of `SimpleOG`" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [], "source": [ "g = SimpleOG();\n", "Q, R = transition_matrices(g);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In case the preceding code was too concise, we can see a more verbose form" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false, "html-class": "collapse" }, "outputs": [ { "data": { "text/plain": [ "verbose_matrices (generic function with 1 method)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function verbose_matrices(g)\n", " @unpack B, M, α, β = g\n", " u(c) = c^α\n", "\n", " #Matrix dimensions. The +1 is due to the 0 state.\n", " n = B + M + 1\n", " m = M + 1\n", "\n", " R = fill(-Inf, n, m) #Start assuming nothing is feasible\n", " Q = zeros(n,m,n) #Assume 0 by default\n", "\n", " #Create the R matrix\n", " #Note: indexing into matrix complicated since Julia starts indexing at 1 instead of 0\n", " #but the state s and choice a can be 0\n", " for a in 0:M\n", " for s in 0:(B + M)\n", " if a <= s #i.e. if feasible\n", " R[s + 1, a + 1] = u(s - a)\n", " end\n", " end\n", " end\n", "\n", " #Create the Q multi-array\n", " for s in 0:(B+M) #For each state\n", " for a in 0:M #For each action\n", " for sp in 0:(B+M) #For each state next period\n", " if( sp >= a && sp <= a + B) # The support of all realizations\n", " Q[s + 1, a + 1, sp + 1] = 1 / (B + 1) # Same prob of all\n", " end\n", " end\n", " @assert sum(Q[s + 1, a + 1, :]) ≈ 1 #Optional check that matrix is stochastic\n", " end\n", " end\n", " return (Q = Q, R = R)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instances of `DiscreteDP` are created using the signature `DiscreteDP(R, Q, β)`.\n", "\n", "Let’s create an instance using the objects stored in `g`" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [], "source": [ "ddp = DiscreteDP(R, Q, g.β);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have an instance `ddp` of `DiscreteDP` we can solve it as follows" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "QuantEcon.DPSolveResult{PFI,Float64}([19.01740221695992, 20.017402216959916, 20.431615779333015, 20.749453024528794, 21.040780991093488, 21.30873018352461, 21.544798161024403, 21.76928181079986, 21.982703576083246, 22.1882432282385, 22.384504796519916, 22.578077363861723, 22.761091269771118, 22.943767083452716, 23.115339958706524, 23.277617618874903], [19.01740221695992, 20.01740221695992, 20.431615779333015, 20.749453024528798, 21.040780991093488, 21.30873018352461, 21.5447981610244, 21.769281810799864, 21.982703576083253, 22.1882432282385, 22.38450479651991, 22.578077363861723, 22.761091269771114, 22.943767083452716, 23.115339958706524, 23.277617618874903], 3, [1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 6, 6], Discrete Markov Chain\n", "stochastic matrix of type Adjoint{Float64,Array{Float64,2}}:\n", "[0.09090909090909091 0.09090909090909091 … 0.0 0.0; 0.09090909090909091 0.09090909090909091 … 0.0 0.0; … ; 0.0 0.0 … 0.09090909090909091 0.09090909090909091; 0.0 0.0 … 0.09090909090909091 0.09090909090909091])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results = solve(ddp, PFI)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let’s see what we’ve got here" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "(:v, :Tv, :num_iter, :sigma, :mc)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fieldnames(typeof(results))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most important attributes are `v`, the value function, and `σ`, the optimal policy" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "16-element Array{Float64,1}:\n", " 19.01740221695992\n", " 20.017402216959916\n", " 20.431615779333015\n", " 20.749453024528794\n", " 21.040780991093488\n", " 21.30873018352461\n", " 21.544798161024403\n", " 21.76928181079986\n", " 21.982703576083246\n", " 22.1882432282385\n", " 22.384504796519916\n", " 22.578077363861723\n", " 22.761091269771118\n", " 22.943767083452716\n", " 23.115339958706524\n", " 23.277617618874903" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.v" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "16-element Array{Int64,1}:\n", " 0\n", " 0\n", " 0\n", " 0\n", " 1\n", " 1\n", " 1\n", " 2\n", " 2\n", " 3\n", " 3\n", " 4\n", " 5\n", " 5\n", " 5\n", " 5" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.sigma .