1,330 research outputs found
Collective Intelligence for Control of Distributed Dynamical Systems
We consider the El Farol bar problem, also known as the minority game (W. B.
Arthur, ``The American Economic Review'', 84(2): 406--411 (1994), D. Challet
and Y.C. Zhang, ``Physica A'', 256:514 (1998)). We view it as an instance of
the general problem of how to configure the nodal elements of a distributed
dynamical system so that they do not ``work at cross purposes'', in that their
collective dynamics avoids frustration and thereby achieves a provided global
goal. We summarize a mathematical theory for such configuration applicable when
(as in the bar problem) the global goal can be expressed as minimizing a global
energy function and the nodes can be expressed as minimizers of local free
energy functions. We show that a system designed with that theory performs
nearly optimally for the bar problem.Comment: 8 page
A Survey of Quantum Learning Theory
This paper surveys quantum learning theory: the theoretical aspects of
machine learning using quantum computers. We describe the main results known
for three models of learning: exact learning from membership queries, and
Probably Approximately Correct (PAC) and agnostic learning from classical or
quantum examples.Comment: 26 pages LaTeX. v2: many small changes to improve the presentation.
This version will appear as Complexity Theory Column in SIGACT News in June
2017. v3: fixed a small ambiguity in the definition of gamma(C) and updated a
referenc
Online Infinite-Dimensional Regression: Learning Linear Operators
We consider the problem of learning linear operators under squared loss
between two infinite-dimensional Hilbert spaces in the online setting. We show
that the class of linear operators with uniformly bounded -Schatten norm is
online learnable for any . On the other hand, we prove an
impossibility result by showing that the class of uniformly bounded linear
operators with respect to the operator norm is \textit{not} online learnable.
Moreover, we show a separation between online uniform convergence and online
learnability by identifying a class of bounded linear operators that is online
learnable but uniform convergence does not hold. Finally, we prove that the
impossibility result and the separation between uniform convergence and
learnability also hold in the agnostic PAC setting.Comment: 17 page
- …