Invited Session Mon.1.MA 141

Monday, 10:30 - 12:00 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Advances in stochastic optimization

 

Chair: David Brown

 

 

Monday, 10:30 - 10:55 h, Room: MA 141, Talk 1

David Brown
Optimal sequential exploration: Bandits, clairvoyants, and wildcats

 

Abstract:
This paper was motivated by the problem of developing an optimal strategy for exploring a large oil and gas field in the North Sea. Where should we drill first? Where do we drill next? The problem resembles a classical multiarmed bandit problem, but probabilistic dependence plays a key role: outcomes at drilled sites reveal information about neighboring targets. Good exploration strategies will take advantage of this information as it is revealed. We develop heuristic policies for sequential exploration problems and complement these heuristics with upper bounds on the performance of an optimal policy. We begin by grouping the targets into clusters of manageable size. The heuristics are derived from a model that treats these clusters as independent. The upper bounds are given by assuming each cluster has perfect information about the results from all other clusters. The analysis relies heavily on results for bandit superprocesses, a generalization of the classical multiarmed bandit problem. We evaluate the heuristics and bounds using Monte Carlo simulation and, in our problem, we find that the heuristic policies are nearly optimal.

 

 

Monday, 11:00 - 11:25 h, Room: MA 141, Talk 2

Ciamac Moallemi
Pathwise optimization for linear convex systems

Coauthors: Vijay V. Desai, Vivek F. Farias

 

Abstract:
We describe the pathwise optimization method, an approach for obtaining lower bounds on the minimal cost of a general class of linear-convex control problems. Our method delivers tight bounds by tractably identifying an optimal information relaxation penalty function. We demonstrate our method on a high-dimensional financial application. We provide theory to show that the bounds generated by our method are provably tighter those of some other commonly used approaches.

 

 

Monday, 11:30 - 11:55 h, Room: MA 141, Talk 3

Constantine Caramanis
Optimization at all levels: Probabilistic Envelope Constraints

 

Abstract:
In optimization under uncertainty, we often seek to provide solutions that provide guaranteed performance at least p% of the time. But what happens the other (1-p)% of the time? Current methodology fails to provide any constraints on these bad events: (1-p)% of the time, all bets are off. In this talk we provide a computationally tractable framework to design optimization solutions that have performance guarantees at all levels of
uncertainty realizations. We call these probabilistic envelope
constraints, and, as we show, they have a surprising connection to an extension of robust optimization.

 

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