Lean management categorification

A. \( LM \rightarrow \quad learning \)

It is surprising and very comforting to note that the very popular 'lean startup' by Eric Ries or the 'getting to plan B' by Mullins & Komisar (KM) demonstrates an obvious relationship between learning to learn (L2L) and lean management (LM)
$$ LM \rightarrow \quad learning $$
Maybe because entrepreneurs have essentially skin in the game , as should have all learner / modeler.
At the heart of lean management, there is the idea that the company is essentially a place of learning; let's count words:
Learn: 292
Know: 123
Problem: 177
Solv: 38
And precisely, a scientific process:
Hypotheses: 67
Assumption: 73
Theor: 31
Test: 206
Feedback: 86
Valid: 74
Experiment: 171
System: 139
Scien: 47
Fail: 132 (yes, failure is included in the scientific learning package!)

LM is the place of a surprising symmetry:
\begin{array}{r c l}
\ product & \quad & startup \\
 \uparrow \quad \downarrow \quad & \rightarrow & \uparrow \quad \downarrow  \quad \\
 learning & \quad & customer \\
\end{array}

The traditional causality is: I learn to produce; LM puts forward : I produce to learn!
Fordism approach is in (product) push mode: Ford produces, the customer buys
LM is in (informational) pull mode: the startup learns from its customer
"The learning about how to build a sustainable business is the outcome of those experiments. For startups, that information is much more important than dollars, awards, or mentions in the press, because it can influence and reshape the next set of ideas. "
"For startups, the role of strategy is to help figure out the right questions to ask"

In detail, the functor LM → Learning is:

\begin{array}{r c l}
\ product & \quad & model \\
 \uparrow \quad \downarrow \quad & \rightarrow & \uparrow \quad \downarrow  \quad \\
 customer & \quad & data \\
\end{array}


More precisely, everything is dynamic: at all times \( t \) LM seeks a minimum viable product, hence the correspondence
\begin{array}{r c l}
\ MVP_t & \rightarrow & model_t \\
\ customer_t & \rightarrow & data_t \\
\end{array}
In fact a set \( data_t \) of data is attached to \( MVP_t \) ( \( model_t \) ): this is the information available at \(t \)

B. Overfit, Regularization


The key to the endless process LM is what corresponds in ML to Active Learning: sequential acquisition of new data:
$$ Model_t → data_t → model_{t + 1} \rightarrow data_{t + 1} ...$$
or in the form of a cycle :

\begin{array}{r c l}
\ model & &  \\
\ \downarrow \quad  \uparrow & &  \\
\ data & & \\
\end{array}
So what we have here is really a learning path
The model is at once:
a. A representation of the domain and,
b. A decision function that allows the exploration of the domain in order to acquire new data.

This learning diagram is similar to the Multi-Armed Bandit (MAB): at each \( t \), ​​one decides which arm to operate, and one observes the reward.
a. Ex1: A / B testing protocol
b. Ex2: H&M in KM, different styles are tested almost simultaneously, and one favors the most successful.

Obviously exploration is expensive, and the whole question is to stay alive until the (relative) completion of the learning process ... this is where the concept of lean / waste (82 occurrences in the text) is looming.
Ries is particularly good at telling his own experience at IMVU. The whole pararagraph 'Talking to customers' is a piece of anthology, absolutely hilarious: the confrontation between the engineer and the 'seventeen-year-old girl' announces a tragi-comedy, and was for Ries the revelation that he has basically lost his time for 6 months! 'There's obviously something wrong', 'deal breaker', 'utterly / fundamentally flawed'...
Ries : 'Here's the question that bothered me most of all: if the goal of these months was to learn these important insights about customers, why did it take so long? How much of our effort contributed to the essential lessons we needed to learn? Could we have learned those lessons earlier if I had not been focused on making the product "better" by adding features and fixing bugs?
Here Ries has a seemingly surprising paragraph if one reads it from the coign of vantage of Statistical Learning: 'optimization versus learning'. In the context of statiscal learning, optimization is almost synonymous with learning.
In line with 'learning fallacy', I would say we have here a case of 'tree hiding the forest': the 6 months lost developing unnecessary features to IMVU, this is an example of over-optimization : This 'model' is demolished when confronting new data.
Carrying the metaphor / functor \( Lean \rightarrow Learn \) further, we get
$$ waste \rightarrow overfit$$
We can be tempted to talk about dynamic regularization: we are looking for the simplest and least expensive model (product) that 'fit' the data.
More precisely: if we calculate the difference between:
a. the ex-post reward \( r_t \): not only measurement of the product's suitability to customer, but more generally learning rate
b. and the ex-ante cost of R&D  \(c_t \),
The regularization at \( t + 1 \) is done according to \( r_t - c_t \).
It is obviously advantageous for this measurement to be as continuous as possible: this is the key message of the LM: the increment of time, or cycle duration, must be as low as possible. 'The biggest advantage of working in small batches is that quality problems can be identified much sooner'.
The evaluation of \( r_t \) is anything but obvious. As Ries explains at length, growth or other 'vanity metrics' do not prove that \( r_t-c_t > 0 \). The 'actionable metrics' must make it possible to correctly evaluate \( r_t \), according to Ries.
Of course the LM approach gives no guaranty to converge before running out of cash!


