140 research outputs found
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
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