- 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here 1 is subtracted from results.sigma because we added 1 to each state and action to create valid indices.\n", "\n", "Since we’ve used policy iteration, these results will be exact unless we hit the iteration bound `max_iter`.\n", "\n", "Let’s make sure this didn’t happen" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results.num_iter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case we converged in only 3 iterations.\n", "\n", "Another interesting object is `results.mc`, which is the controlled chain defined by $ Q_{\\sigma^*} $, where $ \\sigma^* $ is the optimal policy.\n", "\n", "In other words, it gives the dynamics of the state when the agent follows the optimal policy.\n", "\n", "Since this object is an instance of MarkovChain from [QuantEcon.jl](http://quantecon.org/quantecon-jl) (see [this lecture](../tools_and_techniques/finite_markov.html) for more discussion), we\n", "can easily simulate it, compute its stationary distribution and so on" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "16-element Array{Float64,1}:\n", " 0.01732186732186732\n", " 0.041210632119723034\n", " 0.05773955773955773\n", " 0.07426848335939244\n", " 0.08095823095823096\n", " 0.09090909090909091\n", " 0.0909090909090909\n", " 0.0909090909090909\n", " 0.09090909090909093\n", " 0.09090909090909091\n", " 0.09090909090909091\n", " 0.0735872235872236\n", " 0.049698458789367884\n", " 0.033169533169533166\n", " 0.016640607549698462\n", " 0.009950859950859951" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stationary_distributions(results.mc)[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here’s the same information in a bar graph\n", "\n", "\n", "\n", " \n", "What happens if the agent is more patient?" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "16-element Array{Float64,1}:\n", " 0.005469129800680602\n", " 0.023213417598444343\n", " 0.03147788040836169\n", " 0.04800680602819641\n", " 0.056271268838113765\n", " 0.09090909090909091\n", " 0.09090909090909093\n", " 0.09090909090909093\n", " 0.09090909090909094\n", " 0.09090909090909093\n", " 0.09090909090909094\n", " 0.0854399611084103\n", " 0.06769567331064659\n", " 0.059431210500729234\n", " 0.042902284880894495\n", " 0.03463782207097716" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_2 = SimpleOG(β=0.99);\n", "Q_2, R_2 = transition_matrices(g_2);\n", "\n", "ddp_2 = DiscreteDP(R_2, Q_2, g_2.β)\n", "\n", "results_2 = solve(ddp_2, PFI)\n", "\n", "std_2 = stationary_distributions(results_2.mc)[1]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bar(std_2, label = \"stationary dist\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see the rightward shift in probability mass." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State-Action Pair Formulation\n", "\n", "The `DiscreteDP` type in fact provides a second interface to setting up an instance.\n", "\n", "One of the advantages of this alternative set up is that it permits use of a sparse matrix for `Q`.\n", "\n", "(An example of using sparse matrices is given in the exercises below)\n", "\n", "The call signature of the second formulation is `DiscreteDP(R, Q, β, s_indices, a_indices)` where\n", "\n", "- `s_indices` and `a_indices` are arrays of equal length `L` enumerating all feasible state-action pairs \n", "- `R` is an array of length `L` giving corresponding rewards \n", "- `Q` is an `L x n` transition probability array \n", "\n", "\n", "Here’s how we could set up these objects for the preceding example" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "QuantEcon.DPSolveResult{PFI,Float64}([19.01740221695992, 