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browsers

Source: vignettes/browsers.Rmd
browsers.Rmd

In this vignette we’ll optimize a set of parameters to prove that our browser is the best browser.

The Problem

Imagine we’re the developers of Arc browser, and we want to prove that it’s better than other any other browser. We have a table of features for each of the browsers, that we can quickly make up.

browsers <- c("Arc", "Chrome", "Firefox", "Opera", "Safari")
features <- c("Speed", "Ease of use", "Customizability", "Privacy", "Extensions",
              "Reading mode", "Ad-blocker")

# Make up ratings from 0 to 10 for each feature
set.seed(8456)
ratings <- parameter(0, features, browsers)
ratings[] <- sample(0:10, size = length(ratings), replace = TRUE)

ratings
#>                  browsers
#> features          Arc Chrome Firefox Opera Safari
#>   Speed             7      2       7     8      4
#>   Ease of use       2      1       7     5      7
#>   Customizability   1     10       9     0      3
#>   Privacy           1      5       8     2      8
#>   Extensions        9      0       7     9      4
#>   Reading mode      0      2      10     0      0
#>   Ad-blocker       10      2       2     8      6

The question is: how important is each feature? Let’s try giving all of them the same weight and calculate the score each browser gets.

colSums(ratings)
#>     Arc  Chrome Firefox   Opera  Safari 
#>      30      22      50      32      32

Nonsense, this would mean Arc is worse than Opera or Safari, and much worse than Firefox! Let’s give each feature ii an optimal weight wiw_i. Then we maximize the gap between Arc’s score and the second best score.

maxwArcScore(w)−SecondBestScore(w) \max_w {\text{ArcScore}(w) - \text{SecondBestScore}(w)}

We’ll make sure each feature matters by having 1<wi<51 < w_i < 5, and make them integers for simplicity.

browser_problem <- lp_problem() |> 
    lp_variable(weights[features], lower = 1, upper = 5, integer = TRUE) |> 
    lp_variable(arc_score) |> 
    lp_variable(second_best) |>
    lp_maximize(arc_score - second_best) |> 
    lp_subject_to(
        arc = {
            arc_ratings <- ratings[, "Arc"]
            arc_score == sum(arc_ratings * weights)
        },
        others = for (b in browsers[browsers != "Arc"]){
            b_ratings <- ratings[, b]
            second_best >= sum(b_ratings * weights)
        }
    )

library(ROI.plugin.highs)
browser_solution <- lp_solve(browser_problem)
browser_solution$variables
#> $weights
#> features
#>           Speed     Ease of use Customizability         Privacy      Extensions 
#>               1               1               2               1               5 
#>    Reading mode      Ad-blocker 
#>               1               5 
#> 
#> $arc_score
#> [1] 107
#> 
#> $second_best
#> [1] 100

Who cares about speed anyway? Extensions are where it’s at. Take a look at the new scores:

optimal_weights <- browser_solution$variables$weights
apply(ratings, 2, \(r) sum(r * optimal_weights))
#>     Arc  Chrome Firefox   Opera  Safari 
#>     107      40      95     100      75

That’s much better. We have successfully proved Arc’s unquestionable superiority!