Multiobjective Bayesian Optimization, aka surrogate modeling etc. What we did back in 2005/6, and what we are up to now, with encouragement to the audience to take part. Cheers!

1. Multiobjective Bayesian
Optimization
Joshua Knowles
j.knowles@cs.bham.ac.uk
University of Birmingham, UK
University of Manchester, UK (Honorary)

2. Boo brexit !

3. Minsky: Do your PhD on a topic no one else is working on

4. Minsky: Do your PhD on a topic no one else is working on
My topic: (Pareto) multiobjective optimization; not many had
done much in 1997
By 2005/6: Many people were working on stochastic search for
multiobjective problems. So, I looked at “Bayesian” approaches
for scalar optimization and adapted them -> ParEGO. I also had
a need...

5. Motivation: automation of
science experiments
Mass spectrometers optimized by ParEGO were used in the HUSERMET
project, a large study of human blood serum in health and disease with over
800 patient subjects and performed in collaboration with GlaxoSmithKline,
AstraZeneca, Stockport NHS Trust and others (see References)

6. EVE - University of Manchester
King, Ross D., et al. "Functional genomic hypothesis generation and
experimentation by a robot scientist." Nature 427.6971 (2004): 247-252.

7. Further motivation
Not the best car on the grid any more. But when it was, it was down
to aerodynamics optimized in a wind-tunnel.

8. Multiobjective optimization

9. Darwin Updated: Pareto solutions in
design space
Adapted species lie in
low-dimensional
manifolds in feature
space!!
Visualization of such
patterns aids
designers and
engineers (cf. Deb)
Figures: from Shoval et
al, Science 336, 2012

10. ParEGO
Knowles, 2005; 2006
•A simple adaptation of Jones et al’s
seminal* EGO method (1998)
•Developed rapidly for real
applications
•One DACE model and
scalarization
•Several weaknesses
•But nevertheless quite popular and
used in applications
*Mockus and Zilinskas had had
similar ideas considerably earlier,
than Jones et al, but EGO put it all
together

11. ParEGO
Knowles, 2005; 2006
•A simple adaptation of Jones et al’s
seminal* EGO method (1998)
•Developed rapidly for real
applications
•One DACE model and
scalarization
•Several weaknesses
•But nevertheless quite popular and
used in applications
*Mockus and Zilinskas had had
similar ideas considerably earlier,
than Jones et al, but EGO put it all
together

12. Antenna optimization with
ParEGO

13. The State of the Art
in MCDM
Swarm
Optimiser
(say)
DM interacts
with
and steers
search.
WHY?
EVIDENCE????

14. What’s new since 2006?
• Handling of noisy samples (Hughes & Knowles, 2007)
• Ephemeral resource constraints (Allmendinger & Knowles, 2010)
• Decision-making during search (Hakanen & Knowles, 2017)
• Machine decision makers (Lopez-Ibanez & Knowles, 2015)
• Many-objective, robust optimization (Purshouse et al; forthcoming)
• Benchmarks for all the above (Working group at 2016 Lorentz centre
workshop; forthcoming)

15. What’s new since 2006?
• Handling of noisy samples (Hughes & Knowles, 2007)
• Ephemeral resource constraints (Allmendinger & Knowles, 2010)
• Decision-making during search (Hakanen & Knowles, 2017)
• Machine decision makers (Lopez-Ibanez & Knowles, 2015)
• Many-objective, robust optimization (Purshouse et al; forthcoming)
• Benchmarks for all the above (Working group at 2016 Lorentz centre
workshop; forthcoming)

16. Ephemeral resource constraints
In experimental work (c. 2008), we discovered a new kind of
constraint that we call:
ephemeral resource constraints
Richard’s whole PhD was about handling these things, because no one else was doing this! (Minsky again)
Allmendinger, Richard, and Joshua Knowles. "On handling ephemeral resource constraints in evolutionary
search." Evolutionary computation 21.3 (2013): 497-531.
Allmendinger, Richard, and Joshua Knowles. Ephemeral resource constraints in optimization and their
effects on evolutionary search. Technical Report MLO-20042010, University of Manchester, 2010.
Allmendinger, Richard, and Joshua Knowles. "On-line purchasing strategies for an evolutionary algorithm
performing resource-constrained optimization." International Conference on Parallel Problem Solving
from Nature. Springer Berlin Heidelberg, 2010.
Allmendinger, Richard, and Joshua Knowles. "Policy learning in resource-constrained optimization."
Proceedings of the 13th annual conference on Genetic and evolutionary computation. ACM, 2011.

