diff --git a/R/AcqFunctionMulti.R b/R/AcqFunctionMulti.R
index 7bdb66ae..5b9543e3 100644
--- a/R/AcqFunctionMulti.R
+++ b/R/AcqFunctionMulti.R
@@ -10,6 +10,15 @@
 #' Wrapping multiple [AcqFunction]s resulting in a multi-objective acquisition function composed of the individual ones.
 #' Note that the optimization direction of each wrapped acquisition function is corrected for maximization.
 #'
+#' For each acquisition function, the same [Surrogate] must be used.
+#' If acquisition functions passed during construction already have been initialized with a surrogate, it is checked whether
+#' the surrogate is the same for all acquisition functions.
+#' If acquisition functions have not been initialized with a surrogate, the surrogate passed during construction or lazy initialization
+#' will be used for all acquisition functions.
+#'
+#' For optimization, [AcqOptimizer] can be used as for any other [AcqFunction], however, the [bbotk::Optimizer] wrapped within the [AcqOptimizer]
+#' must support multi-objective optimization as indicated via the `multi-crit` property.
+#'
 #' @family Acquisition Function
 #' @export
 #' @examples
@@ -159,7 +168,7 @@ AcqFunctionMulti = R6Class("AcqFunctionMulti",
     },
 
     #' @field acq_functions (list of [AcqFunction])\cr
-    #'   Points to the list of the individual acqusition functions.
+    #'   Points to the list of the individual acquisition functions.
     acq_functions = function(rhs) {
       if (!missing(rhs) && !identical(rhs, private$.acq_functions)) {
         stop("$acq_functions is read-only.")
@@ -168,7 +177,7 @@ AcqFunctionMulti = R6Class("AcqFunctionMulti",
     },
 
     #' @field acq_function_ids (character())\cr
-    #'   Points to the ids of the individual acqusition functions.
+    #'   Points to the ids of the individual acquisition functions.
     acq_function_ids = function(rhs) {
       if (!missing(rhs) && !identical(rhs, private$.acq_function_ids)) {
         stop("$acq_function_ids is read-only.")
@@ -202,6 +211,13 @@ AcqFunctionMulti = R6Class("AcqFunctionMulti",
         set(values, j = j, value = - values[[j]])
       }
       values
+    },
+
+    deep_clone = function(name, value) {
+      switch(name,
+        .acq_functions = value$clone(deep = TRUE),
+        value
+      )
     }
   )
 )
diff --git a/R/AcqOptimizer.R b/R/AcqOptimizer.R
index 7c895940..3eec8339 100644
--- a/R/AcqOptimizer.R
+++ b/R/AcqOptimizer.R
@@ -9,10 +9,13 @@
 #' \item{`n_candidates`}{`integer(1)`\cr
 #'   Number of candidate points to propose.
 #'   Note that this does not affect how the acquisition function itself is calculated (e.g., setting `n_candidates > 1` will not
-#'   result in computing the q- or multi-Expected Improvement) but rather the top `n-candidates` are selected from the
+#'   result in computing the q- or multi-Expected Improvement) but rather the top `n_candidates` are selected from the
 #'   [bbotk::Archive] of the acquisition function [bbotk::OptimInstance].
 #'   Note that setting `n_candidates > 1` is usually not a sensible idea but it is still supported for experimental reasons.
-#'   Default is `1`.}
+#'   Note that in the case of the acquisition function [bbotk::OptimInstance] being multi-criteria, due to using an [AcqFunctionMulti],
+#'   selection of the best candidates is performed via non-dominated-sorting.
+#'   Default is `1`.
+#' }
 #' \item{`logging_level`}{`character(1)`\cr
 #'   Logging level during the acquisition function optimization.
 #'   Can be `"fatal"`, `"error"`, `"warn"`, `"info"`, `"debug"` or `"trace"`.
@@ -20,24 +23,26 @@
 #' }
 #' \item{`warmstart`}{`logical(1)`\cr
 #'   Should the acquisition function optimization be warm-started by evaluating the best point(s) present in the [bbotk::Archive] of
-#'   the actual [bbotk::OptimInstance]?
+#'   the actual [bbotk::OptimInstance] (which is contained in the archive of the [AcqFunction])?
 #'   This is sensible when using a population based acquisition function optimizer, e.g., local search or mutation.
 #'   Default is `FALSE`.
+#'   Note that in the case of the [bbotk::OptimInstance] being multi-criteria, selection of the best point(s) is performed via non-dominated-sorting.
 #' }
 #' \item{`warmstart_size`}{`integer(1) | "all"`\cr
-#'   Number of best points selected from the [bbotk::Archive] that are to be used for warm starting.
-#'   Can also be "all" to use all available points.
+#'   Number of best points selected from the [bbotk::Archive] of the actual [bbotk::OptimInstance] that are to be used for warm starting.
+#'   Can either be an integer or "all" to use all available points.
 #'   Only relevant if `warmstart = TRUE`.
 #'   Default is `1`.
 #' }
 #' \item{`skip_already_evaluated`}{`logical(1)`\cr
-#'   It can happen that the candidate resulting of the acquisition function optimization was already evaluated in a previous
-#'   iteration. Should this candidate proposal be ignored and the next best point be selected as a candidate?
+#'   It can happen that the candidate(s) resulting of the acquisition function optimization were already evaluated on the actual [bbotk::OptimInstance].
+#'   Should such candidate proposals be ignored and only candidates that were yet not evaluated be considered?
 #'   Default is `TRUE`.
 #' }
 #' \item{`catch_errors`}{`logical(1)`\cr
 #'   Should errors during the acquisition function optimization be caught and propagated to the `loop_function` which can then handle
 #'   the failed acquisition function optimization appropriately by, e.g., proposing a randomly sampled point for evaluation?
+#'   Setting this to `FALSE` can be helpful for debugging.
 #'   Default is `TRUE`.
 #' }
 #' }
@@ -123,6 +128,8 @@ AcqOptimizer = R6Class("AcqOptimizer",
 
