6,203 research outputs found
Optimal Reinforcement Learning for Gaussian Systems
The exploration-exploitation trade-off is among the central challenges of
reinforcement learning. The optimal Bayesian solution is intractable in
general. This paper studies to what extent analytic statements about optimal
learning are possible if all beliefs are Gaussian processes. A first order
approximation of learning of both loss and dynamics, for nonlinear,
time-varying systems in continuous time and space, subject to a relatively weak
restriction on the dynamics, is described by an infinite-dimensional partial
differential equation. An approximate finite-dimensional projection gives an
impression for how this result may be helpful.Comment: final pre-conference version of this NIPS 2011 paper. Once again,
please note some nontrivial changes to exposition and interpretation of the
results, in particular in Equation (9) and Eqs. 11-14. The algorithm and
results have remained the same, but their theoretical interpretation has
change
Monte Carlo Bayesian Reinforcement Learning
Bayesian reinforcement learning (BRL) encodes prior knowledge of the world in
a model and represents uncertainty in model parameters by maintaining a
probability distribution over them. This paper presents Monte Carlo BRL
(MC-BRL), a simple and general approach to BRL. MC-BRL samples a priori a
finite set of hypotheses for the model parameter values and forms a discrete
partially observable Markov decision process (POMDP) whose state space is a
cross product of the state space for the reinforcement learning task and the
sampled model parameter space. The POMDP does not require conjugate
distributions for belief representation, as earlier works do, and can be solved
relatively easily with point-based approximation algorithms. MC-BRL naturally
handles both fully and partially observable worlds. Theoretical and
experimental results show that the discrete POMDP approximates the underlying
BRL task well with guaranteed performance.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
On the role of synaptic stochasticity in training low-precision neural networks
Stochasticity and limited precision of synaptic weights in neural network
models are key aspects of both biological and hardware modeling of learning
processes. Here we show that a neural network model with stochastic binary
weights naturally gives prominence to exponentially rare dense regions of
solutions with a number of desirable properties such as robustness and good
generalization performance, while typical solutions are isolated and hard to
find. Binary solutions of the standard perceptron problem are obtained from a
simple gradient descent procedure on a set of real values parametrizing a
probability distribution over the binary synapses. Both analytical and
numerical results are presented. An algorithmic extension aimed at training
discrete deep neural networks is also investigated.Comment: 7 pages + 14 pages of supplementary materia
Cover Tree Bayesian Reinforcement Learning
This paper proposes an online tree-based Bayesian approach for reinforcement
learning. For inference, we employ a generalised context tree model. This
defines a distribution on multivariate Gaussian piecewise-linear models, which
can be updated in closed form. The tree structure itself is constructed using
the cover tree method, which remains efficient in high dimensional spaces. We
combine the model with Thompson sampling and approximate dynamic programming to
obtain effective exploration policies in unknown environments. The flexibility
and computational simplicity of the model render it suitable for many
reinforcement learning problems in continuous state spaces. We demonstrate this
in an experimental comparison with least squares policy iteration
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