Why a Population Converges to Stability

Gradient Descent Converges to Minimizers

We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.

Reinforcement learning with function approximation converges to a region

Why so much stability ?

Niemi (1969), in an important but neglected paper, found that when orderings were drawn from a simulation based on the impartial culture, the greater the proportion of voter orderings that were single-peaked (a condition he called partial single-peakedness), the more likely was there to be a transitive group ordering. Niemi also found that the likelihood of transitivity increased with n, group ...

Why Price Stability ?

The Maastricht Treaty contains the following statutory mandate: “The primary objective of the ESCB shall to be to maintain price stability.“ But why attach such importance to price stability and what does “price stability” mean? The latter question contains an historical component, the former is of a theoretical nature. I will therefore deal with the “what” and the “why” of my theme in the foll...

Reinforcement Learning with Function Approximation Converges to a Region

Many algorithms for approximate reinforcement learning are not known to converge. In fact, there are counterexamples showing that the adjustable weights in some algorithms may oscillate within a region rather than converging to a point. This paper shows that, for two popular algorithms, such oscillation is the worst that can happen: the weights cannot diverge, but instead must converge to a bou...