3,902 research outputs found
Comparison between algebraic and topological K-theory of locally convex algebras
This paper is concerned with the algebraic K-theory of locally convex
algebras stabilized by operator ideals, and its comparison with topological
K-theory. We show that the obstruction for the comparison map between algebraic
and topological K-theory to be an isomorphism is (absolute) algebraic cyclic
homology and prove the existence of an 6-term exact sequence.
We show that cyclic homology vanishes in the case when J is the ideal of
compact operators and L is a Frechet algebra with bounded app. unit. This
proves the generalized version of Karoubi's conjecture due to Mariusz Wodzicki
and announced in his paper "Algebraic K-theory and functional analysis", First
European Congress of Mathematics, Vol. II (Paris, 1992), 485--496, Progr.
Math., 120, Birkh\"auser, Basel, 1994.
We also consider stabilization with respect to a wider class of operator
ideals, called sub-harmonic. We study the algebraic K-theory of the tensor
product of a sub-harmonic ideal with an arbitrary complex algebra and prove
that the obstruction for the periodicity of algebraic K-theory is again cyclic
homology.
The main technical tools we use are the diffeotopy invariance theorem of
Cuntz and the second author (which we generalize), and the excision theorem for
infinitesimal K-theory, due to the first author.Comment: Final version, to appear in Advances in Mathematic
VIME: Variational Information Maximizing Exploration
Scalable and effective exploration remains a key challenge in reinforcement
learning (RL). While there are methods with optimality guarantees in the
setting of discrete state and action spaces, these methods cannot be applied in
high-dimensional deep RL scenarios. As such, most contemporary RL relies on
simple heuristics such as epsilon-greedy exploration or adding Gaussian noise
to the controls. This paper introduces Variational Information Maximizing
Exploration (VIME), an exploration strategy based on maximization of
information gain about the agent's belief of environment dynamics. We propose a
practical implementation, using variational inference in Bayesian neural
networks which efficiently handles continuous state and action spaces. VIME
modifies the MDP reward function, and can be applied with several different
underlying RL algorithms. We demonstrate that VIME achieves significantly
better performance compared to heuristic exploration methods across a variety
of continuous control tasks and algorithms, including tasks with very sparse
rewards.Comment: Published in Advances in Neural Information Processing Systems 29
(NIPS), pages 1109-111
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