Month: March 2021

Posted by Ji Hun Kim and Richard Wu, Software Engineers, Stadia

Over the years, online multiplayer games have exploded in popularity, captivating millions of players across the world. This popularity has also exponentially increased demands on game designers, as players expect games to be well-crafted and balanced — after all, it’s no fun to play a game where a single strategy beats all the rest.

In order to create a positive gameplay experience, game designers typically tune the balance of a game iteratively:

1. Stress-test through thousands of play-testing sessions from test users
2. Incorporate feedback and re-design the game
3. Repeat 1 & 2 until both the play-testers and game designers are satisfied

This process is not only time-consuming but also imperfect — the more complex the game, the easier it is for subtle flaws to slip through the cracks. When games often have many different roles that can be played, with dozens of interconnecting skills, it makes it all the more difficult to hit the right balance.

Today, we present an approach that leverages machine learning (ML) to adjust game balance by training models to serve as play-testers, and demonstrate this approach on the digital card game prototype Chimera, which we’ve previously shown as a testbed for ML-generated art. By running millions of simulations using trained agents to collect data, this ML-based game testing approach enables game designers to more efficiently make a game more fun, balanced, and aligned with their original vision.

Chimera
We developed Chimera as a game prototype that would heavily lean on machine learning during its development process. For the game itself, we purposefully designed the rules to expand the possibility space, making it difficult to build a traditional hand-crafted AI to play the game.

The gameplay of Chimera revolves around the titular chimeras, creature mash-ups that players aim to strengthen and evolve. The objective of the game is to defeat the opponent’s chimera. These are the key points in the game design:

• Players may play:
  • creatures, which can attack (through their attack stat) or be attacked (against their health stat), or
  • spells, which produce special effects.
• Creatures are summoned into limited-capacity biomes, which are placed physically on the board space. Each creature has a preferred biome and will take repeated damage if placed on an incorrect biome or a biome that is over capacity.
• A player controls a single chimera, which starts off in a basic “egg” state and can be evolved and strengthened by absorbing creatures. To do this, the player must also acquire a certain amount of link energy, which is generated from various gameplay mechanics.
• The game ends when a player has successfully brought the health of the opponent’s chimera to 0.

Learning to Play Chimera
As an imperfect information card game with a large state space, we expected Chimera to be a difficult game for an ML model to learn, especially as we were aiming for a relatively simple model. We used an approach inspired by those used by earlier game-playing agents like AlphaGo, in which a convolutional neural network (CNN) is trained to predict the probability of a win when given an arbitrary game state. After training an initial model on games where random moves were chosen, we set the agent to play against itself, iteratively collecting game data, that was then used to train a new agent. With each iteration, the quality of the training data improved, as did the agent’s ability to play the game.

The ML agent’s performance against our best hand-crafted AI as training progressed. The initial ML agent (version 0) picked moves randomly.

For the actual game state representation that the model would receive as input, we found that passing an “image” encoding to the CNN resulted in the best performance, beating all benchmark procedural agents and other types of networks (e.g. fully connected). The chosen model architecture is small enough to run on a CPU in reasonable time, which allowed us to download the model weights and run the agent live in a Chimera game client using Unity Barracuda.

An example game state representation used to train the neural network.

In addition to making decisions for the game AI, we also used the model to display the estimated win probability for a player over the course of the game.

Balancing Chimera
This approach enabled us to simulate millions more games than real players would be capable of playing in the same time span. After collecting data from the games played by the best-performing agents, we analyzed the results to find imbalances between the two of the player decks we had designed.

First, the Evasion Link Gen deck was composed of spells and creatures with abilities that generated extra link energy used to evolve a player’s chimera. It also contained spells that enabled creatures to evade attacks. In contrast, the Damage-Heal deck contained creatures of variable strength with spells that focused on healing and inflicting minor damage. Although we had designed these decks to be of equal strength, the Evasion Link Gen deck was winning 60% of the time when played against the Damage-Heal deck.

When we collected various stats related to biomes, creatures, spells, and chimera evolutions, two things immediately jumped out at us:

1. There was a clear advantage in evolving a chimera — the agent won a majority of the games where it evolved its chimera more than the opponent did. Yet, the average number of evolves per game did not meet our expectations. To make it more of a core game mechanic, we wanted to increase the overall average number of evolves while keeping its usage strategic.
2. The T-Rex creature was overpowered. Its appearances correlated strongly with wins, and the model would always play the T-Rex regardless of penalties for summoning into an incorrect or overcrowded biome.