     #' @description
     #' Helper for print outputs.
+    #'
+    #' @return (`character(1)`).
     format = function() {
       sprintf("<%s>", class(self)[1L])
     },
@@ -139,7 +146,7 @@ AcqOptimizer = R6Class("AcqOptimizer",
     #' @description
     #' Optimize the acquisition function.
     #'
-    #' @return [data.table::data.table()] with 1 row per optimum and x as columns.
+    #' @return [data.table::data.table()] with 1 row per candidate.
     optimize = function() {
       is_multi_acq_function = self$acq_function$codomain$length > 1L
 
diff --git a/R/ResultAssigner.R b/R/ResultAssigner.R
index e558ac0d..e6f6997f 100644
--- a/R/ResultAssigner.R
+++ b/R/ResultAssigner.R
@@ -36,6 +36,8 @@ ResultAssigner = R6Class("ResultAssigner",
 
     #' @description
     #' Helper for print outputs.
+    #'
+    #' @return (`character(1)`).
     format = function() {
       sprintf("<%s>", class(self)[1L])
     },
diff --git a/R/Surrogate.R b/R/Surrogate.R
index b9e0dd17..a3c6e2c0 100644
--- a/R/Surrogate.R
+++ b/R/Surrogate.R
@@ -69,6 +69,8 @@ Surrogate = R6Class("Surrogate",
 
     #' @description
     #' Helper for print outputs.
+    #'
+    #' @return (`character(1)`).
     format = function() {
       sprintf("<%s>", class(self)[1L])
     },
diff --git a/man/AcqOptimizer.Rd b/man/AcqOptimizer.Rd
index b4c143b1..035c6d6e 100644
--- a/man/AcqOptimizer.Rd
+++ b/man/AcqOptimizer.Rd
@@ -13,10 +13,13 @@ Wraps an \link[bbotk:Optimizer]{bbotk::Optimizer} and \link[bbotk:Terminator]{bb
 \item{\code{n_candidates}}{\code{integer(1)}\cr
 Number of candidate points to propose.
 Note that this does not affect how the acquisition function itself is calculated (e.g., setting \code{n_candidates > 1} will not
-result in computing the q- or multi-Expected Improvement) but rather the top \code{n-candidates} are selected from the
+result in computing the q- or multi-Expected Improvement) but rather the top \code{n_candidates} are selected from the
 \link[bbotk:Archive]{bbotk::Archive} of the acquisition function \link[bbotk:OptimInstance]{bbotk::OptimInstance}.
 Note that setting \code{n_candidates > 1} is usually not a sensible idea but it is still supported for experimental reasons.
-Default is \code{1}.}
+Note that in the case of the acquisition function \link[bbotk:OptimInstance]{bbotk::OptimInstance} being multi-criteria, due to using an \link{AcqFunctionMulti},
+selection of the best candidates is performed via non-dominated-sorting.
+Default is \code{1}.
+}
 \item{\code{logging_level}}{\code{character(1)}\cr
 Logging level during the acquisition function optimization.
 Can be \code{"fatal"}, \code{"error"}, \code{"warn"}, \code{"info"}, \code{"debug"} or \code{"trace"}.
@@ -24,24 +27,26 @@ Default is \code{"warn"}, i.e., only warnings are logged.
 }
 \item{\code{warmstart}}{\code{logical(1)}\cr
 Should the acquisition function optimization be warm-started by evaluating the best point(s) present in the \link[bbotk:Archive]{bbotk::Archive} of
-the actual \link[bbotk:OptimInstance]{bbotk::OptimInstance}?
+the actual \link[bbotk:OptimInstance]{bbotk::OptimInstance} (which is contained in the archive of the \link{AcqFunction})?
 This is sensible when using a population based acquisition function optimizer, e.g., local search or mutation.
 Default is \code{FALSE}.
+Note that in the case of the \link[bbotk:OptimInstance]{bbotk::OptimInstance} being multi-criteria, selection of the best point(s) is performed via non-dominated-sorting.
 }
 \item{\code{warmstart_size}}{\code{integer(1) | "all"}\cr
-Number of best points selected from the \link[bbotk:Archive]{bbotk::Archive} that are to be used for warm starting.
-Can also be "all" to use all available points.
+Number of best points selected from the \link[bbotk:Archive]{bbotk::Archive} of the actual \link[bbotk:OptimInstance]{bbotk::OptimInstance} that are to be used for warm starting.
+Can either be an integer or "all" to use all available points.
 Only relevant if \code{warmstart = TRUE}.
 Default is \code{1}.
 }
 \item{\code{skip_already_evaluated}}{\code{logical(1)}\cr
-It can happen that the candidate resulting of the acquisition function optimization was already evaluated in a previous
-iteration. Should this candidate proposal be ignored and the next best point be selected as a candidate?
+It can happen that the candidate(s) resulting of the acquisition function optimization were already evaluated on the actual \link[bbotk:OptimInstance]{bbotk::OptimInstance}.
+Should such candidate proposals be ignored and only candidates that were yet not evaluated be considered?
 Default is \code{TRUE}.
 }
 \item{\code{catch_errors}}{\code{logical(1)}\cr
 Should errors during the acquisition function optimization be caught and propagated to the \code{loop_function} which can then handle
 the failed acquisition function optimization appropriately by, e.g., proposing a randomly sampled point for evaluation?
+Setting this to \code{FALSE} can be helpful for debugging.
 Default is \code{TRUE}.
 }
 }
@@ -152,6 +157,9 @@ Helper for print outputs.
 \if{html}{\out{<div class="r">}}\preformatted{AcqOptimizer$format()}\if{html}{\out{</div>}}
 }
 
