To produce forecast means (instead of forecast medians) it is necessary to adjust the back-transformation function relative to the forecast variance.
bias_adjust(bt, sd)More details about bias adjustment can be found in the transformations vignette: read the vignette:
vignette("transformations", package = "fable")
adj_fn <- bias_adjust(function(x) exp(x), 1:10)
y <- rnorm(10)
exp(y)
#> [1] 0.4926518 2.0161103 1.3106371 0.8837291 0.3126670 1.5142774 0.4004691
#> [8] 0.7507029 2.1712723 0.6279498
adj_fn(y)
#> [1] 0.7389777 6.0483308 7.2085039 7.9535616 4.2210045 28.7712704
#> [7] 10.2119618 24.7731960 90.1078014 32.0254392