From these insights, we made some adjustments to the game. To emphasize chimera evolution as a core mechanism in the game, we decreased the amount of link energy required to evolve a chimera from 3 to 1. We also added a “cool-off” period to the T-Rex creature, doubling the time it took to recover from any of its actions.

Repeating our ‘self-play’ training procedure with the updated rules, we observed that these changes pushed the game in the desired direction — the average number of evolves per game increased, and the T-Rex’s dominance faded.

One example comparison of the T-Rex’s influence before and after balancing. The charts present the number of games won (or lost) when a deck initiates a particular spell interaction (e.g., using the “Dodge” spell to benefit a T-Rex). Left: Before the changes, the T-Rex had a strong influence in every metric examined — highest survival rate, most likely to be summoned ignoring penalties, most absorbed creature during wins. Right: After the changes, the T-Rex was much less overpowered.

By weakening the T-Rex, we successfully reduced the Evasion Link Gen deck’s reliance on an overpowered creature. Even so, the win ratio between the decks remained at 60/40 rather than 50/50. A closer look at the individual game logs revealed that the gameplay was often less strategic than we would have liked. Searching through our gathered data again, we found several more areas to introduce changes in.

To start, we increased the starting health of both players as well as the amount of health that healing spells could replenish. This was to encourage longer games that would allow a more diverse set of strategies to flourish. In particular, this enabled the Damage-Heal deck to survive long enough to take advantage of its healing strategy. To encourage proper summoning and strategic biome placement, we increased the existing penalties on playing creatures into incorrect or overcrowded biomes. And finally, we decreased the gap between the strongest and weakest creatures through minor attribute adjustments.

New adjustments in place, we arrived at the final game balance stats for these two decks:

Conclusion
Normally, identifying imbalances in a newly prototyped game can take months of playtesting. With this approach, we were able to not only discover potential imbalances but also introduce tweaks to mitigate them in a span of days. We found that a relatively simple neural network was sufficient to reach high level performance against humans and traditional game AI. These agents could be leveraged in further ways, such as for coaching new players or discovering unexpected strategies. We hope this work will inspire more exploration in the possibilities of machine learning for game development.

Acknowledgements
This project was conducted in collaboration with many people. Thanks to Ryan Poplin, Maxwell Hannaman, Taylor Steil, Adam Prins, Michal Todorovic, Xuefan Zhou, Aaron Cammarata, Andeep Toor, Trung Le, Erin Hoffman-John, and Colin Boswell. Thanks to everyone who contributed through playtesting, advising on game design, and giving valuable feedback.

This is the final post in a four-part introduction to time-series forecasting with torch. These posts have been the story of a quest for multiple-step prediction, and by now, we’ve seen three different approaches: forecasting in a loop, incorporating a multi-layer perceptron (MLP), and sequence-to-sequence models. Here’s a quick recap.

• As one should when one sets out for an adventurous journey, we started with an in-depth study of the tools at our disposal: recurrent neural networks (RNNs). We trained a model to predict the very next observation in line, and then, thought of a clever hack: How about we use this for multi-step prediction, feeding back individual predictions in a loop? The result , it turned out, was quite acceptable.

• Then, the adventure really started. We built our first model “natively” for multi-step prediction, relieving the RNN a bit of its workload and involving a second player, a tiny-ish MLP. Now, it was the MLP’s task to project RNN output to several time points in the future. Although results were pretty satisfactory, we didn’t stop there.

• Instead, we applied to numerical time series a technique commonly used in natural language processing (NLP): sequence-to-sequence (seq2seq) prediction. While forecast performance was not much different from the previous case, we found the technique to be more intuitively appealing, since it reflects the causal relationship between successive forecasts.

Today we’ll enrich the seq2seq approach by adding a new component: the attention module. Originally introduced around 20141, attention mechanisms have gained enormous traction, so much so that a recent paper title starts out “Attention is Not All You Need”2.

The idea is the following.

In the classic encoder-decoder setup, the decoder gets “primed” with an encoder summary just a single time: the time it starts its forecasting loop. From then on, it’s on its own. With attention, however, it gets to see the complete sequence of encoder outputs again every time it forecasts a new value. What’s more, every time, it gets to zoom in on those outputs that seem relevant for the current prediction step.