20.017402216959916, 20.431615779333015, 20.749453024528794, 21.040780991093488, 21.30873018352461, 21.544798161024403, 21.76928181079986, 21.982703576083246, 22.1882432282385, 22.384504796519916, 22.578077363861723, 22.761091269771118, 22.943767083452716, 23.115339958706524, 23.277617618874903], [19.01740221695992, 20.01740221695992, 20.431615779333015, 20.749453024528798, 21.040780991093488, 21.30873018352461, 21.5447981610244, 21.769281810799864, 21.982703576083253, 22.1882432282385, 22.38450479651991, 22.578077363861723, 22.761091269771114, 22.943767083452716, 23.115339958706524, 23.277617618874903], 3, [1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6, 6, 6], Discrete Markov Chain\n", "stochastic matrix of type Array{Float64,2}:\n", "[0.09090909090909091 0.09090909090909091 … 0.0 0.0; 0.09090909090909091 0.09090909090909091 … 0.0 0.0; … ; 0.0 0.0 … 0.09090909090909091 0.09090909090909091; 0.0 0.0 … 0.09090909090909091 0.09090909090909091])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B = 10\n", "M = 5\n", "α = 0.5\n", "β = 0.9\n", "u(c) = c^α\n", "n = B + M + 1\n", "m = M + 1\n", "\n", "s_indices = Int64[]\n", "a_indices = Int64[]\n", "Q = zeros(0, n)\n", "R = zeros(0)\n", "\n", "b = 1 / (B + 1)\n", "\n", "for s in 0:(M + B)\n", " for a in 0:min(M, s)\n", " s_indices = [s_indices; s + 1]\n", " a_indices = [a_indices; a + 1]\n", " q = zeros(1, n)\n", " q[(a + 1):((a + B) + 1)] .= b\n", " Q = [Q; q]\n", " R = [R; u(s-a)]\n", " end\n", "end\n", "\n", "ddp = DiscreteDP(R, Q, β, s_indices, a_indices);\n", "results = solve(ddp, PFI)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises\n", "\n", "In the stochastic optimal growth lecture [dynamic programming lecture](optgrowth.html), we solve a\n", "[benchmark model](optgrowth.html#benchmark-growth-mod) that has an analytical solution to check we could replicate it numerically.\n", "\n", "The exercise is to replicate this solution using `DiscreteDP`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions\n", "\n", "These were written jointly by Max Huber and Daisuke Oyama." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup\n", "\n", "Details of the model can be found in [the\n", "lecture](https://julia.quantecon.org/dynamic_programming/optgrowth.html). As in the lecture,\n", "we let $ f(k) = k^{\\alpha} $ with $ \\alpha = 0.65 $,\n", "$ u(c) = \\log c $, and $ \\beta = 0.95 $." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "0.95" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "α = 0.65\n", "f(k) = k.^α\n", "u_log(x) = log(x)\n", "β = 0.95" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we want to solve a finite state version of the continuous state\n", "model above. We discretize the state space into a grid of size\n", "`grid_size = 500`, from $ 10^{-6} $ to `grid_max=2`." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "1.0e-6:0.004008014028056112:2.0" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "grid_max = 2\n", "grid_size = 500\n", "grid = range(1e-6, grid_max, length = grid_size)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We choose the action to be the amount of capital to save for the next\n", "period (the state is the capital stock at the beginning of the period).\n", "Thus the state indices and the action indices are both `1`, …,\n", "`grid_size`. Action (indexed by) `a` is feasible at state (indexed\n", "by) `s` if and only if `grid[a] < f([grid[s])` (zero consumption is\n", "not allowed because of the log utility).\n", "\n", "Thus the Bellman equation is:\n", "\n", "$$\n", "v(k) = \\max_{0 < k' < f(k)} u(f(k) - k') + \\beta v(k'),\n", "$$\n", "\n", "where $ k^{\\prime} $ is the capital stock in the next period.\n", "\n", "The transition probability array `Q` will be highly sparse (in fact it\n", "is degenerate as the model is deterministic), so we formulate the\n", "problem with state-action pairs, to represent `Q` in sparse matrix\n", "format.