C. symmetries?

But most notably, Ries gives no explicit method to guess the symmetries of the domain.

This part is entirely human black box, discretionary. Assumptions come from art, not science. 'As far as exploration is costless and continuous, you can explore randomly' seems to be the cartoon message of Ries. For example, in the case of Caroline at HP, nothing is said except 'testing'.
When Ries insists on metrics (or post analysis), in fact it is indeed representation, therefore symmetries fundamentally. For example, in the case of Grockit, the initial assumption itself is revised: 'In fact, over time, through dozens of tests, it became clear that the key to student engagement was to offer them a combination of social and solo features. Students preferred having a choice of how to study.'
But a fully symmetrized $$ Social \leftrightarrow solo $$
would have warned against a pure social approach.
Actually, we can argue that Ries gives tree heuristics to guess the symmetries:
 a. The five whys has a strong flavor of hierarchical discovery, and in fact target (ground) symmetries.
 b. Transfer learning: notably from manufacturing, and Toyota.
 c. Catalog of Pivots:
  Zoom-in / out
  Customer segment (or need)
  Value capture
  Engine of growth
  ..
In all cases, Category Theory is closer : isn't "Pivot" a wonderful intuition of ... symmetry ?
Of course, MK's 'analogs and antilogs' is quite in line with Cat.
Incidentally, Ries gives examples of \( Learn * customer \), \( Learn *student \) actions without ever giving a model other than 'testing'. To give a single example, the \( social \leftrightarrow solo \) symmetry seems linked to concepts like mimicry (CF for example the recent theory of mirror neurons) on the one hand and to something as a need of intellectual order / Compression (CF the magical theory of creativity of Schmidhuber)
The statistical learning is: \( Learn * data \), and many methods exist.
But it is especially in the case of Sciences (Mathematics, Physics, Biology, ...) that the action
$$ S = Learn * phenomena $$
manifests oneself through a gigantic theoretical and empirical production.
If the action is \( Learn * Object \), then it seems interesting to learn the functor
$$ Learn * X \rightarrow S $$
whatever X is
In finance (and beyond in social science), the functor was formalized through the econophysics. To give an example: RFIM = Random Field Ising model is according to Bouchaud et al. a paradigm - i.e. a symmetry - plausible, CF eg "Crises and collective socio-economic phenomena: simple models and challenges"

Incidentally, the recent interest of physics for statistical learning (CF Mezard 'physics-statistics-and-information-the-defi-of-mass-data' in La Jaune et la Rouge, the Mallat site at ENS, "Learning as categorification III ", etc.) marks a re-symmetrization:
$$ S \leftrightarrow Learn * X $$
But as Mezard says: "Contrary to what is sometimes said, the irruption of massive data into the study of complex systems is not going to take the place of theory. It is always necessary and even more difficult to understand, analyze, and build a model, but the theorist can rely on new and powerful statistical tools. "

Conclusion: The Lean Management approach is motivated mainly by the constraint of profitability. This constraint, if it has the merit of bringing reflection (from the entrepreneur) back to (the objective observation of) reality, is essentially a  transfer from the (~millenary) experimental method in sciences.
Why not to push this transfer / Categorification further ?

