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## Peter Frazier Joins ORIE Faculty

After graduating from the California Institute of Technology (Caltech) with a degree in physics and in engineering and applied sciences, Peter Frazier worked as a software engineer, co-founding a company and earning a couple of patents along the way. He returned to school in 2005 to earn a Ph.D. in operations research and financial engineering from Princeton, obtaining a provisional patent during his thesis work there. Now he has joined the ORIE faculty, focusing his research at the intersection of statistical learning and operations research and teaching courses in optimal learning and Monte Carlo methods in financial engineering in his first year.

"By collecting information, we give ourselves the opportunity to learn and make better decisions in the future," Frazier observes, but "collecting information incurs a cost," which may be high, for example if frequent inconvenient blood tests would give better information about a chronic medical condition such as vulnerability to strokes, or if finding the best design for a product or manufacturing process requires testing potential designs using time-consuming computer experiments. The cost of collecting information must be balanced against its contribution to decision making, something which may depend on the sequential process of arriving at the decision. Frazier describes the process of collecting information in the course of sequential decision making as "optimal learning."

#### An Example of Optimal Learning

As an example, Frazier and colleagues applied optimal learning to Ewing's sarcoma, a bone cancer that impacts children in a devastating way. A medical research group at Georgetown University has discovered a chemical compound that blocks the effect of the genetic defect that causes Ewing's sarcoma, and is striving to find derivatives of the compound that will improve the efficiency of this blocking. However there are many potential derivatives to test, each of which takes days to synthesize. The research group is looking for a way to determine, at each step of the way, which derivative to work with next, based on the data they have so far and on the likelihood that derivatives with similar structure have similar properties.

Working under the supervision of Frazier and his thesis adviser, Professor Warren Powell of Princeton, Princeton undergraduate student Diana Negoescu applied a method, the Correlated Knowledge Gradient (CKG) algorithm due to Frazier, Powell and Savas Dayanik, to the task of directing the sequence of derivatives so as to make best use of a limited testing budget. Under the method, each test informs the choice of the next so as to maximize the knowledge gained. Results so far indicate that the CKG algorithm could be used to improve efficiency in drug discovery for Ewing’s sarcoma," Frazier told a symposium on targeted therapy for childhood cancer at Georgetown University in April.

#### A Wide Scope of Applications

The characteristics of this example are shared by problems in a wide variety of areas in which Frazier has worked, including computer simulation, logistics, inventory control and neuroscience (including finding that certain monkey behavior could be explained in terms of the evolution of optimal action strategies) as well as medicine and healthcare.

In the latter domain, Frazier is advising a Master of Engineering team that is working to save the cost of laboratory inventory at Cayuga Medical Center in Ithaca. "I view theory and application as complementary," Frazier says. "People tend to think about the value of theory to applications - if you understand things in a principled way it can be helpful in solving problems in the real world. But the value of applications to theory is under-appreciated," he continued. "When you have an application to work on, you may find out that your theory may not be fully applicable, which can inspire theoretical advances."

#### Optimal Learning with Multiple Objectives

Recently Frazier began working with Taimoor Akhtar, a Ph.D. student of Professor Christine Shoemaker, who is a member of the Field of Operations Research in Civil and Environmental Engineering. They are analyzing a problem involving the optimal placement of wells in order to assess groundwater contamination, an issue of particular interest in Ithaca and surrounding areas as well as elsewhere.

Unlike traditional optimization problems, in which a specific goal -- minimizing cost or maximizing profit -- is the objective, Akhtar's problem has multiple objectives which must be weighed against each other, often by a decision maker who is not a part of the analytical process. This problem has interested Frazier in multi-objective problems that, like the groundwater problem, also entail time-consuming simulations. "Taimoor took my optimal learning course," said Frazier, "and recognized the potential for the ideas I taught in his own research area. In turn, I was introduced to a new class of problems to which these ideas can be extended."

#### Welcome from Professor Topaloglu

Professor Huseyin Topaloglu, who was also a student of Professor Powell's at Princeton, commented that "Peter's work sits at a very interesting intersection of statistics and optimization. Many problems in medicine, information technology and operations management require making a choice among a huge number of options when we have the chance to test only a tiny fraction of the options. Peter's work demonstrates how we can carefully try out a few options, make inferences about the options we have not tried out, and ultimately make the best choice from the large option set."

#### From Software Engineering to Operations Research

Prior to his graduate work, Frazier, who is from Rhinebeck, NY, was co-founder and software developer at Via Works in Glendale, CA, a software developer at Wirecache in San Diego, CA, and a senior software engineer at NCR's Teradata Division in Rancho Bernardo, CA. At Teradata he worked on various research problems and came up with patented inventions relating to the balanced allocation of multiple (computing) resources and the smoothing of data observations. Although he enjoyed computer programming and researching some of the problems he encountered there, he recognized that there were inherent limitations on how deeply he could pursue an interesting topic in the commercial environment. He decided to go to graduate school but was unsure of what subject to pursue. In his investigations he came across operations research (which was not a field at Caltech) and recognized that it matched what he wanted to do. "It involved applicable math, computing, decision making, finding the best way to do something, and coping with uncertainty," he said.

As a graduate student Frazier received recognition from INFORMS in various student paper competitions on computing, decision analysis, and "doing good with good OR."

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