Limits of Optimization.

Optimization is about finding the best available object with respect to an objective function. Mathematics and quantitative sciences have been highly successful in formulating problems as optimization problems, and constructing clever processes that find optimal objects from sets of objects. As computers have become readily available to most people, optimization and optimized processes play a very broad role in societies. It is not obvious, however, that the optimization processes that work for mathematics and abstract objects should be readily applied to complex and open social systems. In this paper we set forth a framework to understand when optimization is limited, particularly for complex and open social systems.

Continuous learning of emergent behavior in robotic matter.

One of the main challenges in robotics is the development of systems that can adapt to their environment and achieve autonomous behavior. Current approaches typically aim to achieve this by increasing the complexity of the centralized controller by, e.g., direct modeling of their behavior, or implementing machine learning. In contrast, we simplify the controller using a decentralized and modular approach, with the aim of finding specific requirements needed for a robust and scalable learning strategy in robots. To achieve this, we conducted experiments and simulations on a specific robotic platform assembled from identical autonomous units that continuously sense their environment and react to it. By letting each unit adapt its behavior independently using a basic Monte Carlo scheme, the assembled system is able to learn and maintain optimal behavior in a dynamic environment as long as its memory is representative of the current environment, even when incurring damage. We show that the physical connection between the units is enough to achieve learning, and no additional communication or centralized information is required. As a result, such a distributed learning approach can be easily scaled to larger assemblies, blurring the boundaries between materials and robots, paving the way for a new class of modular "robotic matter" that can autonomously learn to thrive in dynamic or unfamiliar situations, for example, encountered by soft robots or self-assembled (micro)robots in various environments spanning from the medical realm to space explorations.