The title of this essay“On finding an ideal partner for life” is the subtitle of a recent blog essay by professor Ho (何毓琦):

Q&A with Tsinghua Students (III) - On Finding An Ideal Partner For Life

http://www.sciencenet.cn/m/user_content.aspx?id=276944

Professor Ho described this important topic from the perspective of “decision and control” and included two major components in his descriptions: (1) a task of stochastic optimization in searching for a partner to get married and (2) a life-long process of adaptation and learning to have fun while getting there (i.e., to finally have an ideal partner).

I happen to be also interested in this subject and have also been spending certain time on researching it. So, I made some comments on his blog to expand his central ideas in a little bit more detail. Hopefully, my explanations may help more readers to “strive towards the optimum through disagreements, quarrels, compromises, understanding, joy, discovery, and ultimate fulfillment”, as professor Ho hoped for.

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I completely agree with professor Ho’s view on this matter. For those who want to learn more on the technical details about the second aspect of professor Ho’s view of “adaptation and learning”, please read the discussions on the following two blog articles:

Go, get married, now! [coolboy]
http://blog.hjenglish.com/coolboy/archive/2005/06/28/77822.html

Is love powerful? [coolboy]
http://blog.hjenglish.com/coolboy/archive/2006/02/07/227419.html

Through an “adaptation and learning” process, it is well said that “getting there is all the fun”. However, most people still hope to start an adaptation and learning process from a good initial condition. Hence, a natural question one wonders would be: can one or how can one put some efforts in the “stochastic optimization” of finding a good life partner before the marriage so that one would have a good initial condition to start the adaptation and learning process?

One plausible solution to this important and practical problem associated with the “stochastic optimization” was given in one of my previous comments and I think it is worth copying here again:

On Optimal Control

http://www.sciencenet.cn/m/user_content.aspx?id=209522

[3]Coolboy:【When there exists “uncertainty” in a system and one has to “fly with maximum speed in the direction of current position and B”, one had better to realize that it is not worthwhile spending great efforts on evaluating local gradient at each step accurately when the “current position” is still close to A and far away from B. If one evaluates the early stage gradient with little accuracy but great efficiency, and gradually increases its accuracy as the iteration solution approaches B, it is possible to avoid the notorious exponential growth problem for the multivariable cost functions.】

In brief, it says that an efficient and appropriate way of performing “stochastic optimization” is to gradually increase the efforts of searching at each step so that “THE optimal solution on expected or average value” can be achieved with the limited or a given resource. Implied in this kind of searching processes is that people often get more experienced when they repeat similar processes.

The next question is: what is or do we have a recipe/algorithm for optimal searching? The answer to this question has also been given in another comment of mine on professor Ho's blog:

Warren Buffett’s Ten Rules for Success

http://www.sciencenet.cn/m/user_content.aspx?id=38150

[4]Coolboy:【When we were in college, we learnt a lesson in our English class entitled “How to Study” that introduced an SQ3R strategy on how to study efficiently: Survey, Question, Read, Recite, and Revise. This SQ3R strategy can also be applied to many other things including how to find a good girlfriend for a boy or how to find a good boyfriend for a girl. For example, you first go through a “survey” process by excluding those who are too old or too young, too this or too that. Then you “question”, casually asking “are you from North or South?” “What color do you like most?” “Do you like seafood or can you cook a nice fish dish?” etc. The measure of how much you can “read” her mind or vice versa should give you an idea of how much commonality you two have. You then review how much you are able to “recite” what you have told her in previous conversation(s), which should give you an objective measure of how much you are actually close to her. If you find the overall score too low after certain period, then you “revise” it to switch to a different one.】

So far, all the discussions have been limited to a qualitative level though both professor Ho and I have used some scientific terminologies. Since many readers of this blog are scientists, it is also worthwhile pointing to the direction of how to implement the above ideas in a precise or quantitative way. I put forward a similar argument in a recent discussion on a hot topic of global warming:

关于全球气候变暖

http://bbs.lasg.ac.cn/bbs/thread-42150-3-1.html

Coolboy:【So far, we have being talking about hydrological cycle and precipitation extremes in a quantitative or a scientific way in which numbers or logical reasoning or facts are the most important. In the early stage of the discussion, we have also mentioned the critical difference between scientific research and philosophical arguments. Therefore, it might be interesting or solely for the purpose of comparison to see a few pieces of writings on hydrological cycle and precipitation extremes in a qualitative manner or from a philosophical point of view. 】

Here, I think one very useful reference that gives great details on modern “stochastic optimization” is the following book:

Spall, J. C., 2003: Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control.  John Wiley & Sons, Inc., New York, 595 pp.

Chapter 7 of the above book contains the algorithm of implementing the original idea that “evaluates the early stage gradient with little accuracy but great efficiency, and gradually increases its accuracy as the iteration solution approaches B.”

Professor Ho mentioned Kalman filter in his replies to my above comments. In terms of the relative importance of determinant versus randomness, we probably can divide the stochastic optimization problems into two categories: (1) those where the determinate processes are dominant with small modifications coming from randomness and (2) those we know little about precise laws governing their changes due to randomness that makes the major contributions to system variations. One well-known example in the first category is the change and control of the state of a spacecraft (or any flying object) where stochastic uncertainties only slightly modify the known dynamical system. In this category, the Kalman filter is always the best method/approach to solve the stochastic optimization problems BECAUSE the Kalman filter fully utilizes the available knowledge/resource of the determinate dynamical system. On the other hand, if one likes to optimize a network of traffic flows by appropriately setting the timings of the traffic lights at all the interactions there is hardly any determinate law that will tell us, as a first order approximation, how the flow will evolve with time. In this case, the gradient needs to be evaluated entirely by the stochastic approximations.

An introductory essay on Kalman filter is given below:

A physicist’s view on Kalman filter  [coolboy]

http://blog.hjenglish.com/coolboy/archive/2008/09/13/1169992.html