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March 2017

Is Peter Thiel disrupting college?

PeterThielNewsweek So Peter Thiel is on the cover of Newsweek for his Thiel Fellowship program where he pays about 25 fellows to skip college, and for obvious reasons of scale this remains as far from disrupting college as it was several years ago when the program was first announced, but it points at important weaknesses of today's higher education system, and for that reason it is worth keeping Thiel's program in the news.

The fact is, a lot of universities say they value both research and teaching, but few research universities value underclassman teaching. (Obviously not all universities are research universities.) While tuition covers on average about half of the operating costs, the research money makes for an appealing additional stream of income, and offers good P.R. opportunities for successful projects. People who earn a PhD have been trained to be good researchers but not necessarily good teachers, and while they hopefully self-select for an academic path due to their interest in teaching, some also choose that path to work on their own research projects with great flexibility, only minimal oversight and an inflated sense of how often their papers are going to be read.

In France (where I went to college), professors are much more teachers than researchers, and that was reflected on their lower pay and the lesser prestige of their positions. There are clear incentives in being viewed as a researcher rather than a teacher, which don't help with tuition costs (because fewer classes to teach so that faculty has time to do research means more manpower is needed, whether as tenured/tenure-track faculty or adjuncts, although the growth in tuition costs has many factors including administrative bloat).

In the worst-case scenario, researchers don't care about teaching and receive tenure because they bring in a lot of research dollars. In a reasonable middle-of-the-road scenario, researchers care about teaching in their area of expertise, where their skill set brings the most added value to the classroom. This rarely includes underclassmen - students with fresh ideas, excited about coming to college, who haven't even declared a major yet. (Teaching students who are not in one's major is often viewed as academic purgatory. Even supposedly smart adults can be so cliquish.)

Those students are supposed to wait patiently until they have learned enough to hopefully make a difference, by which time they might have begun to wonder what the big hoopla about college was all about. Certainly, everyone has to know the basics of his or her field before he or she can make a meaningful contribution, but many of the required courses of freshman or sophomore year are of the "you can't call yourself an engineer if you haven't taken thermodynamics or calculus I" variety, without a clear explanation of how it is going to be useful, and all the energy and fresh thinking a student could have brought shrivels unused.

A favorite saying in universities has become "We teach them how to think", as opposed to teaching students skills they can use in the workforce. The reasoning is that the skill set may change, but if students know how to think and learn by themselves, they will be able to adapt. It is a good point in theory, but in practice it is often used as a cop-out for some professors to avoid updating what they teach. (If you already taught them how to think twenty years ago, then why should you update your slides on, say, inventory theory from twenty years ago?) 

I like Thiel's idea because it builds on the enthusiasm of many students when they graduate from high school (although the program itself is too small to impact higher education, but at least it helps students who have become so bored with college they would have dropped out) and because it offers close advising opportunities with successful professionals. I do disagree with the idea that the right alternative to college is to start a company, but at least it is clear where to look for individuals who can advise the students in that case: successful entrepreneurs.

Young graduates have become so obsessed with mentors, sponsors and advisors because they feel left to their own devices in a professional world where they or their bosses might change companies after a year. This is also reflected in the number of applications for YCombinator and its media coverage. (The Launchpad provides a great glimpse into how the company operates.) I'm not sure if college students have the same drive to find mentors, and those who don't want to become professors may not see the point in finding a mentor among their teachers, except if they hope for a recommendation for graduate school. It is telling that you have to wait until postdoctoral fellowship for your boss - the director of your research lab - to be formally called your mentor: this is the only time in academia where the job of your direct supervisor is most aligned with the job you are training for, since many PhD students before the post-doc stage may go to non-research jobs in industry.

But having a professor as an advisor/mentor provides a unique opportunity to receive guidance from someone with understanding of the career path the student seeks for himself and no emotional or financial involvement in the student's success, unlike parents or entrepreneurs who fund a startup in exchange for a cut of the profits. While the whole idea is to find someone who has been in the position the student is in now and has succeeded through the challenge, people who choose academic careers might be more inclined, personality-wise, to help others find success (although this is painting the situation in broad strokes, they tend to find satisfaction in the success of people they have trained), while people in industry might be a little more driven by a sense of personal accomplishment and less interested in giving back to their professional community until they are much older. In many universities, though, the lines are blurring now with the increased emphasis of research - an individual accomplishment, or a group accomplishment outside the classroom and with enough prestige bestowed on the head of the research lab. This leaves underclassmen with even fewer opportunities for guidance and advice. And not every underclassman will want guidance and advice - many might want to be left alone, after years of being monitored by their parents - but college represents a unique time where students can forge long-lasting relationships with adults who don't have a direct stake in their success.

Of course, students can join plenty of extracurricular clubs and keep themselves busy if they find their classroom experience lacking, but the "breadth" model of education, where you collect a lot of skills in a shallow manner to earn the right of call yourself a well-rounded individual, is becoming outdated. What you need to become competitive nowadays is to have a deep skill set. Universities like to think that skill set is gained through a Master's degree, since that amounts to six years of tuition (four for college and two for the Master's, although not necessarily from the same people) instead of four, and that will be true for some people, in addition to being critically important for innovation in science and engineering. (William Hewlett did graduate with a Bachelor's from Stanford, a Master's from MIT and an Electrical Engineer from Stanford, which basically means he dropped out of the PhD program - not college - to start HP with David Packard, also a Stanford grad.) 

But making it more expensive and lengthy to complete one's education is only going to further shut out segments of the population who could make great contributions to the workforce. There needs to be college options for students who want to learn skills more directly applicable to the workforce. This is when certain professors start spitting out the words "vocational training" as something beneath them. But what Thiel is doing is also vocational training, and no one would think of condescending to his fellows. 

