active_admin.css.scss

@import 'active_admin/mixins';
@import 'active_admin/base';
@import 'jquery.ui.autocomplete';

active_admin.js.coffee

#= require active_admin/base
#= require jquery.ui.autocomplete

$ ->
  $('.autocomplete').each (index, input) ->
    $input = $(input)
    $hiddenInput = $($(input).data('hidden-input'))

    $input
      .autocomplete
        minLength: 3
        delay: 600
        source: (request, response) ->
          $.ajax
            url: $input.data('url')
            dataType: 'json'
            data: 
              term: request.term
            success: (data) -> response(data)
        select: (event, ui) ->
          $input.val(ui.item.label)
          $hiddenInput.val(ui.item.id)
          false
      .data('ui-autocomplete')._renderItem = (ul, item) ->
        $('<li></li>')
         .data('item.autocomplete', item)
         .append('<a>' + item.label + '</a>')
         .appendTo(ul)

autocomplete_serializer.rb

class AutocompleteSerializer < ActiveModel::Serializer
  attribute :id
  attribute :label

private

  def label
    object.name
  end
end

Gemfile

gem 'active_model_serializers'
gem 'activeadmin'
gem 'jquery-ui-rails'

posts.rb

ActiveAdmin.register Post do
  form do |f|
    f.inputs 'Details' do
      f.input :user,
        as: :string,
        input_html: {
          class: 'autocomplete',
          id: 'post_user_name',
          name: '',
          value: f.object.user.try(:name),
          data: {
            url: autocomplete_admin_users_path,
            hidden_input: '#post_user_id',
          },
        }

      f.input :user_id, as: :hidden
    end
  end
end

users.rb

ActiveAdmin.register User do
  collection_action :autocomplete, method: :get do
    users = User.where('LOWER(name) ILIKE ?', "#{params[:term]}%")
    render json: users, each_serializer: AutocompleteSerializer, root: false
  end
end