From 3fb6028676fa1dd6c55260b6ee85988a92f879bb Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Laure=CE=B7t?= Date: Tue, 2 Jan 2024 11:44:10 +0100 Subject: [PATCH] flakify --- .gitignore | 1 + TD/notebook.jl | 252 ++++++++++ TP1/notebook.jl | 1002 ++----------------------------------- export_html.jl | 38 ++ flake.lock | 80 +++ flake.nix | 59 +++ notebook_exos.jl | 1229 ---------------------------------------------- 7 files changed, 461 insertions(+), 2200 deletions(-) create mode 100644 .gitignore create mode 100644 TD/notebook.jl create mode 100644 export_html.jl create mode 100644 flake.lock create mode 100644 flake.nix delete mode 100644 notebook_exos.jl diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..e2f5dd2 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +result \ No newline at end of file diff --git a/TD/notebook.jl b/TD/notebook.jl new file mode 100644 index 0000000..40f9bfe --- /dev/null +++ b/TD/notebook.jl @@ -0,0 +1,252 @@ +### A Pluto.jl notebook ### +# v0.19.36 + +using Markdown +using InteractiveUtils + +# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). +macro bind(def, element) + quote + local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end + local el = $(esc(element)) + global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) + el + end +end + +# ╔═╡ f70b9ab6-3a97-4d41-b1a1-268085565bcb +# ╠═╡ show_logs = false +# https://github.com/fonsp/Pluto.jl/wiki/%F0%9F%8E%81-Package-management#advanced-set-up-an-environment-with-pkgactivate +begin + using Pkg + Pkg.activate() +end + +# ╔═╡ ec777da4-8ef0-44b4-8d56-38b31790a5b7 +begin + using PlutoUI # pour les objets Pluto + TableOfContents(depth=4) +end + +# ╔═╡ dc4eb528-82b2-11ed-3ca2-c321ff8ef647 +html""" +
+ + Exercices - Reinforcement learning
+ Laurent Fainsin
+ 2021 - 2022 + +
+""" + +# ╔═╡ 7fb608fa-da53-47d3-a585-235b4692c4dd +md""" +# Exercice 1 - Finite Horizon MDP + +> Revenue management: Littlewood’s model +> +> An airplane has 20 seats available, and the sell closes in 50 days. At every time epoch, the airplane decides the selling price: Either ``p_1`` = 5, and then it will sell a seat with probability ``q_1`` = 0.1, or ``p_2`` = 1, and then it will sell a seat with probability ``q_2`` = 0.8. +""" + +# ╔═╡ 58baae0a-ae46-443c-8c08-8743a13eb860 +md""" +D'après l'énoncé on a: + +$\mathcal{S} = \left\{ s_1, s_2 \right\}$ + +$\mathcal{A} = \left\{ p_1, p_2 \right\}$ + +$\mathcal{R} = \left\{ p_1 q_1, p_2 q_2 \right\}$ +""" + +# ╔═╡ dc2fcab2-7b23-47e3-b53a-0ad966645afd +md""" +D'après l'équation d'optimalité de Bellmann: + +$V(s) = r(s) + \gamma \sum_{s'} p(s,s')V(s')$ + +Dans notre cas on a donc (``\gamma = 1``): + +$V_T(s_1) = p_1 q_1 + q_1 V_{T-1}(s_1) + (1-q_1) V_{T-1}(s_2)$ +$V_T(s_2) = p_2 q_2 + q_2 V_{T-1}(s_2) + (1-q_2) V_{T-1}(s_1)$ +""" + +# ╔═╡ a6100c90-9a12-43d8-8ec3-dbf04b4ab5d1 +md""" +On peut alors poser: + +$P = \begin{pmatrix} +q_1 & 1-q_1 \\ +q_2 & 1-q_2 +\end{pmatrix}$ + +$R = \begin{pmatrix} +p_1 q_1 \\ +p_2 q_2 +\end{pmatrix}$ + +$V_T = \begin{pmatrix} +V_T(s_1) \\ +V_T(s_2) +\end{pmatrix}$ + +tel que l'on puisse reformuler Bellmann: + +$V_T = R + \gamma P V_{T-1}$ +""" + +# ╔═╡ a5df336b-3db1-441d-845b-3ddb0aa3213a +md""" +En selectionnant la valeur maximale de ``V_T`` on en déduit la politique optimal pour ce jour ``T``. Intuitivement on choisi le prix ``p_2`` si l'on souhaite maximiser notre gain. On peut le vérifier numériquement: +""" + +# ╔═╡ a30def9e-50f0-4aa2-8e79-6d10ecee5bee +begin + p1_slider = @bind p1 Slider(0:1:10, default=5, show_value=true) + q1_slider = @bind q1 Slider(0:0.1:1, default=0.1, show_value=true) + + p2_slider = @bind p2 Slider(0:1:10, default=1, show_value=true) + q2_slider = @bind q2 Slider(0:0.1:1, default=0.8, show_value=true) + + md""" + ``p_1``: $(p1_slider) ``\quad\quad`` + ``q_1``: $(q1_slider) + + ``p_2``: $(p2_slider) ``\quad\quad`` + ``q_2``: $(q2_slider) + """ +end + +# ╔═╡ 3176c1f0-c1fa-4c74-9133-f4371e584b6c +P = [ + q1 1-q1 + q2 1-q2 +] + +# ╔═╡ f5566288-5ef4-495c-8442-a59f17f0814b +R = [ + p1 * q1 + p2 * q2 +] + +# ╔═╡ f01bd868-a180-4327-98bf-de2298673523 +γ = 1 + +# ╔═╡ f8c9b0c8-3f81-441b-b673-f07ed2ae3e5a +begin + text = ""; + T = 50; + + V = [0 ; 0]; + text *= "``V_{50} = $(V)``\n\n"; + + for t in 1:T + V = R + γ * P * V; + choix = argmax(V); + V_display = round.(V, digits=2); + text *= "``V_{$(T-t)} = $(V_display) → p_$(choix)``\n\n"; + end + + Markdown.parse(text) +end + +# ╔═╡ 73a0d6a0-94a9-45b3-9db9-6cc0c845ab95 +md""" +# Exercice 2 - Infinite Horizon MDP + +> See figure +> +> What is the optimal policy (for total discounted reward) for various values of ``\gamma`` ? +""" + +# ╔═╡ 3b87e4e9-81c9-48d9-9f58-e6271f975c40 +md""" +Équation d'optimalité pour nos deux états (``s_0`` and ``s_1``): + +``V_\star(s_0) = \max( 10 + \gamma V_\star(s_1), 1 + \gamma V_\star(s_0) )`` + +``V_\star(s_1) = \max( 0 + \gamma V_\star(s_1), -15 + \gamma V_\star(s_0) )`` +""" + +# ╔═╡ 045e6ef0-84a8-4ad1-bc7c-0494599fd825 +md""" +Si ``\gamma \approx 0``: + +``V_\star(s_0) \approx \max(10, 1) = 10`` + +``V_\star(s_1) \approx \max(0, -15) = 0`` +""" + +# ╔═╡ 8cd6c607-2094-4fa0-b1d8-445842ac5091 +md""" +Si ``\gamma \approx 1``: + +``V_\star(s_0) = 1 + \gamma V_\star(s_0) \implies V_\star(s_0) = \displaystyle\frac{1}{1-\gamma}`` + +``V_\star(s_0) = -15 + V_\star(s_0) \implies V_\star(s_1) = -15 + \displaystyle\frac{1}{1-\gamma}`` +""" + +# ╔═╡ fe6dc66f-2627-4c13-b32a-9751b2ff3a73 +md""" +Si l'on résoud ces deux dernières équations on a: + +``\gamma = 0.9`` + +``\gamma = \displaystyle\frac{15}{16} \approx 0.94`` +""" + +# ╔═╡ fdd906ab-2224-4c26-9fb9-d9855bfda257 +md""" +Par disjonction des cas: +""" + +# ╔═╡ 65dcb2b0-1021-45a6-afe7-a95f6e139636 +md""" +Si ``\gamma \in [0, 0.9]``: + +``V_\star(s_0) = 1 + \gamma V_\star(s_0)`` + +``V_\star(s_1) = \gamma V_\star(s_1)`` +""" + +# ╔═╡ 69a4815d-1a84-400c-ae2b-4753e6c96abc +md""" +Si ``\gamma \in [0.9, 0.94]``: + +``V_\star(s_0) = 10 + \gamma V_\star(s_1)`` + +``V_\star(s_1) = \gamma V_\star(s_1)`` +""" + +# ╔═╡ 0b1a0996-d98d-43a5-8d4e-3faa6ded79a8 +md""" +Si ``\gamma \in [0.94, 1]``: + +``V_\star(s_0) = 1 + \gamma V_\star(s_0)`` + +``V_\star(s_1) = -15 + \gamma V_\star(s_0)`` +""" + +# ╔═╡ Cell order: +# ╟─f70b9ab6-3a97-4d41-b1a1-268085565bcb +# ╟─ec777da4-8ef0-44b4-8d56-38b31790a5b7 +# ╟─dc4eb528-82b2-11ed-3ca2-c321ff8ef647 +# ╟─7fb608fa-da53-47d3-a585-235b4692c4dd +# ╟─58baae0a-ae46-443c-8c08-8743a13eb860 +# ╟─dc2fcab2-7b23-47e3-b53a-0ad966645afd +# ╟─a6100c90-9a12-43d8-8ec3-dbf04b4ab5d1 +# ╟─a5df336b-3db1-441d-845b-3ddb0aa3213a +# ╟─a30def9e-50f0-4aa2-8e79-6d10ecee5bee +# ╟─3176c1f0-c1fa-4c74-9133-f4371e584b6c +# ╟─f5566288-5ef4-495c-8442-a59f17f0814b +# ╟─f01bd868-a180-4327-98bf-de2298673523 +# ╟─f8c9b0c8-3f81-441b-b673-f07ed2ae3e5a +# ╟─73a0d6a0-94a9-45b3-9db9-6cc0c845ab95 +# ╟─3b87e4e9-81c9-48d9-9f58-e6271f975c40 +# ╟─045e6ef0-84a8-4ad1-bc7c-0494599fd825 +# ╟─8cd6c607-2094-4fa0-b1d8-445842ac5091 +# ╟─fe6dc66f-2627-4c13-b32a-9751b2ff3a73 +# ╟─fdd906ab-2224-4c26-9fb9-d9855bfda257 +# ╟─65dcb2b0-1021-45a6-afe7-a95f6e139636 +# ╟─69a4815d-1a84-400c-ae2b-4753e6c96abc +# ╟─0b1a0996-d98d-43a5-8d4e-3faa6ded79a8 diff --git a/TP1/notebook.jl b/TP1/notebook.jl index 9e3bdc7..7204a1f 100644 --- a/TP1/notebook.jl +++ b/TP1/notebook.jl @@ -1,5 +1,5 @@ ### A Pluto.jl notebook ### -# v0.19.19 +# v0.19.36 #> [frontmatter] #> title = " TP1 - Reinforcement learning " @@ -19,6 +19,14 @@ macro bind(def, element) end end +# ╔═╡ 02b1e10c-653e-4660-90b5-2eae7f19f1f7 +# ╠═╡ show_logs = false +# https://github.com/fonsp/Pluto.jl/wiki/%F0%9F%8E%81-Package-management#advanced-set-up-an-environment-with-pkgactivate +begin + using Pkg + Pkg.activate() +end + # ╔═╡ 26fdd17e-f03a-4835-93be-85303fe526d8 begin using Plots # pour le tracé de figures @@ -105,11 +113,11 @@ On définit notre environnement comme une grille 3x4: # ╔═╡ 28b769a6-dd3c-43ab-bae0-646d8ebc35d6 begin - ARROW_SYMBOLS = ["←", "↑", "↓", "→"] - DEATH_SYMBOL = "☠" - SUCCESS_SYMBOL = "✓" - WALL_SYMBOL = "■" - EMPTY_SYMBOL = "□" + ARROW_SYMBOLS = ["⬅️", "⬆️", "⬇️", "➡️"] + DEATH_SYMBOL = "☠️" + SUCCESS_SYMBOL = "🏆" + WALL_SYMBOL = "🧱" + EMPTY_SYMBOL = "🟫" [ EMPTY_SYMBOL EMPTY_SYMBOL EMPTY_SYMBOL SUCCESS_SYMBOL @@ -298,7 +306,7 @@ begin local diffs = Vector{Float64}() for _ in 1:MAX_ITERATIONS local V_old = V_random - V_random = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random + global V_random = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random append!(diffs, norm(V_random - V_old)) if isapprox(V_random, V_old) break @@ -345,8 +353,8 @@ begin V_random2 = rand(length(REWARDS)) local diffs = Vector{Float64}() for _ in 1:MAX_ITERATIONS - V_random1 = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random1 - V_random2 = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random2 + global V_random1 = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random1 + global V_random2 = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random2 append!(diffs, norm(V_random1 - V_random2)) if isapprox(V_random1, V_random2) break @@ -924,7 +932,7 @@ begin local pi_k = argmax.(eachrow([V_g V_h V_b V_d])) - P_pi_k = sparse(zeros(11, 11)) + global P_pi_k = sparse(zeros(11, 11)) for i in 1:11 if pi_k[i] == 1 P_pi_k[i, :] = P_g[i, :] @@ -970,11 +978,11 @@ begin for (i, gamma) in enumerate(gammas) - P_pi_k = P_pi_0 + global P_pi_k2 = P_pi_0 k = 0 - while true - V_pi_k = Matrix(I(length(REWARDS)) - gamma * P_pi_k) \ REWARDS + while true + V_pi_k = Matrix(I(length(REWARDS)) - gamma * P_pi_k2) \ REWARDS local V_g = REWARDS + Matrix(gamma * P_g) * V_pi_k local V_h = REWARDS + Matrix(gamma * P_h) * V_pi_k @@ -983,22 +991,22 @@ begin local pi_k = argmax.