Free Energy and the Generalized Optimality Equations for Sequential Decision Making

The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees that include both adversarial and stochastic environments. We derive generalized sequential optimality equations that not only include the Bellman optimality equations as a limit case, but also lead to well-known decision-rules such as Expectimax, Minimax and Expectiminimax. We show how these decision-rules can be derived from a single free energy principle that assigns a resource parameter to each node in the decision tree. These resource parameters express a concrete computational cost that can be measured as the amount of samples that are needed from the distribution that belongs to each node. The free energy principle therefore provides the normative basis for generalized optimality equations that account for both adversarial and stochastic environments.Comment: 10 pages, 2 figure

Smooth markets: A basic mechanism for organizing gradient-based learners

With the success of modern machine learning, it is becoming increasingly important to understand and control how learning algorithms interact. Unfortunately, negative results from game theory show there is little hope of understanding or controlling general n-player games. We therefore introduce smooth markets (SM-games), a class of n-player games with pairwise zero sum interactions. SM-games codify a common design pattern in machine learning that includes (some) GANs, adversarial training, and other recent algorithms. We show that SM-games are amenable to analysis and optimization using first-order methods.Comment: 18 pages, 3 figure

Contract enforcement, litigation, and economic development

This paper introduces a model of litigation in a growth framework. Investors use litigation to enforce their financial contracts with entrepreneurs. A contest ensues in which both agents hire lawyers to increase their probability of winning the trial. The issue and the cost of the contest determine how much investors are willing to lend. More lawyers are hired when judicial efficiency is lower and damages are higher. Higher judicial efficiency and tighter restrictions on the supply of lawyers benefit the economy, while the impact of higher damages is ambiguous. Some empirical evidence is also presented