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The Other Online Learning

If you search for “online learning” with any major search engine, it’s interesting to note that zero of the results are for online machine learning. This may not be a mistake if you are committed to a global ordering. In other words, the number of people specifically interested in the least interesting top-10 online human learning result might exceed the number of people interested in online machine learning, even given the presence of the other 9 results. The essential observation here is that the process of human learning is a big business (around 5% of GDP) effecting virtually everyone.

The internet is changing this dramatically, by altering the economics of teaching. Consider two possibilities:

  1. The classroom-style teaching environment continues as is, with many teachers for the same subject.
  2. All the teachers for one subject get together, along with perhaps a factor of 2 more people who are experts in online delivery. They spend a factor of 4 more time designing the perfect lecture & learning environment as verified by extensive study.

These two approaches have a similar economic cost, with the additional effort in the second approach being offset by the fact that it is a one-time effort rather than an annual effort.

I’m sure many people prefer the classroom approach, because it’s traditional, because a teacher can adjust dynamically and intelligently to the student, and because a teacher provides ancillary benefits such as day care and child abuse detection. Nevertheless, the second approach represents a compelling alternative addressing education. For classes commonly taught through high school, it’s difficult to imagine how good a learning experience could be after millions of hours spent refining to create the perfect approach. Imagine repeating a lecture over-and-over, testing the resulting student understanding a {day, week, month, year, decade} later to such an extent that every slide, every sentence, and every exercise is optimized for excellent learning. We could even imagine adapting the lecture to the learning style of each student.

The process of converting to the second approach has been slow, but it seems to be picking up. This suggests we can expect several things:

  1. Shakeout Like all new approaches, there is room for early adopters to win while the established old order suffers. We can expect the most severe impact on pure teaching institutions which do not adopt the newer approaches. Research universities will be insulated in two ways: much of their revenue comes from research grants anyways while the new approach creates a flight to excellence, which the research universities can lay some claim to. At one extreme, I understand that only 4-5% of the operating budget for Caltech comes from student tuition.
  2. Centralized Testing. Although class lessons can be taught at a distance, and exercises worked out by students, there is great room for cheating. The remedy for this is a strong centralized testing service. This already exists in the form of SAT, GRE, and AP tests, because grade inflation and nonuniform standards are common across schools. If a student can ace these tests after taking online learning classes, then there is a real sense in which colleges accepting students are satisfied by their qualifications. We can expect this to become more true, and perhaps to see more employer-oriented tests. We can also expect that testable subjects have an inherent advantage in online learning. As centralized testing is a difficult market to break into, the existing systems have a substantial advantage here.
  3. Digitization. Doing online learning brings all the advantages and disadvantages of any other digital media. These include perfect replicability, essentially free distribution, and difficult economics—on one hand the approach could be vastly valuable while on the other it’s difficult to charge someone for something they can get free. The economics imply that there is room for a major charity or state government to accomplish a great deal which might be difficult to accomplish in a business model.
  4. Gaps. There are areas of teaching which are not amenable to online instruction. For example, teaching people to do research remains in the apprentice model. Similarly, letters of recommendation remain an aspect of the apprentice model. Subjects of relatively small interest such as individual research directions may not merit the effort of a highly polished online instruction system. Similarly, many elements of our current education system are not related to formal education, but rather are about students meeting students, teachers acting as daycare for students, or simply structuring the day for learning. Mechanisms achieving the same ends with online human learning systems are necessary, and the conflation of goals represented by the traditional education approach will retard (but not stop) the adoption of online learning approaches. This process has already taken a decade, and we can expect more decades to come.

For those of us interested in online machine learning, it’s natural to question the relationship with online human learning. The practices differ entirely, but the theory still applies, as there are no clauses in the theorem statements of the form “if the learning agent is not a human then…” When you examine the theorem statements for applicability to online human learning, there are a few ideas which may transfer well. One of these is the necessity and techniques for handling exploration problems. If there are two ways to teach a subject, then you could simply try both and take the best. But if your resources are limited then a UCB approach provides a more efficient mechanism for doing this testing. Similarly, if a student has a set of known attributes, contextual-bandit approaches suggest a sound mechanism for personalization of lessons.

Much of our other theory about the process of online learning may be helpful in a heuristic-motivating manner, but it appears typically too pessimistic to accurately capture what is possible. For example, a common technique to explain an idea when teaching is to simply cover a few extreme cases from which all others are some interpolation. The closest common machine learning analogue to this is some active learning algorithms, where a learning algorithm chooses which examples to label. But, of course, this is not an accurate model, because it’s not the student, but rather the teacher which is choosing the examples. A setting more suitable for student and teacher has been studied in learning theory (see the bibliography here for a link into the citation tree). However, these results are typically rather brittle, so it’s not clear yet that we have understood the right way to formalize this process.

