Rough solutions of the Einstein Constraint Equations on Asymptotically Flat Manifolds without Near-CMC Conditions

In this article we consider the conformal decomposition of the Einstein constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in 2009 by Holst, Nagy, and Tsogtgerel and by Maxwell, we establish existence of coupled non-CMC weak solutions for AF manifolds. As is the case for the analogous existence results for non-CMC solutions on closed manifolds and compact manifolds with boundary, our results here avoid the near-CMC assumption by assuming that the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small. The non-CMC rough solutions results here for AF manifolds may be viewed as extending to AF manifolds the 2009 and 2014 results on rough far-from-CMC positive Yamabe solutions for closed and compact manifolds with boundary. Similarly, our results may be viewed as extending the recent 2014 results for AF manifolds of Dilts, Isenberg, Mazzeo and Meier, and of Holst and Meier; while their results are restricted to smoother background metrics and data, the results here allow the regularity to be extended down to the minimum regularity allowed by the background metric and the matter, further completing the rough solution program initiated by Maxwell and Choquet-Bruhat in 2004.Comment: 82 pages. Version 2 has minor changes reflecting comments and minor typos fixed. Version 3 updates a bibliography entr

Emergence of Addictive Behaviors in Reinforcement Learning Agents

This paper presents a novel approach to the technical analysis of wireheading in intelligent agents. Inspired by the natural analogues of wireheading and their prevalent manifestations, we propose the modeling of such phenomenon in Reinforcement Learning (RL) agents as psychological disorders. In a preliminary step towards evaluating this proposal, we study the feasibility and dynamics of emergent addictive policies in Q-learning agents in the tractable environment of the game of Snake. We consider a slightly modified settings for this game, in which the environment provides a "drug" seed alongside the original "healthy" seed for the consumption of the snake. We adopt and extend an RL-based model of natural addiction to Q-learning agents in this settings, and derive sufficient parametric conditions for the emergence of addictive behaviors in such agents. Furthermore, we evaluate our theoretical analysis with three sets of simulation-based experiments. The results demonstrate the feasibility of addictive wireheading in RL agents, and provide promising venues of further research on the psychopathological modeling of complex AI safety problems