Interdicting a criminal with limited police resources is a challenging task as the criminal changes location over time. The size of the large transportation network further adds to the difficulty of this scenario. To tackle this issue, we consider the concept of a layered graph. At each time stamp, we create a copy of the entire transportation network to track the possible movements of both players, the attacker and the defenders. We consider a Stackelberg game in a dynamic crime scenario where the attacker changes location over time while the defenders attempt to interdict the attacker on his escape route. Given a set of defender strategies, the optimal attacker strategy is determined by applying Dijkstra's algorithm on the layered networks. Here, the attacker aims to minimize while the defenders aim to maximize the probability of interdiction. We develop an approximation algorithm on the layered networks to find near-optimal strategy for defenders. The efficacy of the developed approach is compared with the adopted MILP approach. We compare the results in terms of computational time and solution quality. The quality of the results demonstrates the need for the developed approach, as it effectively solves the complex problem within a short amount of time.

Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy-preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential objective for the Machine Learning community. Previously proposed approaches only consider single-level programming. In this paper, we extend existing single-level optimization programming approaches and thus propose Differentiating through Bilevel Optimization Programming (BiGrad) for end-to-end learning of models that use Bilevel Programming as a layer. BiGrad has wide applicability and can be used in modern machine learning frameworks. BiGrad is applicable to both continuous and combinatorial Bilevel optimization problems. We describe a class of gradient estimators for the combinatorial case which reduces the requirements in terms of computation complexity; for the case of the continuous variable, the gradient computation takes advantage of the push-back approach (i.e. vector-jacobian product) for an efficient implementation. Experiments show that the BiGrad successfully extends existing single-level approaches to Bilevel Programming.

Operating vehicles in adversarial environments between a recurring origin-destination pair requires new planning techniques. Such a technique, presented in this paper, is a game inspired by Ruckle’s original contribution. The goal of the first player is to minimize the expected casualties undergone by a moving agent. The goal of the second player is to maximize this damage. The outcome of the game is obtained via a linear program that solves the corresponding minmax optimization problem over this outcome. The formulation originally proposed by Feron and Joseph is extended to different environment models in order to compute routing strategies over unstructured environments. To compare these methods for increasingly accurate representations of the environment, a grid-based model is chosen to represent the environment and the existence of a sufficient network size is highlighted. A global framework for the generation of realistic routing strategies between any two points is described. Finally the practicality of the proposed framework is illustrated on real world environments.

We try to perform geometrization of psychology by representing mental states, <>, by points of a metric space, <>. Evolution of ideas is described by dynamical systems in metric mental space. We apply the mental space approach for modeling of flows of unconscious and conscious information in the human brain. In a series of models, Models 1-4, we consider cognitive systems with increasing complexity of psychological behavior determined by structure of flows of ideas. Since our models are in fact models of the AI-type, one immediately recognizes that they can be used for creation of AI-systems, which we call psycho-robots, exhibiting important elements of human psyche. Creation of such psycho-robots may be useful improvement of domestic robots. At the moment domestic robots are merely simple working devices (e.g. vacuum cleaners or lawn mowers) . However, in future one can expect demand in systems which be able not only perform simple work tasks, but would have elements of human self-developing psyche. Such AI-psyche could play an important role both in relations between psycho-robots and their owners as well as between psycho-robots. Since the presence of a huge numbers of psycho-complexes is an essential characteristic of human psychology, it would be interesting to model them in the AI-framework.