(eachrow([V_g V_h V_b V_d])) - P_pi_k = sparse(zeros(11, 11)) + P_pi_k2 = sparse(zeros(11, 11)) for i in 1:11 if pi_k[i] == 1 - P_pi_k[i, :] = P_g[i, :] + P_pi_k2[i, :] = P_g[i, :] elseif pi_k[i] == 2 - P_pi_k[i, :] = P_h[i, :] + P_pi_k2[i, :] = P_h[i, :] elseif pi_k[i] == 3 - P_pi_k[i, :] = P_b[i, :] + P_pi_k2[i, :] = P_b[i, :] else - P_pi_k[i, :] = P_d[i, :] + P_pi_k2[i, :] = P_d[i, :] end end k += 1 - if isapprox(P_star, P_pi_k) || k >= MAX_ITERATIONS + if isapprox(P_star, P_pi_k2) || k >= MAX_ITERATIONS break end end @@ -1024,955 +1032,9 @@ md""" On observe qu'il y a convergence de la politique généralement en dessous de 5 itérations. Cependant pour certaines combinaisons d'hyperparamètres on remarque qu'il n'y a pas convergence. 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-[[deps.Zstd_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927" -uuid = "3161d3a3-bdf6-5164-811a-617609db77b4" -version = "1.5.2+0" - -[[deps.fzf_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "868e669ccb12ba16eaf50cb2957ee2ff61261c56" -uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09" -version = "0.29.0+0" - -[[deps.libaom_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4" -uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" -version = "3.4.0+0" - -[[deps.libass_jll]] -deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] -git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" -uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" -version = "0.15.1+0" - -[[deps.libblastrampoline_jll]] -deps = ["Artifacts", "Libdl", "OpenBLAS_jll"] -uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" -version = "5.1.1+0" - -[[deps.libfdk_aac_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" -uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" -version = "2.0.2+0" - -[[deps.libpng_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] -git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" -uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" -version = "1.6.38+0" - -[[deps.libvorbis_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] -git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" -uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" -version = "1.3.7+1" - -[[deps.nghttp2_jll]] -deps = ["Artifacts", "Libdl"] -uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" -version = "1.48.0+0" - -[[deps.p7zip_jll]] -deps = ["Artifacts", "Libdl"] -uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" -version = "17.4.0+0" - -[[deps.x264_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" -uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" -version = "2021.5.5+0" - -[[deps.x265_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" -uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" -version = "3.5.0+0" - -[[deps.xkbcommon_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] -git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a" -uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" -version = "1.4.1+0" -""" - # ╔═╡ Cell order: -# ╠═26fdd17e-f03a-4835-93be-85303fe526d8 +# ╟─02b1e10c-653e-4660-90b5-2eae7f19f1f7 +# ╟─26fdd17e-f03a-4835-93be-85303fe526d8 # ╟─56ac3473-24f4-42d7-84e1-cfce6a70d8d5 # ╟─ccf4d63e-7ace-11ed-2123-d9dbb62bd308 # ╟─9f2879c1-c22b-4067-ad20-4e4c56cc8d00 @@ -1993,10 +1055,10 @@ version = "1.4.1+0" # ╟─03c17428-5ab9-42e7-bf79-92eb846f11cb # ╟─c65d0dbc-ecd7-4320-9b3a-a1b9c0545f9a # ╟─ad547684-bcbe-44f4-9fc1-f327d2db4584 -# ╠═d3703ab8-912c-417d-acd9-29590ec1134b +# ╟─d3703ab8-912c-417d-acd9-29590ec1134b # ╟─1319b304-5126-4825-8076-e113e4dd3635 # ╟─3ea3f177-c576-4b9e-a54b-c427e29a8491 -# ╠═e94fe8a6-274b-4121-b1fc-063d3710c2f7 +# ╟─e94fe8a6-274b-4121-b1fc-063d3710c2f7 # ╟─80090d5f-d56c-4844-a04f-444ed49e5f34 # ╟─98362798-aae4-4540-9e98-cc7371802552 # ╟─30874daf-7b0e-4335-9a50-d19389cf1620 @@ -2040,5 +1102,3 @@ version = "1.4.1+0" # ╟─a1eaf48e-f92f-4554-942e-f6303ebaa084 # ╟─8d5b2cc2-2e21-47df-b821-189de5d357a3 # ╟─0c6fd7ed-5180-41bd-9958-29cc9f3ce73b -# ╟─00000000-0000-0000-0000-000000000001 -# ╟─00000000-0000-0000-0000-000000000002 diff --git a/export_html.jl b/export_html.jl new file mode 100644 index 0000000..c6581ed --- /dev/null +++ b/export_html.jl @@ -0,0 +1,38 @@ +using Pluto + +function export_html(notebook_path, html_path) + # load notebook + notebook = Pluto.load_notebook(Pluto.tamepath(notebook_path)); + topology = Pluto.updated_topology(notebook.topology, notebook, notebook.cells) + + # create offline workspace + workspace = Pluto.WorkspaceManager.make_workspace( + ( + Pluto.ServerSession(), + notebook, + ), + is_offline_renderer=true, + ) + + # run all the cells of the notebook + for cell in notebook.cells + Pluto.run_single!( + workspace, + cell, + topology.nodes[cell], + topology.codes[cell], + ) + end + + # convert notebook outputs to html + html_contents = Pluto.generate_html(notebook); + + # write to html file + open(html_path, "w") do html_file + write(html_file, html_contents); + end +end + +# TODO: use loop cli args +export_html("exos.jl", "exos.html") +export_html("index.jl", "index.html") diff --git a/flake.lock b/flake.lock new file mode 100644 index 0000000..c545e07 --- /dev/null +++ b/flake.lock @@ -0,0 +1,80 @@ +{ + "nodes": { + "flake-parts": { + "inputs": { + "nixpkgs-lib": "nixpkgs-lib" + }, + "locked": { + "lastModified": 1701473968, + "narHash": "sha256-YcVE5emp1qQ8ieHUnxt1wCZCC3ZfAS+SRRWZ2TMda7E=", + "owner": "hercules-ci", + "repo": "flake-parts", + "rev": "34fed993f1674c8d06d58b37ce1e0fe5eebcb9f5", + "type": "github" + }, + "original": { + "owner": "hercules-ci", + "repo": "flake-parts", + "type": "github" + } + }, + "nixpkgs": { + "locked": { + "lastModified": 1703637592, + "narHash": "sha256-8MXjxU0RfFfzl57Zy3OfXCITS0qWDNLzlBAdwxGZwfY=", + "owner": "NixOS", + "repo": "nixpkgs", + "rev": "cfc3698c31b1fb9cdcf10f36c9643460264d0ca8", + "type": "github" + }, + "original": { + "owner": "NixOS", + "ref": "nixos-unstable", + "repo": "nixpkgs", + "type": "github" + } + }, + "nixpkgs-lib": { + "locked": { + "dir": "lib", + "lastModified": 1701253981, + "narHash": "sha256-ztaDIyZ7HrTAfEEUt9AtTDNoCYxUdSd6NrRHaYOIxtk=", + "owner": "NixOS", + "repo": "nixpkgs", + "rev": "e92039b55bcd58469325ded85d4f58dd5a4eaf58", + "type": "github" + }, + "original": { + "dir": "lib", + "owner": "NixOS", + "ref": "nixos-unstable", + "repo": "nixpkgs", + "type": "github" + } + }, + "root": { + "inputs": { + "flake-parts": "flake-parts", + "nixpkgs": "nixpkgs", + "systems": "systems" + } + }, + "systems": { + "locked": { + "lastModified": 