17. Overview
= Ephemeral-Resource-Constrained
Optimization Problem (ERCOP)
+

18. 40 Years Earlier...
Conic rings were not always available in the size demanded by the Evolution Strategy.
Low-tech Solution: order rings and wait ‘idly’ until arrival
Schwefel optimized jet nozzles experimentally (1970)

19. Ephemeral resource constraints
We have not been Bayesian about this at all so far. We did
some reinforcement learning approaches (tedious to train
but we found good generalization). And some other
heuristics!
We think this could be a rich vein, however.

20. Benchmarking
Requirements
Tests for multiobjective surrogate-assisted methods and
Bayesian optimization
NB: The following slides are edits of slides jointly written originally by Tea Tusar,
Ilya Loschilov, Boris Naujoks, Daniel Horn, Dimo Brockhoff and Joshua Knowles, as
part of a seminar presentation at the Lorentz Center, Leiden, NL, in March 2016

21. Compared to what?
When do we expect Bayesian optimization methods to be
uncompetitive?
How do we select the right method to benchmark against?
There have been some nice collaborative benchmarking initiatives in
recent years. One of the well known ones is the
BBOB – the Black-box optimization benchmarking framework.

22. Benchmarking purpose
Benchmarking = Functions + Settings
+ Performance
measures
+ Implementation
issues
Q. How can we extend current benchmarks to be useful for
surrogate-assisted and MO development? Answer:
focus on “settings” for the first time

23. Benchmarking framework
(BBOB)
24 continuous functions in 5 different categories, 15 instances per
function
Separable, moderate, ill-conditioned,
multimodal (w. / without global structure)
Next BBOB: bi-objective
55 functions, 5 instances per function
Mixture of classes described above
Anytime performance (from 1 to millions of f.e.)
Measured with hypervolume

24. Anytime, multi-objective
Hypervolume

25. Proposed New Settings
Temporal aspects
On real-world benchmarks
Starting from and improving existing solutions
Pareto front prediction (without solutions in decision space)
Mixed-integer
Noise on objective values? (Not new to BBOB)
Constraints.
Report on runtime (wall clock)

26. Temporal Aspects
Parallel evaluation (aka batch)
At different fixed budgets
Heterogeneous evaluation time
(per objective)
Optimizers that may be used
• Large batch size
DoE designs, latin hypercube, space- filling,
random search. These are non-adaptive
• Flexible batch size
EA, multipoint surrogates
• Sequential algorithms
EGO, Bayesian optimization

27. Improving Existing Solutions
Motivation. Practitioners often start from existing solutions, provided
from an extrinsic source. Whereas in EMO, we often start from scratch
Implementation. We provide some initial sub-optimal solutions
Research questions
How much do methods differ in their ability to improve solutions
quickly?
How does this differ with the type of solution provided, e.g. local
optima, well-spread solutions

28. Pareto front prediction
Motivation
Finding bounds is classical
optimization goal
In MCDM, the decision maker is
interested by the potential for
improvement. Can use this for
interactively steering
It can provide stopping criteria
(particularly important in expensive
settings) Implementation:
Optimizer must provide prediction
of Pareto front – a fixed number of
points (at any time)
Inspired by prediction of PFs by Mickael Binois

29. Conclusions
Claim: Benchmarking frameworks such as BBOB stimulate
large-scale comparison studies that improve
understanding and development of methods
We have identified settings we believe will extend MO
benchmarking usefully for Bayesian optimization
(expensive MO optimization) developers and practitioners
LOOK OUT for our forthcoming EMO paper ;-(

30. Thanks
Thanks for your attention!
Thanks very much to the organizers, and those who moved
their talks for me
Thanks to a long list of collaborators and forerunners, who
can be found on my webpages, and of course cited in
papers
http://www.cs.bham.ac.uk/~jdk