fix tutorial

Author: BatyLeo

docs/src/tutorials/warcraft.jl

@@ -85,4 +85,4 @@ final_gap = compute_gap(b, test_dataset, model, maximizer)
 #
 θ = model(x)
 y = maximizer(θ)
-plot_data(b, DataSample(; x, θ, y))
+plot_data(b, DataSample(; x, θ_true=θ, y_true=y))

docs/src/warcraft.md

@@ -0,0 +1,155 @@
+```@meta
+EditURL = "tutorials/warcraft.jl"
+```
+
+# Path-finding on image maps
+
+In this tutorial, we showcase DecisionFocusedLearningBenchmarks.jl capabilities on one of its main benchmarks: the Warcraft benchmark.
+This benchmark problem is a simple path-finding problem where the goal is to find the shortest path between the top left and bottom right corners of a given image map.
+The map is represented as a 2D image representing a 12x12 grid, each cell having an unknown travel cost depending on the terrain type.
+
+First, let's load the package and create a benchmark object as follows:
+
+````@example warcraft
+using DecisionFocusedLearningBenchmarks
+b = WarcraftBenchmark()
+````
+
+## Dataset generation
+
+These benchmark objects behave as generators that can generate various needed elements in order to build an algorithm to tackle the problem.
+First of all, all benchmarks are capable of generating datasets as needed, using the [`generate_dataset`](@ref) method.
+This method takes as input the benchmark object for which the dataset is to be generated, and a second argument specifying the number of samples to generate:
+
+````@example warcraft
+dataset = generate_dataset(b, 50);
+nothing #hide
+````
+
+We obtain a vector of [`DataSample`](@ref) objects, containing all needed data for the problem.
+Subdatasets can be created through regular slicing:
+
+````@example warcraft
+train_dataset, test_dataset = dataset[1:45], dataset[46:50]
+````
+
+And getting an individual sample will return a [`DataSample`](@ref) with four fields: `x`, `instance`, `θ`, and `y`:
+
+````@example warcraft
+sample = test_dataset[1]
+````
+
+`x` correspond to the input features, i.e. the input image (3D array) in the Warcraft benchmark case:
+
+````@example warcraft
+x = sample.x
+````
+
+`θ_true` correspond to the true unknown terrain weights. We use the opposite of the true weights in order to formulate the optimization problem as a maximization problem:
+
+````@example warcraft
+θ_true = sample.θ_true
+````
+
+`y_true` correspond to the optimal shortest path, encoded as a binary matrix:
+
+````@example warcraft
+y_true = sample.y_true
+````
+
+`instance` is not used in this benchmark, therefore set to nothing:
+
+````@example warcraft
+isnothing(sample.instance)
+````
+
+For some benchmarks, we provide the following plotting method [`plot_data`](@ref) to visualize the data:
+
+````@example warcraft
+plot_data(b, sample)
+````
+
+We can see here the terrain image, the true terrain weights, and the true shortest path avoiding the high cost cells.
+
+## Building a pipeline
+
+DecisionFocusedLearningBenchmarks also provides methods to build an hybrid machine learning and combinatorial optimization pipeline for the benchmark.
+First, the [`generate_statistical_model`](@ref) method generates a machine learning predictor to predict cell weights from the input image:
+
+````@example warcraft
+model = generate_statistical_model(b)
+````
+
+In the case of the Warcraft benchmark, the model is a convolutional neural network built using the Flux.jl package.
+
+````@example warcraft
+θ = model(x)
+````
+
+Note that the model is not trained yet, and its parameters are randomly initialized.
+
+Finally, the [`generate_maximizer`](@ref) method can be used to generate a combinatorial optimization algorithm that takes the predicted cell weights as input and returns the corresponding shortest path:
+
+````@example warcraft
+maximizer = generate_maximizer(b; dijkstra=true)
+````
+
+In the case o fthe Warcraft benchmark, the method has an additional keyword argument to chose the algorithm to use: Dijkstra's algorithm or Bellman-Ford algorithm.
+
+````@example warcraft
+y = maximizer(θ)
+````
+
+As we can see, currently the pipeline predicts random noise as cell weights, and therefore the maximizer returns a straight line path.
+
+````@example warcraft
+plot_data(b, DataSample(; x, θ, y))
+````
+
+We can evaluate the current pipeline performance using the optimality gap metric:
+
+````@example warcraft
+starting_gap = compute_gap(b, test_dataset, model, maximizer)
+````
+
+## Using a learning algorithm
+
+We can now train the model using the InferOpt.jl package:
+
+````@example warcraft
+using InferOpt
+using Flux
+using Plots
+
+perturbed_maximizer = PerturbedMultiplicative(maximizer; ε=0.2, nb_samples=100)
+loss = FenchelYoungLoss(perturbed_maximizer)
+
+starting_gap = compute_gap(b, test_dataset, model, maximizer)
+
+opt_state = Flux.setup(Adam(1e-3), model)
+loss_history = Float64[]
+for epoch in 1:50
+    val, grads = Flux.withgradient(model) do m
+        sum(loss(m(sample.x), sample.y) for sample in train_dataset) / length(train_dataset)
+    end
+    Flux.update!(opt_state, model, grads[1])
+    push!(loss_history, val)
+end
+
+plot(loss_history; xlabel="Epoch", ylabel="Loss", title="Training loss")
+````
+
+````@example warcraft
+final_gap = compute_gap(b, test_dataset, model, maximizer)
+````
+
+````@example warcraft
+θ = model(x)
+y = maximizer(θ)
+plot_data(b, DataSample(; x, θ, y))
+````
+
+---
+
+*This page was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*
+