This is a particularly useful strategy in translation: In generating the next word, a model will need to know what part of the source sentence to focus on. How much the technique helps with numerical sequences, in contrast, will likely depend on the features of the series in question.

Data input

As before, we work with vic_elec, but this time, we partly deviate from the way we used to employ it. With the original, bi-hourly dataset, training the current model takes a long time, longer than readers will want to wait when experimenting. So instead, we aggregate observations by day. In order to have enough data, we train on years 2012 and 2013, reserving 2014 for validation as well as post-training inspection.

vic_elec_daily <- vic_elec %>%
  select(Time, Demand) %>%
  index_by(Date = date(Time)) %>%
  summarise(
    Demand = sum(Demand) / 1e3) 

elec_train <- vic_elec_daily %>% 
  filter(year(Date) %in% c(2012, 2013)) %>%
  as_tibble() %>%
  select(Demand) %>%
  as.matrix()

elec_valid <- vic_elec_daily %>% 
  filter(year(Date) == 2014) %>%
  as_tibble() %>%
  select(Demand) %>%
  as.matrix()

elec_test <- vic_elec_daily %>% 
  filter(year(Date) %in% c(2014), month(Date) %in% 1:4) %>%
  as_tibble() %>%
  select(Demand) %>%
  as.matrix()

train_mean <- mean(elec_train)
train_sd <- sd(elec_train)

We’ll attempt to forecast demand up to fourteen days ahead. How long, then, should be the input sequences? This is a matter of experimentation; all the more so now that we’re adding in the attention mechanism. (I suspect that it might not handle very long sequences so well).

Below, we go with fourteen days for input length, too, but that may not necessarily be the best possible choice for this series.

n_timesteps <- 7 * 2
n_forecast <- 7 * 2

elec_dataset <- dataset(
  name = "elec_dataset",
  
  initialize = function(x, n_timesteps, sample_frac = 1) {
    
    self$n_timesteps <- n_timesteps
    self$x <- torch_tensor((x - train_mean) / train_sd)
    
    n <- length(self$x) - self$n_timesteps - 1
    
    self$starts <- sort(sample.int(
      n = n,
      size = n * sample_frac
    ))
    
  },
  
  .getitem = function(i) {
    
    start <- self$starts[i]
    end <- start + self$n_timesteps - 1
    lag <- 1
    
    list(
      x = self$x[start:end],
      y = self$x[(start+lag):(end+lag)]$squeeze(2)
    )
    
  },
  
  .length = function() {
    length(self$starts) 
  }
)

batch_size <- 32

train_ds <- elec_dataset(elec_train, n_timesteps, sample_frac = 0.5)
train_dl <- train_ds %>% dataloader(batch_size = batch_size, shuffle = TRUE)

valid_ds <- elec_dataset(elec_valid, n_timesteps, sample_frac = 0.5)
valid_dl <- valid_ds %>% dataloader(batch_size = batch_size)

test_ds <- elec_dataset(elec_test, n_timesteps)
test_dl <- test_ds %>% dataloader(batch_size = 1)

Model

Model-wise, we again encounter the three modules familiar from the previous post: encoder, decoder, and top-level seq2seq module. However, there is an additional component: the attention module, used by the decoder to obtain attention weights.

Encoder

The encoder still works the same way. It wraps an RNN, and returns the final state.

encoder_module <- nn_module(
  
  initialize = function(type, input_size, hidden_size, num_layers = 1, dropout = 0) {
    
    self$type <- type
    
    self$rnn <- if (self$type == "gru") {
      nn_gru(
        input_size = input_size,
        hidden_size = hidden_size,
        num_layers = num_layers,
        dropout = dropout,
        batch_first = TRUE
      )
    } else {
      nn_lstm(
        input_size = input_size,
        hidden_size = hidden_size,
        num_layers = num_layers,
        dropout = dropout,
        batch_first = TRUE
      )
    }
    
  },
  
  forward = function(x) {
    
    x <- self$rnn(x)
    
    # return last states for all layers
    # per layer, a single tensor for GRU, a list of 2 tensors for LSTM
    x <- x[[2]]
    x
    
  }
)

Attention module

In basic seq2seq, whenever it had to generate a new value, the decoder took into account two things: its prior state, and the previous output generated. In an attention-enriched setup, the decoder additionally receives the complete output from the encoder. In deciding what subset of that output should matter, it gets help from a new agent, the attention module.

