Constrained MDPs and the reward hypothesis

It's been a looong ago that I posted on this blog. But this should not mean the blog is dead. Slow and steady wins the race, right? Anyhow, I am back and today I want to write about constrained Markovian Decision Process (CMDPs). The post is prompted by a recent visit of Eugene Feinberg , a pioneer of CMDPs, of our department, and also by a growing interest in CMPDs in the RL community (see this , this , or this paper). For impatient readers, a CMDP is like an MDP except that there are multiple reward functions, one of which is used to set the optimization objective, while the others are used to restrict what policies can do. Now, it seems to me that more often than not the problems we want to solve are easiest to specify using multiple objectives (in fact, this is a borderline tautology!). An example, which given our current sad situation is hard to escape, is deciding what interventions a government should apply to limit the spread of a virus while maintaining economic

Student Response Systems

There are plenty Student Response Systems (SRSs) out there. Which one to choose? This brief document summarizes what I have found on the web before the Fall of 2012.

Radio communication-based systems

The systems differ in a few characteristics. The first is what type of devices the students can use. Classical, iClicker like systems require the student buy a device which communicates with a receiver that the teacher should possess. Since our school uses iClickers, let me focus on them. The overall cost of first generation iClickers is $10/device, assuming the student sells back the device to the bookstore (which they can). This is not a major cost but who likes to pay when you don’t have to? The first limitation of iClicker-like systems is that they are bound to the smart classrooms and the computers there. Thus, if you are like me and use your own computer for projection, you will need to switch between screens to show the results of a poll. This makes the use of iClicker quite cumbersome. A second major limitation of iClickers is that they are limited to multiple choice questions. In particular, they don’t allow free text entry, numerical responses, or other type of test questions (like matching). Free text and numerical responses are very useful for assessing the knowledge of students and designing meaningful multiple choice questions is hard and time-consuming.

Systems accepting text input from non-smart phones

An alternative to iClickers is to use systems that uses Wifi networks or the texting capabilities of conventional phones with texting capabilities. Wifi capable devices include smartphones, tablets and laptops.
The systems that I have found that support texting (i.e., receiving input from non-smart phones) are Poll Everywhere, LectureTools and Top Hat Monocle. These also support input from Web-capable devices. Their pricing differs quite a bit. Poll Everywhere allows instructors to pay for the semester. The price currently is USD350. LectureTools requires you to pay for two semesters at the price of USD800. Top Hat Monocle does not allow the instructors to pay. The per student price is USD20 for a semester, or USD38 for five years.
As said before, all these systems support Wifi and texting. I had a chance to test Poll Everywhere and LectureTools. I had some problems with LectureTools (importing my slides did not work). The concept of LectureTools is that you keep your slides on the web, tightly integrated with the questions. They support during the presentation annotation of slides, which is nice. However, overall LectureTools was not as smooth and easy to use as Poll Everywhere. For example, I could not figure out given the limited amount of time how the students will connect on the web to my questions. Poll Everywhere was really easy to use, on the other hand. It supports Powerpoint and Keynote. Compared to Top Hat Monocle, Poll Everywhere is not as feature rich (Top Hat Monocle has games, for example), but I was happy with the functionality Poll Everywhere provided.

