Saturday, September 04, 2021

Harvard Shopping Period, Here We Go Again

I was looking at today's Harvard Crimson, and noted that Harvard's shopping period looks ready to be vanished again.  Shopping period is that wonderful Harvard tradition where students don't preregister for classes, but instead they choose classes after the first week, after having a chance to go to a lecture or two and see how they like it.  I encourage students -- and faculty -- to push back against efforts that restrict student flexibility in choosing their classes.  While administrators hate it, I still think it's better for students to avoid strong forms of preregistration.   

In fact, I realized I've been fighting this fight for quite a while -- here's something I wrote about when the administration under Larry Summers tried to get rid of it, from this blog back in 2008, and here's a Crimson article from 2002, where I spoke out against the plan for moving to preregistration that the blog post refers to. 

More recently, in 2018-2019, I found myself on the "Course Registration Committee", a committee that initially seemed similarly designed to find a way to move Harvard from shopping period to preregistration.  But a few of us on the committee made convincing arguments that shopping period had many benefits, and the disappearance of shopping period seemed at least somewhat further delayed, while a better solution was found. 

Then the pandemic.  Shopping period seemed impossible in the chaos, and things were more ad hoc (although there was, last year, a push for "class previews" of some sort before the beginning of classes).  This seems to give an opening to remove shopping period again.   

I'm not saying there aren't ways to change the system to make it better.  I'm not blind to the issues of shopping period -- not having a determined class size before classes begin is problematic for some classes.  I believe the committee people who have continued to look at the issue are trying to make things better going forward.  But the push always seems to be to make a system which is easier for administrators, and somehow correspondingly that is worse for the students.  Students should have the flexibility to see classes and teachers before committing, which to me means either a shopping period, or a structure that allows them to easily change classes for the first couple of weeks with negligible overhead.  I suppose one could design an add/drop system with the flexibility I'd have in mind, but it never seems to work that way in practice -- students end up needing signatures and approvals of various flavors, because (I think) it's in the best interest of administrators to make it hard for students to change classes once classes begin.  (Having 60 people sign up for a class but then having 30 people leave in the first week is possibly worse than the shopping period approach of not having sign-ups before the class at all, but it's a lot easier to disincentivize students from switching out (or in) with a preregistration system, so that problem disappears, at the cost of student flexibility.)  

As an example of a "non-shopping" issue I've seen this semester, first-year students at Harvard first semester are "limited" to four classes.  (There may be a way to get an exception to this, but I understand it would be rare exception.)  So this semester, with no shopping period, first years have to choose their 4 classes -- without seeing them -- and then manage a confusing add/drop process if they don't like them.  The older students generally know how to play the game -- they sign up for 5 or even 6 classes (if they can) and drop the ones they don't like, because dropping is generally easier than adding.  But first years don't have that flexibility because the 4-course rule is enforced at signup.  (I advise some first year students, and this problem came up.)  

I'm sure many non-Harvard people reading this think the shopping period system sounds crazy, and maybe a few think Harvard students are bizarrely spoiled.  Perhaps they're right.  But I found as a student it was wonderful, and shaped my future in powerful ways by encouraging me to explore.  You walk into a class you thought you should take, and find the professor puts you to sleep;  or you get dragged to a class by a friend, and find an inspiring subject you had no idea you would like.  I believe my college experience would have been lessened significantly without shopping period.  

As a faculty member, shopping period is clearly a pain, but I think a manageable one.   Back in 2002-2003, the faculty pushed back against preregistration (see this old Crimson article), but it seems opinions have shifted over time;  many faculty seemed to have moved to thinking it's not worth it, which is probably in their own self-interest.  Having been on both sides, I'm still strongly in favor of shopping period.  I suppose if I ever get into administration I may see things differently.  

I hope there are (younger) defenders out there, in the students and faculty, to push to make sure any changes still favor student choice over administrative convenience, and lead to the best outcomes for students.  

Monday, August 09, 2021

Queues with Small Advice

I have had papers rejected, with comments of the form that the results seem too easy, and are at the level of a homework assignment.  Generally, I think these reviewers miss the point.  The fact that the results seem easy may be because the point isn't the derivation but the conception and framing of the problem.  I actually think that generally it's an interesting subclass of good papers that can be and are turned into homework assignments.

A new-ish paper of mine, Queues with Small Advice, was recently accepted to the very new SIAM Conference on Applied and Computational Discrete Algorithms (ACDA21), which took place July 19-21.  This conference focuses on algorithms with a close tie to applications.  Some people unfamiliar with theory conferences might think that algorithms work would naturally be tied to applications, but I've generally found that algorithmic work tied to applications is more negatively reviewed in theory conferences.  Indeed, that type of work is much more likely to receive comments of the form that the results seem too easy, and are at the level of a homework assignment.  So perhaps this new conference will fill an important role and hole in the current slate of theory conferences. 

