Behavioral analysis of differential hebbian learning in closed-loop systems

Understanding closed loop behavioral systems is a non-trivial problem, especially when they change during learning. Descriptions of closed loop systems in terms of information theory date back to the 1950s, however, there have been only a few attempts which take into account learning, mostly measuring information of inputs. In this study we analyze a specific type of closed loop system by looking at the input as well as the output space. For this, we investigate simulated agents that perform differential Hebbian learning (STDP). In the first part we show that analytical solutions can be found for the temporal development of such systems for relatively simple cases. In the second part of this study we try to answer the following question: How can we predict which system from a given class would be the best for a particular scenario? This question is addressed using energy, input/output ratio and entropy measures and investigating their development during learning. This way we can show that within well-specified scenarios there are indeed agents which are optimal with respect to their structure and adaptive properties