From Simplistic to Complex Systems in Economics

The applicability of complex systems theory in economics is evaluated and compared with standard approaches to economic theorizing based upon constrained optimization. A complex system is defined in the economic context and differentiated from complex systems in physio-chemical and biological settings. It is explained why it is necessary to approach economic analysis from a network, rather than a production and utility function perspective, when we are dealing with complex systems. It is argued that much of heterodox thought, particularly in neo-Schumpeterian and neo-Austrian evolutionary economics, can be placed within a complex systems perspective upon the economy. The challenge is to replace prevailing 'simplistic' theories, based in constrained optimization, with 'simple' theories, derived from network representations in which value is created through the establishment of new connections between elements.

A Resource-Constrained Optimal Control Model for Crackdown on Illicit Drug Markets

In this paper we present a budget-constrained optimal control model aimed at finding the optimal enforcement profile for a street-level, illicit drug crackdown operation. The objective is defined as minimizing the number of dealers dealing at the end of the crackdown operation, using this as a surrogate measure of residual criminal activity. Analytical results show that optimal enforcement policy will invariably use the budget resources completely. Numerical analysis using realistic estimates of parameters shows that crackdowns normally lead to significant results within a matter of a week, and if they do not, it is likely that they will be offering very limited success even if pursued for a much longer duration. We also show that a ramp-up enforcement policy will be most effective in collapsing a drug market if the drug dealers are risk-seeking, and the policy of using maximum enforcement as early as possible is usually optimal in the case when the dealers are risk averse or risk neutral. The work then goes on to argue that the underlying model has some general characteristics that are both reasonable and intuitive, allowing possible applications in focussed, local enforcement operations on other similar illegal activities.crackdown enforcement;illicit drug markets;optimal control

f-Divergence constrained policy improvement

To ensure stability of learning, state-of-the-art generalized policy iteration algorithms augment the policy improvement step with a trust region constraint bounding the information loss. The size of the trust region is commonly determined by the Kullback-Leibler (KL) divergence, which not only captures the notion of distance well but also yields closed-form solutions. In this paper, we consider a more general class of f-divergences and derive the corresponding policy update rules. The generic solution is expressed through the derivative of the convex conjugate function to f and includes the KL solution as a special case. Within the class of f-divergences, we further focus on a one-parameter family of $\alpha$-divergences to study effects of the choice of divergence on policy improvement. Previously known as well as new policy updates emerge for different values of $\alpha$. We show that every type of policy update comes with a compatible policy evaluation resulting from the chosen f-divergence. Interestingly, the mean-squared Bellman error minimization is closely related to policy evaluation with the Pearson $\chi^2$-divergence penalty, while the KL divergence results in the soft-max policy update and a log-sum-exp critic. We carry out asymptotic analysis of the solutions for different values of $\alpha$ and demonstrate the effects of using different divergence functions on a multi-armed bandit problem and on common standard reinforcement learning problems