This, then, is the attention module’s raison d’être: Given current decoder state and well as complete encoder outputs, obtain a weighting of those outputs indicative of how relevant they are to what the decoder is currently up to. This procedure results in the so-called attention weights: a normalized score, for each time step in the encoding, that quantify their respective importance.

Attention may be implemented in a number of different ways. Here, we show two implementation options, one additive, and one multiplicative.

Additive attention

In additive attention, encoder outputs and decoder state are commonly either added or concatenated (we choose to do the latter, below). The resulting tensor is run through a linear layer, and a softmax is applied for normalization.

attention_module_additive <- nn_module(
  
  initialize = function(hidden_dim, attention_size) {
    
    self$attention <- nn_linear(2 * hidden_dim, attention_size)
    
  },
  
  forward = function(state, encoder_outputs) {
    
    # function argument shapes
    # encoder_outputs: (bs, timesteps, hidden_dim)
    # state: (1, bs, hidden_dim)
    
    # multiplex state to allow for concatenation (dimensions 1 and 2 must agree)
    seq_len <- dim(encoder_outputs)[2]
    # resulting shape: (bs, timesteps, hidden_dim)
    state_rep <- state$permute(c(2, 1, 3))$repeat_interleave(seq_len, 2)
    
    # concatenate along feature dimension
    concat <- torch_cat(list(state_rep, encoder_outputs), dim = 3)
    
    # run through linear layer with tanh
    # resulting shape: (bs, timesteps, attention_size)
    scores <- self$attention(concat) %>% 
      torch_tanh()
    
    # sum over attention dimension and normalize
    # resulting shape: (bs, timesteps) 
    attention_weights <- scores %>%
      torch_sum(dim = 3) %>%
      nnf_softmax(dim = 2)
    
    # a normalized score for every source token
    attention_weights
  }
)

Multiplicative attention

In multiplicative attention, scores are obtained by computing dot products between decoder state and all of the encoder outputs. Here too, a softmax is then used for normalization.

attention_module_multiplicative <- nn_module(
  
  initialize = function() {
    
    NULL
    
  },
  
  forward = function(state, encoder_outputs) {
    
    # function argument shapes
    # encoder_outputs: (bs, timesteps, hidden_dim)
    # state: (1, bs, hidden_dim)

    # allow for matrix multiplication with encoder_outputs
    state <- state$permute(c(2, 3, 1))
 
    # prepare for scaling by number of features
    d <- torch_tensor(dim(encoder_outputs)[3], dtype = torch_float())
       
    # scaled dot products between state and outputs
    # resulting shape: (bs, timesteps, 1)
    scores <- torch_bmm(encoder_outputs, state) %>%
      torch_div(torch_sqrt(d))
    
    # normalize
    # resulting shape: (bs, timesteps) 
    attention_weights <- scores$squeeze(3) %>%
      nnf_softmax(dim = 2)
    
    # a normalized score for every source token
    attention_weights
  }
)

Decoder

Once attention weights have been computed, their actual application is handled by the decoder. Concretely, the method in question, weighted_encoder_outputs(), computes a product of weights and encoder outputs, making sure that each output will have appropriate impact.

The rest of the action then happens in forward(). A concatenation of weighted encoder outputs (often called “context”) and current input is run through an RNN. Then, an ensemble of RNN output, context, and input is passed to an MLP. Finally, both RNN state and current prediction are returned.

decoder_module <- nn_module(
  
  initialize = function(type, input_size, hidden_size, attention_type, attention_size = 8, num_layers = 1) {
    
    self$type <- type
    
    self$rnn <- if (self$type == "gru") {
      nn_gru(
        input_size = input_size,
        hidden_size = hidden_size,
        num_layers = num_layers,
        batch_first = TRUE
      )
    } else {
      nn_lstm(
        input_size = input_size,
        hidden_size = hidden_size,
        num_layers = num_layers,
        batch_first = TRUE
      )
    }
    
    self$linear <- nn_linear(2 * hidden_size + 1, 1)
    
    self$attention <- if (attention_type == "multiplicative") attention_module_multiplicative()
      else attention_module_additive(hidden_size, attention_size)
    
  },
  
  weighted_encoder_outputs = function(state, encoder_outputs) {

    # encoder_outputs is (bs, timesteps, hidden_dim)
    # state is (1, bs, hidden_dim)
    # resulting shape: (bs * timesteps)
    attention_weights <- self$attention(state, encoder_outputs)
    
