A proposal for a tool that helps handling variability and remains compliant with falsifiability

On one hand, automatics is based on proofs before the experiment in order to validate an a priori (partially) known deterministic interaction between the robot and its environment; in return, the experimenter may expect the reliability of the real system based on his model. On another hand, statistical methods are used when the environment is supposed unknown; in return, the robot may own adaptation capabilities but its behavior is not predictable before the experiment and is not necessary reliable. We believe that the core issue for the first approach (that we call deterministic approach) relies on the fact it cannot handle the variety of all the possible situations in an unconstrain environment (we call this the variability issue). Oppositely, we think that the statistical approach is essentially missing a validating stage before the experiment in order to possibly falsify a proposed model. The aim of this article is to suggest a methodology that combines both a validating stage before the experiment and the creation of models that handle unknown environments. To do this, we suggest models that own a validation statement and internal parameters that fix a compromise between falsifiability and robustness. For simple cases, we show that it is possible to fix internal parameters in order to meet the two antagonist constraints. As a consequence, we stress that the precision of the model has a lower bound and we determine a Heisenberg-like uncertainty principle. 1. Context of our study 1.1 The variability challenge Nowadays, several scientific areas are facing complexity. Nature is complex by itself; artifacts made by humans may be too. However, in some cases, scientific breakthroughs give a framework that breaks the complexity and permit to reduce a physical phenomenon to a model. For example, the trajectory of Earth (which is a complex system by itself) around the Sun may be well approximated by using only a few variables (mass, velocity and position) and by neglecting the other planets of the solar system. Those cases, which I call ”favorable cases”, gave birth to scientific theories (like Newton’s theory of gravitation) which are falsifiable in Popper’sense (Popper, 1968). In particular, these theories enable the prediction of what will happen and what will never happen in reality. At the opposite, biological systems even the simplest may not be reduced in such a way, mainly because they are bound to variability. Variability appears when an entity behaves differently when facing apparently equal situations or when apparently equal entities behaves differently when facing the same situation. In these cases, a system or components of a system cannot be easily isolated to model a phenomenon in an analytical manner. It is interesting to draw a parallel with the study of the behavior of a mobile robot which interacts with a complex and a priori unknown environment. Even if human have built the robot and has programmed it, one must admit that it is not possible to know precisely before the experiment what it will do and will never do: the robot behavior is not really predictable (see (Nehmzow and Walkery, 2003)). Hence it is not possible to calculate the reliability of the robot behavior before the experiment. The biological and artifact cases share the fact that something in the phenomenon remains unknown by the scientist but cannot be neglected; this carries poor or context dependent results. Ad hoc algorithms or learning capabilities may be implemented for artifacts to cope with discovery of a priori unknown characteristics of the environment. However, taking a very simple example from the reinforcement learning domain ha l-0 03 42 19 6, v er si on 1 29 N ov 2 00 8 Author manuscript, published in "Towards Autonomous RObotic Systems (TAROS 2005), London : United Kingdom (2005)"