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ALT 2009

I attended ALT (“Algorithmic Learning Theory”) for the first time this year. My impression is ALT = 0.5 COLT, by attendance and also by some more intangible “what do I get from it?” measure. There are many differences which can’t quite be described this way though. The program for ALT seems to be substantially more diverse than COLT, which is both a weakness and a strength.

One paper that might interest people generally is:

Alexey Chernov and Vladimir Vovk, Prediction with Expert Evaluators’ Advice. The basic observation here is that in the online learning with experts setting you can simultaneously compete with several compatible loss functions simultaneously. Restated, debating between competing with log loss and squared loss is a waste of breath, because it’s almost free to compete with them both simultaneously. This might interest anyone who has run into “which loss function?” debates that come up periodically.

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Vowpal Wabbit Open Source Project

Today brings a new release of the Vowpal Wabbit fast online learning software. This time, unlike the previous release, the project itself is going open source, developing via github. For example, the lastest and greatest can be downloaded via:

git clone git://github.com/JohnLangford/vowpal_wabbit.git

If you aren’t familiar with git, it’s a distributed version control system which supports quick and easy branching, as well as reconciliation.

This version of the code is confirmed to compile without complaint on at least some flavors of OSX as well as Linux boxes.

As much of the point of this project is pushing the limits of fast and effective machine learning, let me mention a few datapoints from my experience.

  1. The program can effectively scale up to batch-style training on sparse terafeature (i.e. 1012 sparse feature) size datasets. The limiting factor is typically i/o.
  2. I started using the the real datasets from the large-scale learning workshop as a convenient benchmark. The largest dataset takes about 10 minutes. (This is using the native features that the organizers intended as a starting point, yet all contestants used. In some cases, that admittedly gives you performance nowhere near to optimal.)
  3. After using this program for awhile, it’s substantially altered my perception of what is a large-scale learning problem. This causes confusion when people brag about computational performance on tiny datasets with only 105 examples 🙂

I would also like to emphasize that this is intended as an open source project rather than merely a code drop, as occurred last time. What I think this project has to offer researchers is an infrastructure for implementing fast online algorithms. It’s reasonably straightforward to implant your own tweaked algorithm, automatically gaining the substantial benefits of the surrounding code that deals with file formats, file caching, buffering, etc… In a very real sense, most of the code is this surrounding stuff, which you don’t have to rewrite to benefit from. For people applying machine learning, there is some obvious value in getting very fast feedback in a batch setting, as well as having an algorithm that actually works in a real online setting.

As one example of the ability to reuse the code for other purposes, an effective general purpose online implementation of the Offset Tree is included. I haven’t seen any other implementation of an algorithm for learning in the agnostic partial label setting, so this code may be of substantial interest for people encountering these sorts of problems.

The difference between this version and the previous is a nearly total rewrite. Some bigger changes are:

  1. We dropped SEG for now, because of code complexity reasons.
  2. Multicore parallelization proceeds in a different fashion—parallelization over features instead of examples. This works better with caches. Note that all parallelization of the core algorithm is meaningless unless you use the -q flag, because otherwise you are i/o bound.
  3. The code is more deeply threaded, with a separate thread for parsing.
  4. There is support for several different loss functions, and it’s easy to add your own.

I’m interested in any bug reports or suggestions for the code. I have substantial confidence that this code can do interesting and useful things, but improving it is a constant and ongoing process.

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Asymmophobia

One striking feature of many machine learning algorithms is the gymnastics that designers go through to avoid symmetry breaking. In the most basic form of machine learning, there are labeled examples composed of features. Each of these can be treated symmetrically or asymmetrically by algorithms.

  1. feature symmetry Every feature is treated the same. In gradient update rules, the same update is applied whether the feature is first or last. In metric-based predictions, every feature is just as important in computing the distance.
  2. example symmetry Every example is treated the same. Batch learning algorithms are great exemplars of this approach.
  3. label symmetry Every label is treated the same. This is particularly noticeable in multiclass classification systems which predict according to arg maxl wl x but it occurs in many other places as well.

Empirically, breaking symmetry well seems to yield great algorithms.