+\subsection{Returns}{
+(\code{character(1)}).
+}
 }
 \if{html}{\out{<hr>}}
 \if{html}{\out{<a id="method-AcqOptimizer-print"></a>}}
@@ -176,7 +184,7 @@ Optimize the acquisition function.
 }
 
 \subsection{Returns}{
-\code{\link[data.table:data.table]{data.table::data.table()}} with 1 row per optimum and x as columns.
+\code{\link[data.table:data.table]{data.table::data.table()}} with 1 row per candidate.
 }
 }
 \if{html}{\out{<hr>}}
diff --git a/man/ResultAssigner.Rd b/man/ResultAssigner.Rd
index a6f5485e..01e0211a 100644
--- a/man/ResultAssigner.Rd
+++ b/man/ResultAssigner.Rd
@@ -89,6 +89,9 @@ Helper for print outputs.
 \if{html}{\out{<div class="r">}}\preformatted{ResultAssigner$format()}\if{html}{\out{</div>}}
 }
 
+\subsection{Returns}{
+(\code{character(1)}).
+}
 }
 \if{html}{\out{<hr>}}
 \if{html}{\out{<a id="method-ResultAssigner-print"></a>}}
diff --git a/man/Surrogate.Rd b/man/Surrogate.Rd
index 73ed916a..db339406 100644
--- a/man/Surrogate.Rd
+++ b/man/Surrogate.Rd
@@ -150,6 +150,9 @@ Helper for print outputs.
 \if{html}{\out{<div class="r">}}\preformatted{Surrogate$format()}\if{html}{\out{</div>}}
 }
 
+\subsection{Returns}{
+(\code{character(1)}).
+}
 }
 \if{html}{\out{<hr>}}
 \if{html}{\out{<a id="method-Surrogate-print"></a>}}
diff --git a/man/mlr_acqfunctions_multi.Rd b/man/mlr_acqfunctions_multi.Rd
index 27c99a3e..344632ff 100644
--- a/man/mlr_acqfunctions_multi.Rd
+++ b/man/mlr_acqfunctions_multi.Rd
@@ -7,6 +7,15 @@
 \description{
 Wrapping multiple \link{AcqFunction}s resulting in a multi-objective acquisition function composed of the individual ones.
 Note that the optimization direction of each wrapped acquisition function is corrected for maximization.
+
+For each acquisition function, the same \link{Surrogate} must be used.
+If acquisition functions passed during construction already have been initialized with a surrogate, it is checked whether
+the surrogate is the same for all acquisition functions.
+If acquisition functions have not been initialized with a surrogate, the surrogate passed during construction or lazy initialization
+will be used for all acquisition functions.
+
+For optimization, \link{AcqOptimizer} can be used as for any other \link{AcqFunction}, however, the \link[bbotk:Optimizer]{bbotk::Optimizer} wrapped within the \link{AcqOptimizer}
+must support multi-objective optimization as indicated via the \code{multi-crit} property.
 }
 \section{Dictionary}{
 
@@ -80,10 +89,10 @@ Other Acquisition Function:
 Surrogate.}
 
 \item{\code{acq_functions}}{(list of \link{AcqFunction})\cr
-Points to the list of the individual acqusition functions.}
+Points to the list of the individual acquisition functions.}
 
 \item{\code{acq_function_ids}}{(character())\cr
-Points to the ids of the individual acqusition functions.}
+Points to the ids of the individual acquisition functions.}
 }
 \if{html}{\out{</div>}}
 }