Alternative Restart Strategies for CMA-ES

This paper focuses on the restart strategy of CMA-ES on multi-modal functions. A first alternative strategy proceeds by decreasing the initial step-size of the mutation while doubling the population size at each restart. A second strategy adaptively allocates the computational budget among the restart settings in the BIPOP scheme. Both restart strategies are validated on the BBOB benchmark; their generality is also demonstrated on an independent real-world problem suite related to spacecraft trajectory optimization

Clues About Bluffing in Clue: Is Conventional Wisdom Wise?

We have used the board game Clue as a pedagogical tool in our course on Artificial Intelligence to teach formal logic through the development of logic-based computational game-playing agents. The development of game-playing agents allows us to experimentally test many game-play strategies and we have encountered some surprising results that refine “conventional wisdom” for playing Clue. In this paper we consider the effect of the oft-used strategy wherein a player uses their own cards when making suggestions (i.e., “bluffing”) early in the game to mislead other players or to focus on acquiring a particular kind of knowledge. We begin with an intuitive argument against this strategy together with a quantitative probabilistic analysis of this strategy’s cost to a player that both suggest “bluffing” should be detrimental to winning the game. We then present our counter-intuitive simulation results from playing computational agents that “bluff” against those that do not that show “bluffing” to be beneficial. We conclude with a nuanced assessment of the cost and benefit of “bluffing” in Clue that shows the strategy, when used correctly, to be beneficial and, when used incorrectly, to be detrimental

Liouville property, Wiener's test and unavoidable sets for Hunt processes

Let $(X,\mathcal W)$ be a balayage space, $1\in \mathcal W$, or - equivalently - let $\mathcal W$ be the set of excessive functions of a Hunt process on a locally compact space $X$ with countable base such that $\mathcal W$ separates points, every function in $\mathcal W$ is the supremum of its continuous minorants and there exist strictly positive continuous $u,v\in \mathcal W$ such that $u/v\to 0$ at infinity. We suppose that there is a Green function $G>0$ for $X$, a metric $\rho$ on $X$ and a decreasing function $g\colon[0,\infty)\to (0,\infty]$ having the doubling property such that $G\approx g\circ\rho$. Assuming that the constant function $1$ is harmonic and balls are relatively compact, is is shown that every positive harmonic function is constant (Liouville property) and that Wiener's test at infinity shows, if a given set $A$ in $X$ is unavoidable, that is, if the process hits $A$ with probability one, wherever it starts. An application yields that locally finite unions of pairwise disjoint balls $B(z,r_z)$, $z\in Z$, which have a certain separation property with respect to a suitable measure $\lambda$ on $X$ are unavoidable if and only if, for some/any point $x_0\in X$, the series $\sum_{z\in Z} g(\rho(x_0,z))/g(r_z)$ diverges. The results generalize and, exploiting a zero-one law for hitting probabilities, simplify recent work by S. Gardiner and M. Ghergu, A. Mimica and Z. Vondra\v cek, and the author

Characterization of symmetric monotone metrics on the state space of quantum systems

The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, initiated by Morozova, Chentsov and Petz, of these metrics by providing a closed and tractable formula for the set of Morozova-Chentsov functions. In addition, we provide a continuously increasing bridge between the smallest and largest symmetric monotone metrics.Comment: Minor revision with new title and abstract as suggested by a refere