  1. feature asymmetry For those who like the “boosting is stepwise additive regression on exponential loss” viewpoint (I don’t entirely), boosting is an example of symmetry breaking on features.
  2. example asymmetry Online learning introduces an example asymmetry. Aside from providing a mechanism for large scale learning, it also enables learning in entirely new (online) settings.
  3. label asymmetry Tree structured algorithms are good instances of example asymmetry. This includes both the older decision tree approaches like C4.5 and some newer ones we’ve worked on. These approaches are exponentially faster in the number of labels than more symmetric approaches.

The examples above are notably important, with good symmetry breaking approaches yielding substantially improved prediction or computational performance. Given such strong evidence that symmetry breaking is a desirable property, a basic question is: Why isn’t it more prevalent, and more thoroughly studied? One reasonable answer is that doing symmetry breaking well requires more serious thought about learning algorithm design, so researchers simply haven’t gotten to it. This answer appears incomplete.

A more complete answer is that many researchers seem to reflexively avoid symmetry breaking. A simple reason for this is the now pervasive use of Matlab in machine learning. Matlab is a handy tool for fast prototyping of learning algorithms, but it has an intrinsic language-level bias towards symmetric approaches since there are builtin primitives for matrix operations. A more complex reason is a pervasive reflex belief in fairness. While this is admirable when reviewing papers, it seems less so when designing learning algorithms. A third related reason seems to be a fear of doing unmotivated things. Anytime symmetry breaking is undertaken, the method for symmetry breaking is in question, and many people feel uncomfortable without a theorem suggesting the method is the right one. Since there are few theorems motivating symmetry breaking methods, it is often avoided.

What methods for symmetry breaking exist?

  1. Randomization. Neural Network learning algorithms which initialize the weights randomly exemplify this. I consider the randomization approach particularly weak. It makes experiments non-repeatable, and it seems like the sort of solution that someone with asymmophobia would come up with if they were forced to do something asymmetric.
  2. Arbitrary. Arbitrary symmetry breaking is something like random, except there is no randomness—you simply declare this feature/label/example comes first and that one second. This seems mildly better than the randomized approach, but still not inspiring.
  3. Data-driven. Boosting is a good example where a data-driven approach drives symmetry breaking (over features). Data-driven approaches for symmetry breaking seem the most sound, as they can result in improved performance.

While there are examples of learning algorithms doing symmetry breaking for features, labels, and examples individually, there aren’t any I know which do all three, well. What would such an algorithm look like?

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Decision by Vetocracy

Few would mistake the process of academic paper review for a fair process, but sometimes the unfairness seems particularly striking. This is most easily seen by comparison:

Paper Banditron Offset Tree Notes
Problem Scope Multiclass problems where only the loss of one choice can be probed. Strictly greater: Cost sensitive multiclass problems where only the loss of one choice can be probed. Often generalizations don’t matter. That’s not the case here, since every plausible application I’ve thought of involves loss functions substantially different from 0/1.
What’s new Analysis and Experiments Algorithm, Analysis, and Experiments As far as I know, the essence of the more general problem was first stated and analyzed with the EXP4 algorithm (page 16) (1998). It’s also the time horizon 1 simplification of the Reinforcement Learning setting for the random trajectory method (page 15) (2002). The Banditron algorithm itself is functionally identical to One-Step RL with Traces (page 122) (2003) in Bianca‘s thesis with the epsilon greedy strategy and a multiclass perceptron with update scaled by the importance weight.
Computational Time O(k) per example where k is the number of choices O(log k) per example Lower bounds on the sample complexity of learning in this setting are a factor of k worse than for supervised learning, implying that many more examples may be needed in practice. Consequently, learning algorithm speed is more important than in standard supervised learning.
Analysis Incomparable. An online regret analysis showing that if a small hinge loss predictor exists, a bounded number of mistakes occur. Also, an algorithm independent analysis of the fully realizable case. Incomparable. A learning reduction analysis showing how the regret of any base classifier bounds policy regret. Also contains a lower bound and comparable analysis of all plausible alternative reductions.
Experiments 1 dataset, comparing with no other approaches to solving the problem. 13 datasets, comparing with 2 other approaches to solve the problem.
Outcome Accepted at ICML Rejected at ICML, NIPS, UAI, and NIPS.

The reviewers of the Banditron paper made the right call. The subject is interesting, and analysis of a new learning domain is of substantial interest. Real advances in machine learning often come as new domains of application. The talk was well attended and generated substantial interest. It’s also important to remember the reviewers of the two papers probably did not overlap, so there was no explicit preference for A over B.