    # resulting shape: (bs, 1, seq_len)
    attention_weights <- attention_weights$unsqueeze(2)
    
    # resulting shape: (bs, 1, hidden_size)
    weighted_encoder_outputs <- torch_bmm(attention_weights, encoder_outputs)
    
    weighted_encoder_outputs
    
  },
  
  forward = function(x, state, encoder_outputs) {
 
    # encoder_outputs is (bs, timesteps, hidden_dim)
    # state is (1, bs, hidden_dim)
    
    # resulting shape: (bs, 1, hidden_size)
    context <- self$weighted_encoder_outputs(state, encoder_outputs)
    
    # concatenate input and context
    # NOTE: this repeating is done to compensate for the absence of an embedding module
    # that, in NLP, would give x a higher proportion in the concatenation
    x_rep <- x$repeat_interleave(dim(context)[3], 3) 
    rnn_input <- torch_cat(list(x_rep, context), dim = 3)
    
    # resulting shapes: (bs, 1, hidden_size) and (1, bs, hidden_size)
    rnn_out <- self$rnn(rnn_input, state)
    rnn_output <- rnn_out[[1]]
    next_hidden <- rnn_out[[2]]
    
    mlp_input <- torch_cat(list(rnn_output$squeeze(2), context$squeeze(2), x$squeeze(2)), dim = 2)
    
    output <- self$linear(mlp_input)
    
    # shapes: (bs, 1) and (1, bs, hidden_size)
    list(output, next_hidden)
  }
  
)

seq2seq module

The seq2seq module is basically unchanged (apart from the fact that now, it allows for attention module configuration). For a detailed explanation of what happens here, please consult the previous post.

seq2seq_module <- nn_module(
  
  initialize = function(type, input_size, hidden_size, attention_type, attention_size, n_forecast, 
                        num_layers = 1, encoder_dropout = 0) {
    
    self$encoder <- encoder_module(type = type, input_size = input_size, hidden_size = hidden_size,
                                   num_layers, encoder_dropout)
    self$decoder <- decoder_module(type = type, input_size = 2 * hidden_size, hidden_size = hidden_size,
                                   attention_type = attention_type, attention_size = attention_size, num_layers)
    self$n_forecast <- n_forecast
    
  },
  
  forward = function(x, y, teacher_forcing_ratio) {
    
    outputs <- torch_zeros(dim(x)[1], self$n_forecast)$to(device = device)
    encoded <- self$encoder(x)
    encoder_outputs <- encoded[[1]]
    hidden <- encoded[[2]]
    # list of (batch_size, 1), (1, batch_size, hidden_size)
    out <- self$decoder(x[ , n_timesteps, , drop = FALSE], hidden, encoder_outputs)
    # (batch_size, 1)
    pred <- out[[1]]
    # (1, batch_size, hidden_size)
    state <- out[[2]]
    outputs[ , 1] <- pred$squeeze(2)
    
    for (t in 2:self$n_forecast) {
      
      teacher_forcing <- runif(1) < teacher_forcing_ratio
      input <- if (teacher_forcing == TRUE) pred$unsqueeze(3) else y[ , t - 1]
      out <- self$decoder(pred$unsqueeze(3), state, encoder_outputs)
      pred <- out[[1]]
      state <- out[[2]]
      outputs[ , t] <- pred$squeeze(2)
      
    }
    
    outputs
  }
  
)

When instantiating the top-level model, we now have an additional choice: that between additive and multiplicative attention. In the “accuracy” sense of performance, my tests did not show any differences. However, the multiplicative variant is a lot faster.

net <- seq2seq_module("gru", input_size = 1, hidden_size = 32, attention_type = "multiplicative",
                      attention_size = 8, n_forecast = n_timesteps)

# training RNNs on the GPU currently prints a warning that may clutter 
# the console
# see https://github.com/mlverse/torch/issues/461
# alternatively, use 
# device <- "cpu"
device <- torch_device(if (cuda_is_available()) "cuda" else "cpu")

net <- net$to(device = device)

Training

Just like last time, in model training, we get to choose the degree of teacher forcing. Below, we go with a fraction of 0.0, that is, no forcing at all.

optimizer <- optim_adam(net$parameters, lr = 0.001)

num_epochs <- 100

train_batch <- function(b, teacher_forcing_ratio) {
  
  optimizer$zero_grad()
  output <- net(b$x$to(device = device), b$y$to(device = device), teacher_forcing_ratio)
  target <- b$y$to(device = device)
  
  loss <- nnf_mse_loss(output, target)
  loss$backward()
  optimizer$step()
  
  loss$item()
  