In any case, I actually do think this paper is in some ways easy (in that the analysis is readily approachable with standard tools), and parts of it would, I believe, make a great homework assignment.  The goal was to show the potential power of using even very simple advice, such as from machine-learning algorithms, in queueing systems.  This seems to me to be a very understudied topic, and fits into the recently growing theme of Algorithms with Predictions.  (The paper was rejected previously from a conference, where the most negative review said "Very accessible and well written paper, which certainly provides motivation to consider problems of this type." but also said "The mathematical analysis in this paper is fairly standard, and in that sense not novel... the paper is interesting, but not advancing sufficiently the state of the art.")  

The paper focuses on the case of 1 bit of advice -- essentially, is the job "short" or "long".  I think this type is advice is a good approach to look at for queueing -- it corresponds naturally to putting a job at the front of the queue, or the back.  And it may be easier for machine-learning algorithms to generate accurately.  Simple is often good in practice.  

Rather than describe the paper further, I'll go ahead and turn it directly into a collection of homework problems.  Feel free to use them or variations you come up with;  hopefully, the students won't find the paper for answers. I personally would be thrilled if one outcome of this paper was that prediction-based problems of this form made their way into problem sets.  (Although, serious question:  who still teaches queueing theory any more?)  

Section 1:  One-Bit Advice (Single Queue)

a)  Consider the standard M/M/1 queue, with Poisson arrivals at rate λ, and exponentially distributed service times of mean 1;  the expected time a job spends in the queue in equilibrium is 1/(1-λ).  Now suppose each job comes with one bit advice;  if the job has service time greater than T, the bit is 1, and if it is smaller than T, the bit is 0.  A "big" job goes to the end of the queue, a "small" job goes to the front.  (Assume the queue is non-preemptive.)  Find the expected time for a job in this queue in equilibrium, as a function of T and λ.

b)  What is the optimal value for T (as a function of λ)? 

c)  Repeat parts a and b, but this time with a preemptive queue.  Does preemption help or hurt performance?

Harder variation:  The above questions, but with an M/G/1 queue (that is, for a general, given service distribution);  derive a formula for the expected time in the system, where the formula may involve terms based on the service distribution.

Easier variation:  Write a simulation, experimentally determine the best threshold, and the improvements from one bit of advice.  Different service time distributions can be tried.  

Section 2:  One-Bit Advice with Predictions (Single Queue)

Where would possibly get a bit of advice in real life?  Perhaps from a machine learning predictor.  But in that case, the advice might turn out to be wrong.  What if our bit of advice is just right most of the time?

a)  Consider the (non-preemptive) M/M/1 queue variation from Section 1 part a above, but now the advice is correct with some probability p.  Find the expected time for a job in this queue in equilibrium, as a function of p, T, and λ.

b)  Repeat part a with a preemptive queue.

Harder variations:  The above questions, but have the probability the advice is correct depend on the size of the job.  A particularly fun example is when the "predicted service time" for a job with true time x is exponentially distributed with mean x, and the prediction bit is 1 if the predicted time is larger than T, and 0 otherwise.  Also, one can again consider general service times.  

Easier variation:  Again, write a simulation and derive experimental results/insights.  

Section 3:  One-Bit Advice with Prediction (Power of 2 Choices)  [harder, grad student level;  needs to know fluid limit models;  I'd stick with sections 1 and 2!]

a)  Derive fluid limit equations for a collection of N queues, where there are two types of jobs:  "large" jobs arrive as a Poisson stream of rate λ₁N and have exponentially distributed service times with mean μ₁ and "small" jobs arrive as a Poisson stream of rate λ₂N and have exponentially distributed service times of mean μ₂.  Each job comes with a bit of advice determining whether it is large or small, but large jobs are mislabelled with probability p₁ and small jobs are mislabelled with probability p₂.  An incoming job selects a queue using "the power of two choices" -- it is up to you to describe how a job determines what is the better of the two choices (there are multiple possibilities) and how jobs are processed within a queue (non-preemptive is suggested).   

[Hint:  the queue state can be represented by the number of jobs that are labelled short that are waiting, the number of jobs that are labelled long that are waiting, and the type of the job currently being serviced.]  

b)  Compare fluid limit results to simulations for 1000 queues to see if your equations seem accurate.  


Tuesday, June 08, 2021

Machine Learning for Algorithms Workshop (July 13-14)

We're having an online workshop on "Machine Learning for Algorithms" on July 13-14, with a great group of speakers.  Announcement below, link at https://fodsi.us/ml4a.html, free registration (but please register in advance)!

In recent years there has been increasing interest in using machine learning to improve the performance of classical algorithms in computer science, by fine-tuning their behavior to adapt to the properties of the input distribution. This "data-driven" or "learning-based" approach to algorithm design has the potential to significantly improve the efficiency of some of the most widely used algorithms. For example, they have been used to design better data structures, online algorithms, streaming and sketching algorithms, market mechanisms and algorithms for combinatorial optimization, similarity search and inverse problems.  This virtual workshop will feature talks from experts at the forefront of this exciting area.

The workshop is organized by Foundations of Data Science Institute (FODSI), a project supported by the NSF TRIPODS program (see fodsi.us). To attend, please register at    
 
https://fodsi.us/ml4a.html