The Kalai-Smorodinski solution for many-objective Bayesian optimization

An ongoing aim of research in multiobjective Bayesian optimization is to extend its applicability to a large number of objectives. While coping with a limited budget of evaluations, recovering the set of optimal compromise solutions generally requires numerous observations and is less interpretable since this set tends to grow larger with the number of objectives. We thus propose to focus on a specific solution originating from game theory, the Kalai-Smorodinsky solution, which possesses attractive properties. In particular, it ensures equal marginal gains over all objectives. We further make it insensitive to a monotonic transformation of the objectives by considering the objectives in the copula space. A novel tailored algorithm is proposed to search for the solution, in the form of a Bayesian optimization algorithm: sequential sampling decisions are made based on acquisition functions that derive from an instrumental Gaussian process prior. Our approach is tested on four problems with respectively four, six, eight, and nine objectives. The method is available in the Rpackage GPGame available on CRAN at https://cran.r-project.org/package=GPGame

Mean field games based on the stable-like processes

In this paper, we investigate the mean field games with K classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process associated with rather general integro-differential generators of L´evy-Khintchine type (with variable coefficients), with the major stress on applications to stable and stable- like processes, as well as their various modifications like tempered stable-like processes or their mixtures with diffusions. We show that nonlinear measure-valued kinetic equations describing the dynamic law of large numbers limit for system with large number N of agents are solvable and that their solutions represent 1/N-Nash equilibria for approximating systems of N agents

Empiricism without Magic: Transformational Abstraction in Deep Convolutional Neural Networks

In artificial intelligence, recent research has demonstrated the remarkable potential of Deep Convolutional Neural Networks (DCNNs), which seem to exceed state-of-the-art performance in new domains weekly, especially on the sorts of very difficult perceptual discrimination tasks that skeptics thought would remain beyond the reach of artificial intelligence. However, it has proven difficult to explain why DCNNs perform so well. In philosophy of mind, empiricists have long suggested that complex cognition is based on information derived from sensory experience, often appealing to a faculty of abstraction. Rationalists have frequently complained, however, that empiricists never adequately explained how this faculty of abstraction actually works. In this paper, I tie these two questions together, to the mutual benefit of both disciplines. I argue that the architectural features that distinguish DCNNs from earlier neural networks allow them to implement a form of hierarchical processing that I call “transformational abstraction”. Transformational abstraction iteratively converts sensory-based representations of category exemplars into new formats that are increasingly tolerant to “nuisance variation” in input. Reflecting upon the way that DCNNs leverage a combination of linear and non-linear processing to efficiently accomplish this feat allows us to understand how the brain is capable of bi-directional travel between exemplars and abstractions, addressing longstanding problems in empiricist philosophy of mind. I end by considering the prospects for future research on DCNNs, arguing that rather than simply implementing 80s connectionism with more brute-force computation, transformational abstraction counts as a qualitatively distinct form of processing ripe with philosophical and psychological significance, because it is significantly better suited to depict the generic mechanism responsible for this important kind of psychological processing in the brain

Horizon-Independent Optimal Prediction with Log-Loss in Exponential Families

We study online learning under logarithmic loss with regular parametric models. Hedayati and Bartlett (2012b) showed that a Bayesian prediction strategy with Jeffreys prior and sequential normalized maximum likelihood (SNML) coincide and are optimal if and only if the latter is exchangeable, and if and only if the optimal strategy can be calculated without knowing the time horizon in advance. They put forward the question what families have exchangeable SNML strategies. This paper fully answers this open problem for one-dimensional exponential families. The exchangeability can happen only for three classes of natural exponential family distributions, namely the Gaussian, Gamma, and the Tweedie exponential family of order 3/2. Keywords: SNML Exchangeability, Exponential Family, Online Learning, Logarithmic Loss, Bayesian Strategy, Jeffreys Prior, Fisher Information1Comment: 23 page

Social Energy - A New Form of Perceiving Capital in Postmodern Economy

The presented paper deals with the issue of social creation of knowledge in the postmodern economic order. The concept of beneficients as a core idea of this conception in connection with thermodynamic analogy in interdisciplinary problem leads to the materialistic and intellectual dual analysis of sustainable phenomenon of development and creation of knowledge. The paper discusses the possibility of a new way of development of institutional economy in the direction of knowledge economy and the change in an approach to an organisation from the traditional systemic to a cooperating community. The presented considerations are a germ of intellectual infrastructure and supporting the process of structural learning and sustainable development with artificial intelligence. It has been suggested that social energy should be considered as an alternative way of perceiving development.entropy, social complex systems, postmodern economy, econophbysics, multiagent economy

Invariance and Randomness in the Nash Program for Coalitional Games

By introducing physical outcomes in coalitional games we note that coalitional games and social choice problems are equivalent (implying that so are the theory of implementation and the Nash program). This clarifies some misunderstandings (in regrad to invariance and randomness), sometimes found in the Nash program.Nash program; implementation; scale invariance; ordinal invariance; randomness