PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison.

PAC-Bayes has recently re-emerged as an effective theory with which one can derive principled learning algorithms with tight performance guarantees. However, applications of PAC-Bayes to bandit problems are relatively rare, which is a great misfortune. Many decision-making problems in healthcare, finance and natural sciences can be modelled as bandit problems. In many of these applications, principled algorithms with strong performance guarantees would be very much appreciated. This survey provides an overview of PAC-Bayes bounds for bandit problems and an experimental comparison of these bounds. On the one hand, we found that PAC-Bayes bounds are a useful tool for designing offline bandit algorithms with performance guarantees. In our experiments, a PAC-Bayesian offline contextual bandit algorithm was able to learn randomised neural network polices with competitive expected reward and non-vacuous performance guarantees. On the other hand, the PAC-Bayesian online bandit algorithms that we tested had loose cumulative regret bounds. We conclude by discussing some topics for future work on PAC-Bayesian bandit algorithms.

Scalable Dissipative Preparation of Many-Body Entanglement.

We present a technique for the dissipative preparation of highly entangled multiparticle states of atoms coupled to common oscillator modes. By combining local spontaneous emission with coherent couplings, we engineer many-body dissipation that drives the system from an arbitrary initial state into a Greenberger-Horne-Zeilinger state. We demonstrate that using our technique highly entangled steady states can be prepared efficiently in a time that scales polynomially with the system size. Our protocol assumes generic couplings and will thus enable the dissipative production of multiparticle entanglement in a wide range of physical systems. As an example, we demonstrate the feasibility of our scheme in state-of-the-art trapped-ion systems.

Grand unification and enhanced quantum gravitational effects.

In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if higher dimensional operators induced by gravity are taken into consideration. We show that the generic size of, and the uncertainty in, these effects from gravity can be larger than the two-loop corrections typically considered in renormalization group analyses of unification. In some cases, gravitational effects of modest size can render unification impossible.