\n", "\n", "We first construct indices for state-action pairs:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "118841" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C = f.(grid) .- grid'\n", "coord = repeat(collect(1:grid_size), 1, grid_size) #coordinate matrix\n", "s_indices = coord[C .> 0]\n", "a_indices = transpose(coord)[C .> 0]\n", "L = length(a_indices)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let’s set up $ R $ and $ Q $" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "hide-output": false }, "outputs": [], "source": [ "R = u_log.(C[C.>0]);" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using SparseArrays\n", "\n", "Q = spzeros(L, grid_size) # Formerly spzeros\n", "\n", "for i in 1:L\n", " Q[i, a_indices[i]] = 1\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We’re now in a position to create an instance of `DiscreteDP`\n", "corresponding to the growth model." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "hide-output": false }, "outputs": [], "source": [ "ddp = DiscreteDP(R, Q, β, s_indices, a_indices);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving the Model" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "10" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "results = solve(ddp, PFI)\n", "v, σ, num_iter = results.v, results.sigma, results.num_iter\n", "num_iter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us compare the solution of the discrete model with the exact\n", "solution of the original continuous model. Here’s the exact solution:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "c_star (generic function with 1 method)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c = f(grid) - grid[σ]\n", "\n", "ab = α * β\n", "c1 = (log(1 - α * β) + log(α * β) * α * β / (1 - α * β)) / (1 - β)\n", "c2 = α / (1 - α * β)\n", "\n", "v_star(k) = c1 + c2 * log(k)\n", "c_star(k) = (1 - α * β) * k.^α" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let’s plot the value functions." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(grid, [v v_star.(grid)], ylim = (-40, -32), lw = 2, label = [\"discrete\" \"continuous\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They are barely distinguishable (although you can see the difference if\n", "you zoom).\n", "\n", "Now let’s look at the discrete and exact policy functions for\n", "consumption." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot(grid, [c c_star.(grid)], lw = 2, label = [\"discrete\" \"continuous\"], legend = :topleft)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These functions are again close, although some difference is visible and\n", "becomes more obvious as you zoom. Here are some statistics:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "121.49819147053378" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "maximum(abs(x - v_star(y)) for (x, y) in zip(v, grid))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a big error, but most of the error occurs at the lowest\n", "gridpoint. Otherwise the fit is reasonable:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "0.012681735127500815" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "maximum(abs(v[idx] - v_star(grid[idx])) for idx in 2:lastindex(v))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The value function is monotone, as expected:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "all(x -> x ≥ 0, diff(v))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison of the solution methods\n", "\n", "Let’s try different solution methods. The results below show that policy\n", "function iteration and modified policy function iteration are much\n", "faster that value function iteration." