Report for PGMO/PRMO
Project STORY (2015)
Stochastic and Robust Optimization Network


Laurent El Ghaoui1 and Michel De Lara2
29 September 2015

1 Overview

The STORY project seeked to foster research on stochastic and robust optimization, with applications in resources management. The one year-long project consisted in the set up of a network to allow collaborations between stochastic and robust optimization researchers from France and California.

2 The STORY Network

The STORY Network goal was to start a collaboration between researchers in France and California, on the topics of stochastic and robust optimization. The following participants have agreed to join the network. Given our choice of the participants, our aim was to foster cooperation between, on the one hand, combinatorial optimization and operations research, and, on the other hand, stochastic and robust optimization. We also expected that the research on robust sketching will interact nicely and provoke new developments. We focused on applications in resource management that mix combinatorics and uncertainty, like is the case in energy (unit commitment, planning of production units maintenance, etc.).

As planned, the budget contributed to organize one workshop in each country.

3 Workshop in the USA

We organized a workshop at UC Berkeley on January 26-27, 2015, on ``Stochastic and Robust Optimization''. The list of participants, and titles for their talk, is given below. As the titles suggest, there was a range of interests represented, from theoretical talks, to talks describing the application of stochastic and robust optimization in energy contexts. During the second day of the workshop, there was a follow-up discussion that entailed future potential collaborations and projects.

     List of participants in the UC Berkeley workshop

4 Workshop in France

As planned, we invited Mike Ludkovski (UC Santa Barbara) to participate to the SESO 2015 International Thematic Week, ``Smart Energy and Stochastic Optimization'', that took place at ENSTA ParisTech and École des Ponts ParisTech, from June 22 to 26, 2015 (organized by P. Carpentier, J.-P. Chancelier and M. De Lara).

Monday 22 June 2015: Mike Ludkowski (UC Santa Barbara, USA), ``Connecting optimal switching control and sequential design''

Abstract: Numerous problems in dynamic optimization of energy assets can be represented in terms of stochastic optimal switching control. In such settings, decision-making is reduced to identifying the best current action among a finite set of choices, for example "pump" vs "withdraw" vs "hold". In turn, this necessitates comparing several expected costs-to-go functionals across a typically multi-dimensional, continuous state space. We propose to reformulate this context as a statistical problem of identifying the maximal response among L >=2 unknown response surfaces that can be noisily sampled through a Monte Carlo simulator. While similar in flavor to Multi-Armed Bandits and Active Learning frameworks, our setting requires joint experimental design both in space and response-index dimensions. To maximize computational efficiency, we propose several novel acquisition functions for the respective sequential design of experiments, including the Gap-UCB and Gap-SUR heuristics. Numerical examples using both synthetic data and a case study in capacity expansion of power generation based on Aid et al (2012) are provided to illustrate our approach. (Joint work with R. Hu (UCSB)).



Footnotes

... Ghaoui1
EECS Department, UC Berkeley, Berkeley CA 94720, USA. Email:
elghaoui@berkeley.edu
... Lara2
École des Ponts ParisTech, Universit√© Paris-Est, CERMICS. Email:
delara@cermics.enpc.fr