1681028828, + "narHash": "sha256-Vy1rq5AaRuLzOxct8nz4T6wlgyUR7zLU309k9mBC768=", + "owner": "nix-systems", + "repo": "default", + "rev": "da67096a3b9bf56a91d16901293e51ba5b49a27e", + "type": "github" + }, + "original": { + "owner": "nix-systems", + "repo": "default", + "type": "github" + } + } + }, + "root": "root", + "version": 7 +} diff --git a/flake.nix b/flake.nix new file mode 100644 index 0000000..062a5fa --- /dev/null +++ b/flake.nix @@ -0,0 +1,59 @@ +{ + inputs = { + nixpkgs.url = "github:NixOS/nixpkgs/nixos-unstable"; + flake-parts.url = "github:hercules-ci/flake-parts"; + systems.url = "github:nix-systems/default"; + }; + + outputs = {flake-parts, ...} @ inputs: + flake-parts.lib.mkFlake {inherit inputs;} { + systems = import inputs.systems; + + perSystem = { + pkgs, + system, + ... + }: rec { + devShells.default = pkgs.mkShell { + packages = packages.notebooks.buildInputs; + }; + + packages.notebooks = pkgs.stdenvNoCC.mkDerivation { + name = "notebooks"; + + src = ./.; + dontUnpack = true; + buildInputs = [ + (pkgs.julia.withPackages [ + "Pluto" + "Plots" + "PlutoUI" + "LinearAlgebra" + "SparseArrays" + "LaTeXStrings" + ]) + ]; + + buildPhase = '' + # TODO: comment this shit + cp $src/TP1/notebook.jl index.jl + cp $src/TD/notebook.jl exos.jl + chmod +w index.jl exos.jl + + cp $src/export_html.jl export_html.jl + + # https://github.com/NixOS/nix/issues/670#issuecomment-1211700127 + export HOME=$(pwd) + + julia export_html.jl + ''; + + installPhase = '' + mkdir -p $out + cp index.html $out + cp exos.html $out + ''; + }; + }; + }; +} diff --git a/notebook_exos.jl b/notebook_exos.jl deleted file mode 100644 index ecc6e94..0000000 --- a/notebook_exos.jl +++ /dev/null @@ -1,1229 +0,0 @@ -### A Pluto.jl notebook ### -# v0.19.19 - -using Markdown -using InteractiveUtils - -# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). -macro bind(def, element) - quote - local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end - local el = $(esc(element)) - global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) - el - end -end - -# ╔═╡ ec777da4-8ef0-44b4-8d56-38b31790a5b7 -begin - using Plots # pour le tracé de figures - using PlutoUI # pour les objets Pluto - using LinearAlgebra # pour les matrices identité - using SparseArrays # pour les matrices creuses - using LaTeXStrings # pour les strings en LaTeX (pour les plots) - TableOfContents(depth=4) -end - -# ╔═╡ dc4eb528-82b2-11ed-3ca2-c321ff8ef647 -html""" -
- - Exercices - Reinforcement learning
- Laurent Fainsin
- 2021 - 2022 - -
-""" - -# ╔═╡ 7fb608fa-da53-47d3-a585-235b4692c4dd -md""" -# Exercice 1 - Finite Horizon MDP - -> Revenue management: Littlewood’s model -> -> An airplane has 20 seats available, and the sell closes in 50 days. At every time epoch, the airplane decides the selling price: Either ``p_1`` = 5, and then it will sell a seat with probability ``q_1`` = 0.1, or ``p_2`` = 1, and then it will sell a seat with probability ``q_2`` = 0.8. -""" - -# ╔═╡ 58baae0a-ae46-443c-8c08-8743a13eb860 -md""" -D'après l'énoncé on a: - -$\mathcal{S} = \left\{ s_1, s_2 \right\}$ - -$\mathcal{A} = \left\{ p_1, p_2 \right\}$ - -$\mathcal{R} = \left\{ p_1 q_1, p_2 q_2 \right\}$ -""" - -# ╔═╡ dc2fcab2-7b23-47e3-b53a-0ad966645afd -md""" -D'après l'équation d'optimalité de Bellmann: - -$V(s) = r(s) + \gamma \sum_{s'} p(s,s')V(s')$ - -Dans notre cas on a donc (``\gamma = 1``): - -$V_T(s_1) = p_1 q_1 + q_1 V_{T-1}(s_1) + (1-q_1) V_{T-1}(s_2)$ -$V_T(s_2) = p_2 q_2 + q_2 V_{T-1}(s_2) + (1-q_2) V_{T-1}(s_1)$ -""" - -# ╔═╡ a6100c90-9a12-43d8-8ec3-dbf04b4ab5d1 -md""" -On peut alors poser: - -$P = \begin{pmatrix} -q_1 & 1-q_1 \\ -q_2 & 1-q_2 -\end{pmatrix}$ - -$R = \begin{pmatrix} -p_1 q_1 \\ -p_2 q_2 -\end{pmatrix}$ - -$V_T = \begin{pmatrix} -V_T(s_1) \\ -V_T(s_2) -\end{pmatrix}$ - -tel que l'on puisse reformuler Bellmann: - -$V_T = R + \gamma P V_{T-1}$ -""" - -# ╔═╡ a5df336b-3db1-441d-845b-3ddb0aa3213a -md""" -En selectionnant la valeur maximale de ``V_T`` on en déduit la politique optimal pour ce jour ``T``. Intuitivement on choisi le prix ``p_2`` si l'on souhaite maximiser notre gain. On peut le vérifier numériquement: -""" - -# ╔═╡ a30def9e-50f0-4aa2-8e79-6d10ecee5bee -begin - p1_slider = @bind p1 Slider(0:1:10, default=5, show_value=true) - q1_slider = @bind q1 Slider(0:0.1:1, default=0.1, show_value=true) - - p2_slider = @bind p2 Slider(0:1:10, default=1, show_value=true) - q2_slider = @bind q2 Slider(0:0.1:1, default=0.8, show_value=true) - - md""" - ``p_1``: $(p1_slider) ``\quad\quad`` - ``q_1``: $(q1_slider) - - ``p_2``: $(p2_slider) ``\quad\quad`` - ``q_2``: $(q2_slider) - """ -end - -# ╔═╡ 3176c1f0-c1fa-4c74-9133-f4371e584b6c -P = [ - q1 1-q1 - q2 1-q2 -] - -# ╔═╡ f5566288-5ef4-495c-8442-a59f17f0814b -R = [ - p1 * q1 - p2 * q2 -] - -# ╔═╡ f01bd868-a180-4327-98bf-de2298673523 -γ = 1 - -# ╔═╡ f8c9b0c8-3f81-441b-b673-f07ed2ae3e5a -begin - text = ""; - T = 50; - - V = [0 ; 0]; - text *= "``V_{50} = $(V)``\n\n"; - - for t in 1:T - V = R + γ * P * V; - choix = argmax(V); - V_display = round.(V, digits=2); - text *= "``V_{$(T-t)} = $(V_display) → p_$(choix)``\n\n"; - end - - Markdown.parse(text) -end - -# ╔═╡ 73a0d6a0-94a9-45b3-9db9-6cc0c845ab95 -md""" -# Exercice 2 - Infinite Horizon MDP - -> See figure -> -> What is the optimal policy (for total discounted reward) for various values of ``\gamma`` ? -""" - -# ╔═╡ 3b87e4e9-81c9-48d9-9f58-e6271f975c40 -md""" -Équation d'optimalité pour nos deux états (``s_0`` and ``s_1``): - -``V_\star(s_0) = \max( 10 + \gamma V_\star(s_1), 1 + \gamma V_\star(s_0) )`` - -``V_\star(s_1) = \max( 0 + \gamma V_\star(s_1), -15 + \gamma V_\star(s_0) )`` -""" - -# ╔═╡ 045e6ef0-84a8-4ad1-bc7c-0494599fd825 -md""" -Si ``\gamma \approx 0``: - -``V_\star(s_0) \approx \max(10, 1) = 10`` - -``V_\star(s_1) \approx \max(0, -15) = 0`` -""" - -# ╔═╡ 8cd6c607-2094-4fa0-b1d8-445842ac5091 -md""" -Si ``\gamma \approx 1``: - -``V_\star(s_0) = 1 + \gamma V_\star(s_0) \implies V_\star(s_0) = \displaystyle\frac{1}{1-\gamma}`` - -``V_\star(s_0) = -15 + V_\star(s_0) \implies V_\star(s_1) = -15 + \displaystyle\frac{1}{1-\gamma}`` -""" - -# ╔═╡ fe6dc66f-2627-4c13-b32a-9751b2ff3a73 -md""" -Si l'on résoud ces deux dernières équations on a: - -``\gamma = 0.9`` - -``\gamma = \displaystyle\frac{15}{16} \approx 0.94`` -""" - -# ╔═╡ fdd906ab-2224-4c26-9fb9-d9855bfda257 -md""" -Par disjonction des cas: -""" - -# ╔═╡ 65dcb2b0-1021-45a6-afe7-a95f6e139636 -md""" -Si ``\gamma \in [0, 0.9]``: - -``V_\star(s_0) = 1 + \gamma