No equilibrium theorem

1. in the classic "How markets slowly digest", Bouchaud et. al (B): "Then begins a kind of hide and seek game, where each side attempts to guess the available liquidity on the other side. A 'tit-for-tat' process then starts, whereby market orders trigger limit orders and limit orders attracts market orders ", 6.5.4
2. Incidentally, tit-for-tat (TT) refers to a strategy of the iterated PD (prisoner dilemma)
3. what can be the meaning of the looming of game theory GT within a paper at distance of Rational Equilibrium approach and critic of K85?
4. We can argue a methodological isomorphism between theoretical physics TP (Physics and learning) and GT
\begin{array}{r c l}
\  TP & \leftrightarrow & GT \\
 (SO (3) / local / etc) \quad symmetries & \rightarrow & (infinite) \quad  strategic \quad regress \\
\end{array}
5. See, for example, 'Rational interaction', 'game theory, symmetry, and scientific discovery', HW Brock
6. We would be tempted to conclude that B "fail to learn": he does not recognize the natural (theoretical) space of the domain he is studying, i.e. the symmetries of the domain
But GT suggests that "physical" dynamics have a good chance of lapsing in finance
7. In physics the causality \( F ^ i = m * a ^ i \) (or even the equations of the field in RG) establishes the causal link between force and acceleration
8. K is still in this paradigm: \( imb = 1 / λ * δp \) CF 'mm second law'
9. As is often the case with this type of article, equilibrium is obtained conditionally only by assumptions of implicit coordination that are not realistic (K explicitly excludes any form of manipulation, insider and mm assume the optimal strategy of other agents)
10. A natural framework is rather the PD: in a game of sharing P&L (= long term equilibrium), the two agents can play cooperation, ie a kind of à la Kyle equilibrium corresponding to a kind of average historical behavior of these Agents), or deviate significantly from them, fooling other expectations
11. More precisely, in K, the fundamental symmetry is written simply
\begin{array}{r c l}
\ & K & \\
 mm & \rightarrow & insider \\
\end{array}
Mm and insider know all about one another, the reasoning rules are CK (common knowledge). They could reverse their respective roles, but they do not, symmetry is only valid in K(nowledge) and not in A(ct)
12. The literature on PD is considerable (and for good reason), but in iterated strategies such as TT or win-stay lose-switch appear not only theoretically (including in an evolutionary framework) but empirically observed (CF Axelrod 84, 'Evolutionary dynamics', Nowak)
13. Note that this takes place in a framework of payoff without any uncertainty: the matrix of the payoffs is perfectly known.
There is therefore no stake in learning a representation of the world
14. Projected in the framework of K, this amounts to saying that the representation (imb) is not an issue
On the other hand, \( \lambda \) can not be stable
And this non-stationarity is fundamental, in the sense that it results from the space symmetry of space (GT) space (finance)
In a GT frame, we now have a substitution in Act between mm and insider:
\begin{array}{r c l}
\ & K, A & \\
 mm & \rightarrow & insider \\
\end{array}
The mm can mimic the insider, and reciprocally

On agent-based models' symmetries

1. I see 4 questions on the methodology of agents-based models, emphasizing the MG: CF 'Minority Games', Challet, Marsili, Zhang
2. pb1: minority (for MG): why not a majority game?
CF 'the $ -game', Andersen, Sornette
3. pb2: rationality of agents? For example for MGs:
a. Basic MG: always active
b. Grand canonical MG: active or not, one single strategy, does not take into account its market impact
c. 'Nash' MG: takes into account his market impact, but does not reason on the presence of others
4. pb3: microstructure? For example for MGs:
a. basic MG: no producers, no market maker
b. evolved MG: producers, no market maker (but see 'the $ -game')
Econophysics have only been recently focused on microstructure (CF eg Farmer)
5. pb4: what is the right symmetry: unconscious (/ emergence / animal / ecology) or conscious (/ convention / human / economy) cooperation?
6. pb4 is perhaps the bottom line: if the market logic is the division between producer and speculator (in MG, or market maker in the $ -game), is it rational from these (types of ' ) Agents not to re-examine (periodically) the terms of partition?
If so, then the framework of analysis is - a conceptual notch above the ABM - that of the iterated PD: CF 'no equilibrium theorem'
7. the ecological approach, CF Farmer 'market force, ecology, and evolution' adopts a symmetry of physicist / biologist: no cross-speculation.
In the mainstream economic literature, a fortiori in the Game Theory, the symmetry 'infinite regress' is a basic axiom.
But even without assuming this 'difficult' faculty, the iterated prisoner dilemma approach, which falls well within the bounded rationality category (H Simon), goes in the direction of a consciousness of the agents of the strategic essence of the game.
8. In the 'insider / market impact' dialogue, the non-cooperative behaviors are
a. Insider: market impact ++
b. Market maker: front-running

