# Announcing NetEcon 2015

I’ve posted before about the growing overlap in topics between the EC & Sigmetrics communities.  Increasingly, the conferences are having sessions on very similar topics, but looking at the topics with very different perspectives.  This was especially true for last year’s conferences.  While some folks manage to cross the boundaries between these two communities, for the most part this has proven difficult (at least for my attempts)…

I think there’s a lot of value in finding ways to bring folks from these two communities together, which is one reason why I’m happy to announce NetEcon 2015, which I’m co-chairing with Patrick Loiseau and Aaron Roth.  NetEcon is a workshop with a long history of bridging CS and Economics, and this year we’re hoping to take advantage of the fact that Sigmetrics and EC are co-located as part of FCRC to bring those two communities together as well.

To highlight this, we have three exciting keynotes lined up.  One from Economics (Rakesh Vohra), one from the EC community (Eva Tardos), and one from the Sigmetrics community (R. Srikant).  Additionally, to be consistent with the differing publication styles across the communities, we will allow accepted papers to have a 1-page abstract appear in the proceedings in order to ensure that the full version of the papers can be published in other venues without issue.

So, there’s no excuse not to send in your best on-going paper or work-in-progress!

# Videos on universal laws and architectures

I’ve posted the beginnings of what I hope will become an extensive library of videos, papers, notes, and slides exploring in more detail both illustrative case studies and theoretical foundations for the universal laws and architectures that I superficially referred to in my previous blog posts.  For the moment, these are simply posted on dropbox, so be sure to download them, since looking at them in a browser may only give a preview…

I’m eager to get feedback on any aspects of the material, and all the sources are available for reuse.

In addition to the introductory and overview material, of particular interest might be a recent paper on heart rate variability, one of the most persistent mysteries in all of medicine and biology, which we resolve in a new but accessible way.  There are tutorial videos in addition to the paper for download.

# Solution to puzzle: produce or learn?

This post is a solution to the puzzle in the last post.

The optimal strategy has a very simple form: there is a time ${t^* \in \{1, \dots, T\}}$ such that (${^*}$ denotes optimal quantities)

• only learn (${l^*(t)=1}$) before time ${t^*}$;
• only produce (${p^*(t)=1}$) from time ${t^*}$ on.

# Another puzzle: produce or learn?

When our kids were small, they were in sports teams (basketballs, baseball, soccer, …).  Their teams would focus on drills early in the season, and tournaments late in the season.  In violin, one studies techniques (scales, etudes, theory, etc.) as well as musicality (interpretation, performance, etc).   In (engineering) research, we spend a lot of time learning the fundamentals (coursework, mathematical tools, analysis/systems/experimental skills, etc.) as well as solving problems in specific applications (research). What is the optimal allocation of one’s effort in these two kinds of activities?

This is a complex and domain-dependent problem.  I suppose there is a lot of serious empirical and modeling research done in social sciences (I’d appreciate pointers if you know any).  But let’s formulate a ridiculously simple model to make a fun puzzle.

1. Consider a finite horizon t = 1, 2, …, T.   The time period t can be a day or a year.  The horizon T can be a project duration or a career.
2. Suppose there are only two kinds of activities, and let’s call them production and learning.  Our task is to decide for each t, the amount of effort we devote to produce and to learn.  Call these amounts p(t) and l(t) respectively.
3. These activities build two kinds of capabilities.  The fundamental capability L(t) at time t depends on the amount of learning we have done up to time t-1, L(t) := L(l(s), s=1, …, t-1).  The production capability P(t) at time t depends on the amount of effort we have devoted to production up to time t-1, P(t) := P(p(s), s=1, …, t-1).   We assume the functions L(l(s), s=1, …, t-1) and P(p(s), s=1, …, t-1) are increasing and time invariant (i.e., they depend only on the amount of effort already devoted, but not on time t).
4. The value/output we create in each period t is proportional to the time p(t) we spend on production multiplied by our overall capability at time t.   Our overall capability is a weighted sum P(t) + mL(t) of fundamental and production capabilities, with m>1.

Goal: choose nonnegative (p(t), l(t), t=1, …, T) so as to maximize the total value ${\sum_{t=1}^T\ p(t) (P(t) + m L(t))}$ subject to ${p(t) + l(t) \leq 1}$ for all t=1, …, T.

The assumption m>1 means that the fundamentals (quality) are more important than mere quantity of production.  The constraint ${p(t) + l(t) \leq 1}$ says that in each period t, we only have a finite amount of energy (assume a total of 1 unit) that can be devoted to produce and learn.  On the one hand, we want to choose a large p(t) because it not only produces value, but also increases future production capabilities P(s), s=t+1, …, T.  On the other hand, since m>1, choosing a large l(t) increases our overall capability more rapidly, enhancing value.  What is the optimal tradeoff?

We pause to comment on our assumptions, some of which can be addressed without complicating our model too much.

Caveats.  On the outset, our model assumes every activity can be cleanly classified as building either the fundamental capability or the production capability.  In reality, many activities contribute to both.  Moreover, the interaction between these two activities is completely ignored, except that they sum to no more than 1 unit.  For example, production (games, performance, research and publication, etc) often provides important incentives and contexts for learning and influences strongly the effectiveness of learning, but our function L is independent of  p(s).  The time invariance assumption in 3 above implies that we retain our capabilities forever after they are built; in reality, we may lose some of them if we don’t continue to practice.  If we think of P(t)+mL(t) as a measure of quality, then our objective function assumes that there is always positive value in production, regardless of its quality.  In reality, production of poor quality may incur negative value, even fatal.

A puzzle

A simple puzzle is the special case where the capabilities depend on (are) the total amounts of effort devoted, i.e.,

${L(t)\ := \ \sum_{s=1}^{t-1} l(s), \ \ \ P(t) \ :=\ \sum_{s=1}^{t-1} p(t) }$

Despite its nonconvexity, the problem can be explicitly solved and the optimal strategy turns out to have a very simple structure.  I will explain the solution in the next post and discuss whether it agrees, to first order, with our intuition and how some of the disagreements can be traced back to our simplifying assumptions.

# A holiday puzzle: solution

I now discuss two solutions to the puzzle described in the last post — one for the special case of a linear grid, and the other for the general 2D grid.  I thank Johan Ugander and Shiva Navabi for very useful pointers (see the Comment in the last post, and a funny nerd snipe comic) — I will return to them below.  But first, here is a simple heuristic solution.