V_\star(s_0)`` - -``V_\star(s_1) = \gamma V_\star(s_1)`` -""" - -# ╔═╡ 69a4815d-1a84-400c-ae2b-4753e6c96abc -md""" -Si ``\gamma \in [0.9, 0.94]``: - -``V_\star(s_0) = 10 + \gamma V_\star(s_1)`` - -``V_\star(s_1) = \gamma V_\star(s_1)`` -""" - -# ╔═╡ 0b1a0996-d98d-43a5-8d4e-3faa6ded79a8 -md""" -Si ``\gamma \in [0.94, 1]``: - -``V_\star(s_0) = 1 + \gamma V_\star(s_0)`` - -``V_\star(s_1) = -15 + \gamma V_\star(s_0)`` -""" - -# ╔═╡ 00000000-0000-0000-0000-000000000001 -PLUTO_PROJECT_TOML_CONTENTS = """ -[deps] -LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" -LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" -Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" -PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" -SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" - 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-[[deps.Xorg_xcb_util_wm_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"] -git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67" -uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361" -version = "0.4.1+1" - -[[deps.Xorg_xkbcomp_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"] -git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b" -uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4" -version = "1.4.2+4" - -[[deps.Xorg_xkeyboard_config_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"] -git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d" -uuid = "33bec58e-1273-512f-9401-5d533626f822" -version = "2.27.0+4" - -[[deps.Xorg_xtrans_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845" -uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" -version = "1.4.0+3" - -[[deps.Zlib_jll]] -deps = ["Libdl"] -uuid = "83775a58-1f1d-513f-b197-d71354ab007a" -version = "1.2.12+3" - 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-[[deps.x265_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] -git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" -uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" -version = "3.5.0+0" - -[[deps.xkbcommon_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] -git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a" -uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" -version = "1.4.1+0" -""" - -# ╔═╡ Cell order: -# ╟─ec777da4-8ef0-44b4-8d56-38b31790a5b7 -# ╟─dc4eb528-82b2-11ed-3ca2-c321ff8ef647 -# ╟─7fb608fa-da53-47d3-a585-235b4692c4dd -# ╟─58baae0a-ae46-443c-8c08-8743a13eb860 -# ╟─dc2fcab2-7b23-47e3-b53a-0ad966645afd -# ╟─a6100c90-9a12-43d8-8ec3-dbf04b4ab5d1 -# ╟─a5df336b-3db1-441d-845b-3ddb0aa3213a -# ╟─a30def9e-50f0-4aa2-8e79-6d10ecee5bee -# ╟─3176c1f0-c1fa-4c74-9133-f4371e584b6c -# ╟─f5566288-5ef4-495c-8442-a59f17f0814b -# ╟─f01bd868-a180-4327-98bf-de2298673523 -# ╟─f8c9b0c8-3f81-441b-b673-f07ed2ae3e5a -# ╟─73a0d6a0-94a9-45b3-9db9-6cc0c845ab95 -# ╟─3b87e4e9-81c9-48d9-9f58-e6271f975c40 -# ╟─045e6ef0-84a8-4ad1-bc7c-0494599fd825 -# ╟─8cd6c607-2094-4fa0-b1d8-445842ac5091 -# ╟─fe6dc66f-2627-4c13-b32a-9751b2ff3a73 -# ╟─fdd906ab-2224-4c26-9fb9-d9855bfda257 -# ╟─65dcb2b0-1021-45a6-afe7-a95f6e139636 -# ╟─69a4815d-1a84-400c-ae2b-4753e6c96abc -# ╟─0b1a0996-d98d-43a5-8d4e-3faa6ded79a8 -# ╟─00000000-0000-0000-0000-000000000001 -# ╟─00000000-0000-0000-0000-000000000002