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "hide-output": false }, "outputs": [], "source": [ "@benchmark results = solve(ddp, PFI)\n", "results = solve(ddp, PFI);" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "hide-output": false }, "outputs": [], "source": [ "@benchmark res1 = solve(ddp, VFI, max_iter = 500, epsilon = 1e-4)\n", "res1 = solve(ddp, VFI, max_iter = 500, epsilon = 1e-4);" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "294" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res1.num_iter" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "σ == res1.sigma" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "hide-output": false }, "outputs": [], "source": [ "@benchmark res2 = solve(ddp, MPFI, max_iter = 500, epsilon = 1e-4)\n", "res2 = solve(ddp, MPFI, max_iter = 500, epsilon = 1e-4);" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "16" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res2.num_iter" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "σ == res2.sigma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Replication of the figures\n", "\n", "Let’s visualize convergence of value function iteration, as in the\n", "lecture." ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w_init = 5log.(grid) .- 25 # Initial condition\n", "n = 50\n", "\n", "ws = []\n", "colors = []\n", "w = w_init\n", "for i in 0:n-1\n", " w = bellman_operator(ddp, w)\n", " push!(ws, w)\n", " push!(colors, RGBA(0, 0, 0, i/n))\n", "end\n", "\n", "plot(grid,\n", " w_init,\n", " ylims = (-40, -20),\n", " lw = 2,\n", " xlims = extrema(grid),\n", " label = \"initial condition\")\n", "\n", "plot!(grid, ws, label = \"\", color = reshape(colors, 1, length(colors)), lw = 2)\n", "plot!(grid, v_star.(grid), label = \"true value function\", color = :red, lw = 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We next plot the consumption policies along the value iteration. First\n", "we write a function to generate the and record the policies at given\n", "stages of iteration." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "compute_policies (generic function with 1 method)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function compute_policies(n_vals...)\n", " c_policies = []\n", " w = w_init\n", " for n in 1:maximum(n_vals)\n", " w = bellman_operator(ddp, w)\n", " if n in n_vals\n", " σ = compute_greedy(ddp, w)\n", " c_policy = f(grid) - grid[σ]\n", " push!(c_policies, c_policy)\n", " end\n", " end\n", " return c_policies\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let’s generate the plots." ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "true_c = c_star.(grid)\n", "c_policies = compute_policies(2, 4, 6)\n", "plot_vecs = [c_policies[1] c_policies[2] c_policies[3] true_c true_c true_c]\n", "l1 = \"approximate optimal policy\"\n", "l2 = \"optimal consumption policy\"\n", "labels = [l1 l1 l1 l2 l2 l2]\n", "plot(grid,\n", " plot_vecs,\n", " xlim = (0, 2),\n", " ylim = (0, 1),\n", " layout = (3, 1),\n", " lw = 2,\n", " label = labels,\n", " size = (600, 800),\n", " title = [\"2 iterations\" \"4 iterations\" \"6 iterations\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dynamics of the capital stock\n", "\n", "Finally, let us work on [Exercise\n", "2](https://julia.quantecon.org/dynamic_programming/optgrowth.html#Exercise-1), where we plot\n", "the trajectories of the capital stock for three different discount\n", "factors, $ 0.9 $, $ 0.94 $, and $ 0.98 $, with initial\n", "condition $ k_0 = 0.1 $." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "discount_factors = (0.9, 0.94, 0.98)\n", "k_init = 0.1\n", "\n", "k_init_ind = findfirst(collect(grid) .≥ k_init)\n", "\n", "sample_size = 25\n", "\n", "ddp0 = DiscreteDP(R, Q, β, s_indices, a_indices)\n", "k_paths = []\n", "labels = []\n", "\n", "for β in discount_factors\n", " ddp0.beta = β\n", " res0 = solve(ddp0, PFI)\n", " k_path_ind = simulate(res0.mc, sample_size, init=k_init_ind)\n", " k_path = grid[k_path_ind.+1]\n", " push!(k_paths, k_path)\n", " push!(labels, \"β = $β\")\n", "end\n", "\n", "plot(k_paths,\n", " xlabel = \"time\",\n", " ylabel = \"capital\",\n", " ylim = (0.1, 0.3),\n", " lw = 2,\n", " markershape = :circle,\n", " label = reshape(labels, 1, length(labels)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Appendix: Algorithms\n", "\n", "This appendix covers the details of the solution algorithms implemented for `DiscreteDP`.