I’ve added an GeForce GTX 1080 Ti into my machine (Running Ubuntu 18.04 and Anaconda with Python 3.7) to utilize the GPU when using PyTorch. Both cards a correctly identified:
$ lspci | grep VGA
03:00.0 VGA compatible controller: NVIDIA Corporation GF119 [NVS 310] (reva1)
04:00.0 VGA compatible controller: NVIDIA Corporation GP102 [GeForce GTX 1080 Ti] (rev a1)

The NVS 310 handles my 2-monitor setup, I only want to utilize the 1080 for PyTorch. I also installed the latest NVIDIA drivers that are currently in the repository and that seems to be fine:
$ nvidia-smi 
Sat Jan 19 12:42:18 2019       
+-----------------------------------------------------------------------------+
| NVIDIA-SMI 390.87                 Driver Version: 390.87                    |
|-------------------------------+----------------------+----------------------+
| GPU  Name        Persistence-M| Bus-Id        Disp.A | Volatile Uncorr. ECC |
| Fan  Temp  Perf  Pwr:Usage/Cap|         Memory-Usage | GPU-Util  Compute M. |
|===============================+======================+======================|
|   0  NVS 310             Off  | 00000000:03:00.0 N/A |                  N/A |
| 30%   60C    P0    N/A /  N/A |    461MiB /   963MiB |     N/A      Default |
+-------------------------------+----------------------+----------------------+
|   1  GeForce GTX 108...  Off  | 00000000:04:00.0 Off |                  N/A |
|  0%   41C    P8    10W / 250W |      2MiB / 11178MiB |      0%      Default |
+-------------------------------+----------------------+----------------------+

+-----------------------------------------------------------------------------+
| Processes:                                                       GPU Memory |
|  GPU       PID   Type   Process name                             Usage      |
|=============================================================================|
|    0                    Not Supported                                       |
+-----------------------------------------------------------------------------+

Driver version 390.xx allows to run CUDA 9.1 (9.1.85) according the the NVIDIA docs 46. Since this is also the version in the Ubuntu repositories, I simple installed the CUDA Toolkit with:
$ sudo apt-get-installed nvidia-cuda-toolkit

And again, this seems be alright:
$ nvcc --version
nvcc: NVIDIA (R) Cuda compiler driver
Copyright (c) 2005-2017 NVIDIA Corporation
Built on Fri_Nov__3_21:07:56_CDT_2017
Cuda compilation tools, release 9.1, V9.1.85

and
$ apt-cache policy nvidia-cuda-toolkit
nvidia-cuda-toolkit:
  Installed: 9.1.85-3ubuntu1
  Candidate: 9.1.85-3ubuntu1
  Version table:
 *** 9.1.85-3ubuntu1 500
        500 http://sg.archive.ubuntu.com/ubuntu bionic/multiverse amd64 Packages
        100 /var/lib/dpkg/status

Lastly, I’ve installed PyTorch from scratch with conda
conda install pytorch torchvision -c pytorch

Also error as far as I can tell:
$ conda list
...
pytorch                   1.0.0           py3.7_cuda9.0.176_cudnn7.4.1_1    pytorch
...

However, PyTorch doesn’t seem to find CUDA:
$ python -c 'import torch; print(torch.cuda.is_available())'
False

In more detail, if I force PyTorch to convert a tensor x to CUDA with x.cuda() I get the error:
Found no NVIDIA driver on your system. Please check that you have an NVIDIA GPU and installed a driver from 82 http://...

What am I’m missing here? I’m new to this, but I think I’ve checked the Web already quite a bit to find any caveats like NVIDIA driver and CUDA toolkit versions?
EDIT: Some more outputs from PyTorch:
print(torch.cuda.device_count())   # --> 0
print(torch.cuda.is_available())   # --> False
print(torch.version.cuda)          # --> 9.0.176