Why was the Offset Tree rejected? One of these rejections is easily explained as a fluke—we ran into a reviewer at UAI who believes that learning by memorization is the way to go. I, and virtually all machine learning people, disagree but some reviewers at UAI aren’t interested or expert in machine learning.

The striking thing about the other 3 rejects is that they all contain a reviewer who doesn’t read the paper. Instead, the reviewer asserts that learning reductions are bogus because for an alternative notion of learning reduction, made up by the reviewer, an obviously useless approach yields a factor of 2 regret bound. I believe this is the same reviewer each time, because the alternative theorem statement drifted over the reviews fixing bugs we pointed out in the author response.

The first time we encountered this review, we assumed the reviewer was just cranky that day—maybe we weren’t quite clear enough in explaining everything as it’s always difficult to get every detail clear in new subject matter. I have sometimes had a very strong negative impression of a paper which later turned out to be unjustified upon further consideration. Sometimes when a reviewer is cranky, they change their mind after the authors respond, or perhaps later, or perhaps never but you get a new set of reviewers the next time.

The second time the review came up, we knew there was a problem. If we are generous to the reviewer, and taking into account the fact that learning reduction analysis is a relatively new form of analysis, the fear that because an alternative notion of reduction is vacuous our notion of reduction might also be vacuous isn’t too outlandish. Fortunately, there is a way to completely address that—we added an algorithm independent lower bound to the draft (which was the only significant change in content over the submissions). This lower bound conclusively proves that our notion of learning reduction is not vacuous as is the reviewer’s notion of learning reduction.

The review came up a third time. Despite pointing out the lower bound quite explicitly, the reviewer simply ignored it. This more-or-less confirms our worst fears. Some reviewer is bidding for the paper with the intent to torpedo review it. They are uninterested in and unwiling to read the content itself.

Shouldn’t author feedback address this? Not if the reviewer ignores it.

Shouldn’t Double Blind reviewing help? Not if the paper only has one plausible source. The general problem area and method of analysis were freely discussed on hunch.net. We withheld public discussion of the algorithm itself for much of the time (except for a talk at CMU) out of respect for the review process.

Why doesn’t the area chair/program chair catch it? It took us 3 interactions to get it, so it seems unrealistic to expect someone else to get it in one interaction. In general, these people are strongly overloaded and the reviewer wasn’t kind enough to boil down the essence of the stated objection as I’ve done above. Instead, they phrase it as an example and do not clearly state the theorem they have in mind or distinguish the fact that the quantification of that theorem differs from the quantification of our theorems. More generally, my observation is that area chairs rarely override negative reviews because:

  1. It risks their reputation since defending a criticized work requires the kind of confidence that can only be inspired by a thorough personal review they don’t have time for.
  2. They may offend the reviewer they invited to review and personally know.
  3. They figure that the average review is similar to the average perception/popularity by the community anyways.
  4. Even if they don’t agree with the reviewer, it’s hard to fully discount the review in their consideration.

I’ve seen these effects create substantial mental gymnastics elsewhere.

Maybe you just ran into a cranky reviewer 3 times randomly Maybe so. However, the odds seem low enough and the 1/2 year cost of getting another sample high enough, that going with the working hypothesis seems indicated.

Maybe the writing needs improving. Often that’s a reasonable answer for a rejection, but in this case I believe not. We’ve run the paper by several people, who did not have substantial difficulties understanding it. They even understand the draft well enough to make a suggestion or two. More generally, no paper is harder to read than the one you picked because you want to reject it.

What happens next? With respect to the Offset Tree, I’m hopeful that we eventually find reviewers who appreciate an exponentially faster algorithm, good empirical results, or the very tight and elegant analysis, or even all three. For the record, I consider the Offset Tree a great paper. It remains a substantial advance on the state of the art, even 2 years later, and as far as I know the Offset Tree (or the Realizable Offset Tree) consistently beat all reasonable contenders both in prediction and computational performance. This is rare and precious, as many papers tradeoff one for the other. It yields a practical algorithm applicable to real problems. It substantially addresses the RL to classification reduction problem. It also has the first nonconstant algorithm independent lower bound for learning reductions.

With respect to the reviewer, I expect remarkably little. The system is designed to protect reviewers, so they have virtually no responsibility for their decisions. This reviewer has a demonstrated capability to sabotage the review process at ICML and NIPS and a demonstrated willingness to continue doing so indefinitely. The process of bidding for papers and making up reasons to reject them seems tedious, but there is no fundamental reason why they can’t continue doing so for several decades if they remain active in academia.