Higher ed at the undergraduate level needs more coordination between courses to make them an integral part of a semester-long project, where students would better see how the different components they learn fit together, (for engineering students) from calculus to ethics courses on the implications of the decisions they make. Projects require project advisors, and that would provide the close interactions with faculty so beneficial for students, even at the underclassman level. (Research experiences for undergraduates are becoming somewhat more popular, but they are insufficient if every student is to become more innovative and creative.) 

The fragmentation of the curriculum puzzles me to no end. Everyone is in charge for a tiny part of the puzzle every semester - and which part often varies from semester to semester - and you just have to hope that with time the pieces don't stop fitting with each other, when instructors make changes to course content without consulting with their colleagues. The one attempt at integration is the capstone project in the fall or spring semester of senior year, but even then there is little involvement of (help by) the faculty members not in charge of supervising the capstone, even when their expertise is more aligned with the project content than the faculty in charge. It would make more sense to use such projects as teaching tools, maybe assign each faculty member a small number of projects to closely supervise, and have them run for longer time periods so that students learn the concepts with an eye on their project. A project-based curriculum is actually the model of Olin College in Massachusetts, and with an admission rate of only 8.8% in 2016, it looks like this model resonates with quite a few students.

I like Olin as a way to bridge Thiel's ideas with the reality of higher ed today but Olin has been around for 15 years now and if universities truly viewed it as the way of the future, more of them would have aligned themselves with its teaching model instead of paying lip service to doing research with undergraduates. You just have to observe the outcry from the University of Houston when the chancellor of the University of Texas system suggested a new campus for UT in Houston (he was ultimately forced to scuttle the plan, more on that some other day) to see how quick universities are at taking action when they feel their interests are threatened. So neither Thiel nor Olin has disrupted higher education yet, but they have brought valuable new options to the higher ed landscape, and perhaps that's good enough. 

On "Robust Fluid Processing Networks" by Bertsimas, Nasrabadi and Paschalidis (2015)

Citation: Dimitris Bertsimas, Ebrahim Nasrabadi and Ioannis Paschalidis. (2015) Robust Fluid Processing Networks IEEE Transactions on Automatic Control, 60(3):715-728. Paper

Summary: Fluid networks provide a deterministic approximation to multiclass processing networks, making them much more tractable than their stochastic counterpart; however, the manager completely disregards randomness and there might be value in incorporating such uncertainty in the decision-making process. The authors' robust optimization approach aims at doing just that by combining the tractability of fluid networks and the practical relevance of including uncertainty in the modeling framework through an approach (robust optimization) that has a track record of leading to reformulated problems of complexity similar to that of the deterministic problems.

Specifically, the authors show that the robust fluid model preserves the computational tractability of the classical fluid problem and retains its original structure. They derive a scheduling policy determining how various classes should be processed at the servers of the network using complementary slackness optimality conditions. They also develop a polynomial-time algorithm under certain conditions. Simulation results demonstrate that the robust fluid policies are near-optimal when the optimal policies can be computed and outperform heuristics when the optimal policies cannot be computed in a tractable manner.


I. Introduction

II. Problem description and fluid model

A. Criss-cross network

This is a simple network where one type goes through two servers (becoming class 1 and then class 3) but must compete with another type (class 2) at the first server. The second type doesn't go through the second server and simply exits the system.

B. A general formulation

The authors define the general problem, formulate its dual and write out the complementary slackness conditions.

III. Robust fluid model

A. Modeling the uncertainty

Uncertainty is incorporated on the arrival and service times (the lambda's and the 1/mu's) using Bertsimas-and-Sim uncertainty sets bounding the deviation from the nominal value by a total amount Gamma_j at server j at each time. 

B. Robust counterpart problem

The authors define the robust problem and re-formulate it in a tractable manner using strong duality arguments. 

C. Robust policies

The authors translate the optimal solution of the robust problem into a dynamic scheduling policy for the control of stochastic networks.  The idea is to give priority on each server to classes with the highest value of a new parameter between 0 and 1 computed using the optimal control found by solving the robust fluid problem.  

IV. A single-server system

In this section the authors show how they can find an optimal control for the robust fluid problem in polynomial time. They show they need to solve at most n linear optimization problems in the single-server case because they pick a class to serve until that class is depleted. Then an optimal policy is to serve each class with service rate the arrival rate and no job will be held in the network. This leads to a piecewise-constant solution with breakpoints the times where a class becomes depleted. 

A. Klimov's problem

All the results can carry over to a single server queue with probabilistic feedback.

V. Simulation results 

The goal is to compare the performance of the robust fluid policy to that of the optimal policy in small-size networks (when the optimal policy can be computed), and to that of reasonable heuristics on moderate to large-size networks. The authors also investigate the sensitivity of the robust policy to the parameter Gamma.

A. Computational remarks

B. Network examples

The authors consider four different network types: the criss-cross network and three types of reentrant networks, where at least one type of jobs cycles back to a server it had already visited. 

VI. Conclusion

Why I like this paper: First, there is the obvious reason that this paper provides a tractable approach to incorporating uncertainty in fluid networks, filling an important gap in the literature between (deterministic) fluid networks and stochastic networks. Also, over 15 years ago when I first started my PhD on robust optimization I did research on fluid networks for about a year before moving to inventory theory. It is fun to see that someone finally solved the problem, and the results are very elegant. I also love anything that uses strong duality or complementary slackness. 

Further reading:

  • Malcolm C. Pullan (1996) A duality theory for separated continuous linear programs. SIAM Journal on Control and Optimization, 34:931-965. The title says it all.
  • Mathieu Ricard (1995) Optimization of Queueing Networks: An Optimal Control Approach. PhD dissertation, MIT. It doesn't have anything about robust optimization in it but the threshold policies derived for various complex settings are impressive.