\n", "\n", "We will make use of the following notions of approximate optimality:\n", "\n", "- For $ \\varepsilon > 0 $, $ v $ is called an $ \\varepsilon $-approximation of $ v^* $ if $ \\lVert v - v^*\\rVert < \\varepsilon $ \n", "- A policy $ \\sigma \\in \\Sigma $ is called $ \\varepsilon $-optimal if $ v_{\\sigma} $ is an $ \\varepsilon $-approximation of $ v^* $ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Value Iteration\n", "\n", "The `DiscreteDP` value iteration method implements value function iteration as\n", "follows\n", "\n", "1. Choose any $ v^0 \\in \\mathbb{R}^n $, and specify $ \\varepsilon > 0 $; set $ i = 0 $. \n", "1. Compute $ v^{i+1} = T v^i $. \n", "1. If $ \\lVert v^{i+1} - v^i\\rVert < [(1 - \\beta) / (2\\beta)] \\varepsilon $,\n", " then go to step 4; otherwise, set $ i = i + 1 $ and go to step 2. \n", "1. Compute a $ v^{i+1} $-greedy policy $ \\sigma $, and return $ v^{i+1} $ and $ \\sigma $. \n", "\n", "\n", "Given $ \\varepsilon > 0 $, the value iteration algorithm\n", "\n", "- terminates in a finite number of iterations \n", "- returns an $ \\varepsilon/2 $-approximation of the optimal value function and an $ \\varepsilon $-optimal policy function (unless `iter_max` is reached) \n", "\n", "\n", "(While not explicit, in the actual implementation each algorithm is\n", "terminated if the number of iterations reaches `iter_max`)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Policy Iteration\n", "\n", "The `DiscreteDP` policy iteration method runs as follows\n", "\n", "1. Choose any $ v^0 \\in \\mathbb{R}^n $ and compute a $ v^0 $-greedy policy $ \\sigma^0 $; set $ i = 0 $. \n", "1. Compute the value $ v_{\\sigma^i} $ by solving\n", " the equation $ v = T_{\\sigma^i} v $. \n", "1. Compute a $ v_{\\sigma^i} $-greedy policy\n", " $ \\sigma^{i+1} $; let $ \\sigma^{i+1} = \\sigma^i $ if\n", " possible. \n", "1. If $ \\sigma^{i+1} = \\sigma^i $, then return $ v_{\\sigma^i} $\n", " and $ \\sigma^{i+1} $; otherwise, set $ i = i + 1 $ and go to\n", " step 2. \n", "\n", "\n", "The policy iteration algorithm terminates in a finite number of\n", "iterations.\n", "\n", "It returns an optimal value function and an optimal policy function (unless `iter_max` is reached)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Modified Policy Iteration\n", "\n", "The `DiscreteDP` modified policy iteration method runs as follows:\n", "\n", "1. Choose any $ v^0 \\in \\mathbb{R}^n $, and specify $ \\varepsilon > 0 $ and $ k \\geq 0 $; set $ i = 0 $. \n", "1. Compute a $ v^i $-greedy policy $ \\sigma^{i+1} $; let $ \\sigma^{i+1} = \\sigma^i $ if possible (for $ i \\geq 1 $). \n", "1. Compute $ u = T v^i $ ($ = T_{\\sigma^{i+1}} v^i $). If $ \\mathrm{span}(u - v^i) < [(1 - \\beta) / \\beta] \\varepsilon $, then go to step 5; otherwise go to step 4. \n", " - Span is defined by $ \\mathrm{span}(z) = \\max(z) - \\min(z) $ \n", "1. Compute $ v^{i+1} = (T_{\\sigma^{i+1}})^k u $ ($ = (T_{\\sigma^{i+1}})^{k+1} v^i $); set $ i = i + 1 $ and go to step 2. \n", "1. Return $ v = u + [\\beta / (1 - \\beta)] [(\\min(u - v^i) + \\max(u - v^i)) / 2] \\mathbf{1} $ and $ \\sigma_{i+1} $. \n", "\n", "\n", "Given $ \\varepsilon > 0 $, provided that $ v^0 $ is such that\n", "$ T v^0 \\geq v^0 $, the modified policy iteration algorithm\n", "terminates in a finite number of iterations.\n", "\n", "It returns an $ \\varepsilon/2 $-approximation of the optimal value function and an $ \\varepsilon $-optimal policy function (unless `iter_max` is reached).\n", "\n", "See also the documentation for `DiscreteDP`." ] } ], "metadata": { "date": 1591310614.7328286, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "discrete_dp.rst", "filename_with_path": "dynamic_programming/discrete_dp", "kernelspec": { "display_name": "Julia 1.4.2", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.2" }, "title": "Discrete State Dynamic Programming" }, "nbformat": 4, "nbformat_minor": 2 }