Systems that use the Web-capable devices

If one is contempt with Web-enabled devices, the number of available SRSs soars high. In fact, one can use any Web-based solution, many of them being free. Starting with the free options, of course, one can create a quiz in Moodle. Controlling what the students see and what they don’t is pretty cumbersome. Moodle is not very well suited for the purpose of live polling.
Another method is to use Twitter. Students are pretty excited about Twitter (from the feedback I got), though I would be careful projecting everything that comes in to the screen -- some moderation might be essential to keep the class under control. Another problem with Twitter is that a tool for analyzing responses to questions would be needed (and I know of no such tool).
The next option is to use Google Forms. The very idea of Google Forms is that information submitted on the web is sent to a Google spreadsheet. Since you need the spreadsheet to get the URL of the form, start by creating a spreadsheet, then insert a form there. Once the form is created (give it a cool skin!), get back to the spreadsheet to get the URL to it. You will send this to the students (maybe compressing it using tinyurl.com, or a similar service). You can control the timing of when the form is accepting input from the spreadsheet. To support ad hoc questions, you can just create an empty form and recycle it through your presentation. If you want to use a fixed set of questions, you will need one form (and thus spreadsheet) per question that you can store on your google drive. The downside of Google Forms is that students can submit as many responses as they wish. With Google Apps, presumably there is a way around this, but this would need to be investigated.
Flisti is an extremely simple web-based polling systems (I guess there are many other similar systems). You go to their webpage, create the poll there and give the poll’s URL to the students. You can view the results of the poll online. I think that users are tracked based on their IP addresses, so no multiple submissions are possible from the same IP address to the same poll. Only multiple choice questions (with multiple answers, possibly) are supported.
Socrative is a fuller Web-based SRS currently under beta-testing. During the beta-testing phase, the system is free. The web-based interface is nice and sleek and it was extremely user-friendly. The teacher can control in real-time which questions are “live” in his/her “classroom”. The classroom is identified by a numbe, that the students go to. The only issue with Socrative is that every activity is limited to 50 students.
QuestionPress is another commercial system. The price for my class is $66. This seems to be a mature systems that I was truly impressed by. All interactions are Web-based. ClickerSchool is similar to QuestionPress, the price is $95 for my class for one semester. ClickerSchool are provided specialized smart phone apps (both for iOS and Android). eClicker, on the other hand, requires the teacher to buy a software. All their software supports Apple products only (Mac OSX and iOS). SRN (studentresponsenetwork.com) offers a campuswide license for $195. This is a client-server system that requires installing software on the teachers’, as well as the students’ computers.
I could not find pricing information on the web for TurningPoint/ResponseWare, which seems to be a mature product (but it cannot be “tried”). The same goes for vClicker.

Which type of system to choose?

The question remains: Which type of system to choose? One factor to consider is how important it is to have other than multiple choice questions in class. Personally, I think that multiple choice questions exist only for historical reasons -- their pedagogical value is rather questionable. Good multiple choice questions are extremely hard and time consuming to create. If this is not convincing enough and you don’t mind switching the projector back and forth between your computer and the one in the classroom, you can stay with iClickers.
In the opposite case, the next thing to consider whether you want to support phones with text input. I have just polled my students and out of the 52 responses so far, 43 can and are willing to bring their laptops to the classroom, 37 carry a smartphone, 6 a tablet and 8 carry a non-Web enabled phone (these are overlapping groups of students). Thus, the vast majority of students are able to use a system that is built around the Web. Since it will always be hard to achieve 100% coverage, one idea is to let the students pair up or form groups of three. Based on the statistics I gathered, overall, I am leaning towards that support of texting input should not be viewed as a major advantage.
However, it should also be mentioned here that a potential danger of using laptops or other fancy, Web-enabled devices is that they represent potential sources of distraction. Thus, with the use of these devices, the teacher will need to face the challenge of competing for the students’ attention with the social networks, email, and ultimately the whole Web.
The next factor consider is the ease of use of the SRS. The teacher may need to create a significant number of questions for every class. Integration with Powerpoint and Keynote may be a plus, but switching between a browser and a presentation software looks easy enough.
Since I will use the chosen SRS only for formative assessment and not for grading (the present common sense is that this would be a bad idea, not talking about that this would indeed require full coverage of the whole class), I don’t care about whether the SRS supports automated grading and keeps the identities.
Based on these considerations, I will probably go with Socrative.

References
I have created a google spreadsheet for comparing the systems listed here, in addition to a few more. The spreadsheet can be found here. The spreadsheet links a few other sources that I have used during my research.

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