1,019,518 research outputs found
Dynamics of Supervised Learning with Restricted Training Sets
We study the dynamics of supervised learning in layered neural networks, in
the regime where the size of the training set is proportional to the number
of inputs. Here the local fields are no longer described by Gaussian
probability distributions. We show how dynamical replica theory can be used to
predict the evolution of macroscopic observables, including the relevant
performance measures, incorporating the old formalism in the limit
as a special case. For simplicity we restrict ourselves
to single-layer networks and realizable tasks.Comment: 36 pages, latex2e, 12 eps figures (to be publ in: Proc Newton Inst
Workshop on On-Line Learning '97
Sim-to-Real Transfer of Robotic Control with Dynamics Randomization
Simulations are attractive environments for training agents as they provide
an abundant source of data and alleviate certain safety concerns during the
training process. But the behaviours developed by agents in simulation are
often specific to the characteristics of the simulator. Due to modeling error,
strategies that are successful in simulation may not transfer to their real
world counterparts. In this paper, we demonstrate a simple method to bridge
this "reality gap". By randomizing the dynamics of the simulator during
training, we are able to develop policies that are capable of adapting to very
different dynamics, including ones that differ significantly from the dynamics
on which the policies were trained. This adaptivity enables the policies to
generalize to the dynamics of the real world without any training on the
physical system. Our approach is demonstrated on an object pushing task using a
robotic arm. Despite being trained exclusively in simulation, our policies are
able to maintain a similar level of performance when deployed on a real robot,
reliably moving an object to a desired location from random initial
configurations. We explore the impact of various design decisions and show that
the resulting policies are robust to significant calibration error
Dynamics of Learning with Restricted Training Sets I: General Theory
We study the dynamics of supervised learning in layered neural networks, in
the regime where the size of the training set is proportional to the number
of inputs. Here the local fields are no longer described by Gaussian
probability distributions and the learning dynamics is of a spin-glass nature,
with the composition of the training set playing the role of quenched disorder.
We show how dynamical replica theory can be used to predict the evolution of
macroscopic observables, including the two relevant performance measures
(training error and generalization error), incorporating the old formalism
developed for complete training sets in the limit as a
special case. For simplicity we restrict ourselves in this paper to
single-layer networks and realizable tasks.Comment: 39 pages, LaTe
On-Line Learning with Restricted Training Sets: An Exactly Solvable Case
We solve the dynamics of on-line Hebbian learning in large perceptrons
exactly, for the regime where the size of the training set scales linearly with
the number of inputs. We consider both noiseless and noisy teachers. Our
calculation cannot be extended to non-Hebbian rules, but the solution provides
a convenient and welcome benchmark with which to test more general and advanced
theories for solving the dynamics of learning with restricted training sets.Comment: 19 pages, eps figures included, uses epsfig macr
The Dynamics of a Genetic Algorithm for a Simple Learning Problem
A formalism for describing the dynamics of Genetic Algorithms (GAs) using
methods from statistical mechanics is applied to the problem of generalization
in a perceptron with binary weights. The dynamics are solved for the case where
a new batch of training patterns is presented to each population member each
generation, which considerably simplifies the calculation. The theory is shown
to agree closely to simulations of a real GA averaged over many runs,
accurately predicting the mean best solution found. For weak selection and
large problem size the difference equations describing the dynamics can be
expressed analytically and we find that the effects of noise due to the finite
size of each training batch can be removed by increasing the population size
appropriately. If this population resizing is used, one can deduce the most
computationally efficient size of training batch each generation. For
independent patterns this choice also gives the minimum total number of
training patterns used. Although using independent patterns is a very
inefficient use of training patterns in general, this work may also prove
useful for determining the optimum batch size in the case where patterns are
recycled.Comment: 28 pages, 4 Postscript figures. Latex using IOP macros ioplppt and
iopl12 which are included. To appear in Journal of Physics A. Also available
at ftp://ftp.cs.man.ac.uk/pub/ai/jls/GAlearn.ps.gz and
http://www.cs.man.ac.uk/~jl
Dynamics of on-line Hebbian learning with structurally unrealizable restricted training sets
We present an exact solution for the dynamics of on-line Hebbian learning in
neural networks, with restricted and unrealizable training sets. In contrast to
other studies on learning with restricted training sets, unrealizability is
here caused by structural mismatch, rather than data noise: the teacher machine
is a perceptron with a reversed wedge-type transfer function, while the student
machine is a perceptron with a sigmoidal transfer function. We calculate the
glassy dynamics of the macroscopic performance measures, training error and
generalization error, and the (non-Gaussian) student field distribution. Our
results, which find excellent confirmation in numerical simulations, provide a
new benchmark test for general formalisms with which to study unrealizable
learning processes with restricted training sets.Comment: 7 pages including 3 figures, using IOP latex2e preprint class fil
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