}

valid_batch <- function(b, teacher_forcing_ratio = 0) {
  
  output <- net(b$x$to(device = device), b$y$to(device = device), teacher_forcing_ratio)
  target <- b$y$to(device = device)
  
  loss <- nnf_mse_loss(output, target)
  
  loss$item()
  
}

for (epoch in 1:num_epochs) {
  
  net$train()
  train_loss <- c()
  
  coro::loop(for (b in train_dl) {
    loss <-train_batch(b, teacher_forcing_ratio = 0.3)
    train_loss <- c(train_loss, loss)
  })
  
  cat(sprintf("nEpoch %d, training: loss: %3.5f n", epoch, mean(train_loss)))
  
  net$eval()
  valid_loss <- c()
  
  coro::loop(for (b in valid_dl) {
    loss <- valid_batch(b)
    valid_loss <- c(valid_loss, loss)
  })
  
  cat(sprintf("nEpoch %d, validation: loss: %3.5f n", epoch, mean(valid_loss)))
}

# Epoch 1, training: loss: 0.83752 
# Epoch 1, validation: loss: 0.83167

# Epoch 2, training: loss: 0.72803 
# Epoch 2, validation: loss: 0.80804 

# ...
# ...

# Epoch 99, training: loss: 0.10385 
# Epoch 99, validation: loss: 0.21259 

# Epoch 100, training: loss: 0.10396 
# Epoch 100, validation: loss: 0.20975 

Evaluation

For visual inspection, we pick a few forecasts from the test set.

net$eval()

test_preds <- vector(mode = "list", length = length(test_dl))

i <- 1

vic_elec_test <- vic_elec_daily %>%
  filter(year(Date) == 2014, month(Date) %in% 1:4)


coro::loop(for (b in test_dl) {
  
  input <- b$x
  output <- net(b$x$to(device = device), b$y$to(device = device), teacher_forcing_ratio = 0)
  preds <- as.numeric(output)
  
  test_preds[[i]] <- preds
  i <<- i + 1
  
})

test_pred1 <- test_preds[[1]]
test_pred1 <- c(rep(NA, n_timesteps), test_pred1, rep(NA, nrow(vic_elec_test) - n_timesteps - n_forecast))

test_pred2 <- test_preds[[21]]
test_pred2 <- c(rep(NA, n_timesteps + 20), test_pred2, rep(NA, nrow(vic_elec_test) - 20 - n_timesteps - n_forecast))

test_pred3 <- test_preds[[41]]
test_pred3 <- c(rep(NA, n_timesteps + 40), test_pred3, rep(NA, nrow(vic_elec_test) - 40 - n_timesteps - n_forecast))

test_pred4 <- test_preds[[61]]
test_pred4 <- c(rep(NA, n_timesteps + 60), test_pred4, rep(NA, nrow(vic_elec_test) - 60 - n_timesteps - n_forecast))

test_pred5 <- test_preds[[81]]
test_pred5 <- c(rep(NA, n_timesteps + 80), test_pred5, rep(NA, nrow(vic_elec_test) - 80 - n_timesteps - n_forecast))


preds_ts <- vic_elec_test %>%
  select(Demand, Date) %>%
  add_column(
    ex_1 = test_pred1 * train_sd + train_mean,
    ex_2 = test_pred2 * train_sd + train_mean,
    ex_3 = test_pred3 * train_sd + train_mean,
    ex_4 = test_pred4 * train_sd + train_mean,
    ex_5 = test_pred5 * train_sd + train_mean) %>%
  pivot_longer(-Date) %>%
  update_tsibble(key = name)


preds_ts %>%
  autoplot() +
  scale_color_hue(h = c(80, 300), l = 70) +
  theme_minimal()

(#fig:unnamed-chunk-11)A sample of two-weeks-ahead predictions for the test set, 2014.

We can’t directly compare performance here to that of previous models in our series, as we’ve pragmatically redefined the task. The main goal, however, has been to introduce the concept of attention. Specifically, how to manually implement the technique – something that, once you’ve understood the concept, you may never have to do in practice. Instead, you would likely make use of existing tools that come with torch (multi-head attention and transformer modules), tools we may introduce in a future “season” of this series.

Thanks for reading!

Photo by David Clode on Unsplash