This experience has substantially altered my understanding and appreciation of the review process at conferences. The bidding mechanism commonly used, coupled with responsibility-free reviewing is an invitation to abuse. A clever abusive reviewer can sabotage perhaps 5 papers per conference (out of 8 reviewed), while maintaining a typical average score. While I don’t believe most people choose papers with intent to sabotage, the capability is there and used by at least one person and possibly others. If, for example, 5% of reviewers are willing to abuse the process this way and there are 100 reviewers, every paper must survive 5 vetoes. If there are 200 reviewers, every paper must survive 10 vetoes. And if there are 400 reviewers, every paper must survive 20 vetoes. This makes publishing any paper that offends someone difficult. The surviving papers are typically inoffensive or part of a fad strong enough that vetoes are held back. Neither category is representative of high quality decision making. These observations suggest that the conference with the most reviewers tend strongly toward faddy and inoffensive papers, both of which often lack impact in the long term. Perhaps this partly explains why NIPS is so weak when people start citation counting. Conversely, this would suggest that smaller conferences and workshops have a natural advantage. Similarly, the reviewing style in theory conferences seems better—the set of bidders for any paper is substantially smaller, implying papers must survive fewer vetos.

This decision making process can be modeled as a group of n decision makers, each of which has the opportunity to veto any action. When n is relatively small, this decision making process might work ok, depending on the decision makers, but as n grows larger, it’s difficult to imagine a worse decision making process. The closest representatives outside of academia I know are deeply bureacratic governments and other large organizations where many people must sign off on something before it takes place. These vetocracies are universally frustrating to interact with. A reasonable conjecture is that any decision making process with a large veto number has poor characteristics.

A basic question is: Is a vetocracy inevitable for large organizations? I believe the answer is no. The basic observation is that the value of n can be logarithmic in the number of participants in an organization rather than linear, as per reviewing under a bidding process. An essential force driving vetocracy creation is a desire to offload responsibility for decisions, so there is no clear decision maker. A large organization not deciding by vetocracy must have a very different structure, with clearly dilineated responsibility.

NIPS provides an almost perfect natural experiment in it’s workshop organization, which involves the very same community of people and subject matter, yet works in a very different manner. There are one or two workshop chairs who are responsible for selecting amongst workshop proposals, after which the content of the workshop is entirely up to the workshop organizers. If a workshop is rejected, it’s clear who is at fault, and if a workshop presentation is rejected, it is often clear by who. Some workshop chairs use a small set of reviewers, but even then the effective veto number remains small. Similarly, if a workshop ends up a flop, it’s relatively easy to see who to blame—either the workshop chair for not predicting it, or the organizers for failing to organize. I can’t think of a single time when I attended both the workshops and the conference that the workshops were less interesting than the conference. My understanding is that this observation is common. Given this discussion, it will be particularly interesting to see how the review process Michael and Leon setup for ICML this year pans out, as it is a system with notably more responsibility assignment than in previous years.

Journals end up looking relatively good with respect to vetocracy avoidance. The ones I’m familiar with have a chief editor who bears responsibility for routing papers to an action editor, who bears responsibility for choosing good reviewers. Every agent except the reviewers is often known by the authors, and the reviewers don’t act as additional vetoers in nearly as strong a manner as reviewers with the opportunity to bid.

This experience has also altered my view of blogging and research. On one hand, I’m very enthusiastic about research in general, and my research in particular, where we are regularly cracking conventionally impossible problems. On the other hand, it seems that some small number of people viewing a discussion silently decide they don’t like it, and veto it given the opportunity. It only takes one to turn strong paper into a years-long odyssey, so public discussion of research directions and topics in a vetocracy is akin to voluntarily wearing a “kick me” sign. While this a problem for me, I expect it to be even worse for the members of a vetocracy in the long term.

It’s hard to imagine any research community surviving without a serious online presence. When a prospective new researcher looks around at existing research, if they don’t find serious online discussion, they’ll assume it doesn’t exist under the “not on the internet so it doesn’t exist” principle. This will starve a field of new people. More generally, there is an opportunity to get feedback about research directions and problems much more rapidly than is otherwise possible, allowing us to avoid research on dead end topics which are pervasive. At some point, it may even seem that people not willing to discuss their research simply avoid doing so because it is critically lacking in one way or another. Since a vetocracy creates a substantial disincentive to discuss research directions online, we can expect that communities sticking with decision by vetocracy to be at a substantial disadvantage.