Le Moigne dixit

1. obviously links  exists between systemics and learning

2.
Jean-Louis Le Moigne "La théorie du système générale"
p XI
La méthodologie appelle et est appelée par
l’épistémologie, qui appelle et est appelée par l’éthique,
qui… Si l’on avait interrogé les fichiers des grandes bibliothèques
scientifiques internationales sur le thème des méthodes d’études
des systèmes complexes vers 1975, je présume que l’on aurait
recensé un petit millier d’entrées bibliographiques. Trente ans plus
tard, un appel sur le Web − via un moteur de recherche − nous
propose plus de 350 millions d’entrées dont plusieurs centaines de
centres de recherches universitaires et presque autant de revues
spécialisées. Foisonnement fort significatif et au demeurant
encourageant quant à la capacité d’adaptation d’institutions
souvent tenues pour conservatrices. Si on limite l’examen à ces
‘notables’, on est certes impressionné par cette vitalité, mais on
s’interroge vite : la plupart des études se présentent sous la forme
de créations et d’applications de ‘méthodes de résolution de
problèmes’ présumés déjà posés ou susceptibles de se poser.
Méthodes de plus en plus informatisées ou informatisables qui
laissent souvent encore à la charge des ‘utilisateurs’ la tâche de
formulation de leur problème dans des termes compatibles avec le
langage informatique dans lequel les méthodes peuvent s’appliquer.
Souvent décrites en termes mathématiques et algorithmiques,
(dynamique des systèmes non linéaires, etc.), ces méthodes se
diversifient de mille façons, en s’aidant des ressources de la simulation
informatique (réseaux neuronaux, etc.) ou des ‘raisonnements
qualitatifs’ (‘qualitative reasoning’, ‘case based reasoning’, etc.). Il est
manifeste qu’en se développant, elles suscitent de nouvelles
explorations, de nouveaux questionnements, et suggèrent des
renouvellements progressifs de leur propre problématique.
Mais dans la plupart des cas, on est surpris par la légèreté de la
critique épistémique interne pouvant légitimer le bon usage de ces
méthodes. Et lorsqu’on cherche à identifier ces bases
conceptuelles, on rencontre sans surprise celles que nous livrent
fort bien les mathématiques ensemblistes et probabilistes que l’on
peut aujourd’hui appeler classiques. Le concept de système
complexe est ici un substitut élégant pour dire ‘très grand système
hyper compliqué, identifiable et dénombrable’. Mais le procédé
n’est-il pas trompeur et, d’une certaine façon, dissuasif ?
La parabole de l’ivrogne cherchant la nuit sa clé sous le
réverbère, moins par conviction de l’avoir perdue là que parce que
c’est le seul endroit où il fait clair, permet de souligner l’enjeu : On
développe des méthodologies de résolution peu ou pas
contextualisées, sans s’attacher à expliciter les fins que ces
méthodes sont censées servir. Et on oublie souvent de se doter de
la capacité critique pouvant orienter une interprétation intelligente
et téléologique de leur utilisation.
Dans le même temps, on ne consacre que peu ou pas d’effort
aux développements de méthodes critiques de ‘formulation de
problèmes’. Ceci parce que l’on craint (à juste titre) de ne disposer
pour ce faire que de méthodes heuristiques, tâtonnantes et
formellement peu ‘élégantes’ pour ‘traiter’ ces problèmes de
formulation de problèmes dont l’énoncé même évoluera au fil de
la recherche. On sait que le développement de telles méthodes fut
rarement gratifiant au regard des académies.
Or ce sont précisément ces méthodes de modélisation (et de
méta-modélisation) qu’il importe aujourd’hui de développer à
nouveau lorsqu’on veut aborder l’examen de systèmes complexes,
quels que soient les domaines considérés. Cette prise de
conscience est sans doute encore trop lente dans nos institutions
d’enseignement, mais elle semble s’accélérer depuis quelques
années, assure-t-on, sous la pression des ‘sociétés civiles’ de plus
en plus attentives à leurs responsabilités dans les domaines de leurs
politiques scientifiques. On citera ici quelques lignes d’une sorte de
‘manifeste’ publié par le CNRS Français en 2002 sous le titre
‘Construire une politique scientifique'...

3. promising Categorification of Systems Engineering by Luzeaux :
D. Luzeaux, “A formal foundation of systems engineering,”
in Complex Systems Design & Management. Springer,
2015, pp. 133–144

4. on line : "Category Theory as a Formal Mathematical Foundation
for Model-Based Systems Engineering"
Mohamed A. Mabrok and Michael J. Ryan