7,876 research outputs found
Solving the L1 regularized least square problem via a box-constrained smooth minimization
In this paper, an equivalent smooth minimization for the L1 regularized least
square problem is proposed. The proposed problem is a convex box-constrained
smooth minimization which allows applying fast optimization methods to find its
solution. Further, it is investigated that the property "the dual of dual is
primal" holds for the L1 regularized least square problem. A solver for the
smooth problem is proposed, and its affinity to the proximal gradient is shown.
Finally, the experiments on L1 and total variation regularized problems are
performed, and the corresponding results are reported.Comment: 5 page
Learning Deep Stochastic Optimal Control Policies using Forward-Backward SDEs
In this paper we propose a new methodology for decision-making under
uncertainty using recent advancements in the areas of nonlinear stochastic
optimal control theory, applied mathematics, and machine learning. Grounded on
the fundamental relation between certain nonlinear partial differential
equations and forward-backward stochastic differential equations, we develop a
control framework that is scalable and applicable to general classes of
stochastic systems and decision-making problem formulations in robotics and
autonomy. The proposed deep neural network architectures for stochastic control
consist of recurrent and fully connected layers. The performance and
scalability of the aforementioned algorithm are investigated in three
non-linear systems in simulation with and without control constraints. We
conclude with a discussion on future directions and their implications to
robotics
Training Recurrent Neural Networks via Dynamical Trajectory-Based Optimization
This paper introduces a new method to train recurrent neural networks using
dynamical trajectory-based optimization. The optimization method utilizes a
projected gradient system (PGS) and a quotient gradient system (QGS) to
determine the feasible regions of an optimization problem and search the
feasible regions for local minima. By exploring the feasible regions, local
minima are identified and the local minimum with the lowest cost is chosen as
the global minimum of the optimization problem. Lyapunov theory is used to
prove the stability of the local minima and their stability in the presence of
measurement errors. Numerical examples show that the new approach provides
better results than genetic algorithm and error backpropagation (EBP) trained
networks
A Neurodynamical System for finding a Minimal VC Dimension Classifier
The recently proposed Minimal Complexity Machine (MCM) finds a hyperplane
classifier by minimizing an exact bound on the Vapnik-Chervonenkis (VC)
dimension. The VC dimension measures the capacity of a learning machine, and a
smaller VC dimension leads to improved generalization. On many benchmark
datasets, the MCM generalizes better than SVMs and uses far fewer support
vectors than the number used by SVMs. In this paper, we describe a neural
network based on a linear dynamical system, that converges to the MCM solution.
The proposed MCM dynamical system is conducive to an analogue circuit
implementation on a chip or simulation using Ordinary Differential Equation
(ODE) solvers. Numerical experiments on benchmark datasets from the UCI
repository show that the proposed approach is scalable and accurate, as we
obtain improved accuracies and fewer number of support vectors (upto 74.3%
reduction) with the MCM dynamical system.Comment: 15 pages, 3 figure
Beyond Feedforward Models Trained by Backpropagation: a Practical Training Tool for a More Efficient Universal Approximator
Cellular Simultaneous Recurrent Neural Network (SRN) has been shown to be a
function approximator more powerful than the MLP. This means that the
complexity of MLP would be prohibitively large for some problems while SRN
could realize the desired mapping with acceptable computational constraints.
The speed of training of complex recurrent networks is crucial to their
successful application. Present work improves the previous results by training
the network with extended Kalman filter (EKF). We implemented a generic
Cellular SRN and applied it for solving two challenging problems: 2D maze
navigation and a subset of the connectedness problem. The speed of convergence
has been improved by several orders of magnitude in comparison with the earlier
results in the case of maze navigation, and superior generalization has been
demonstrated in the case of connectedness. The implications of this
improvements are discussed
Neural network design for J function approximation in dynamic programming
This paper shows that a new type of artificial neural network (ANN) -- the
Simultaneous Recurrent Network (SRN) -- can, if properly trained, solve a
difficult function approximation problem which conventional ANNs -- either
feedforward or Hebbian -- cannot. This problem, the problem of generalized maze
navigation, is typical of problems which arise in building true intelligent
control systems using neural networks. (Such systems are discussed in the
chapter by Werbos in K.Pribram, Brain and Values, Erlbaum 1998.) The paper
provides a general review of other types of recurrent networks and alternative
training techniques, including a flowchart of the Error Critic training design,
arguable the only plausible approach to explain how the brain adapts
time-lagged recurrent systems in real-time. The C code of the test is appended.
As in the first tests of backprop, the training here was slow, but there are
ways to do better after more experience using this type of network.Comment: 50p, 30 figs. Pang did most of the work here. Werbos created the
designs. With her agreement, Werbos included this in int'l patent WO 97/46929
published 12/11/97. In 1997 Pang and Baras showed SRNs improve performance in
a realistic communications task. The code draws on ch.8 of Werbos, Roots of
Backpropagation, Wiley 1994, containing the 1974 thesis which first presented
true backprop. Werbos later trained the SRN on 6 easy mazes, with steady
gains on 6 hard mazes used for testin
Reinforcement Learning for Batch Bioprocess Optimization
Bioprocesses have received a lot of attention to produce clean and
sustainable alternatives to fossil-based materials. However, they are generally
difficult to optimize due to their unsteady-state operation modes and
stochastic behaviours. Furthermore, biological systems are highly complex,
therefore plant-model mismatch is often present. To address the aforementioned
challenges we propose a Reinforcement learning based optimization strategy for
batch processes.
In this work, we applied the Policy Gradient method from batch-to-batch to
update a control policy parametrized by a recurrent neural network. We assume
that a preliminary process model is available, which is exploited to obtain a
preliminary optimal control policy. Subsequently, this policy is updatedbased
on measurements from thetrueplant. The capabilities of our proposed approach
were tested on three case studies (one of which is nonsmooth) using a more
complex process model for thetruesystemembedded with adequate process
disturbance. Lastly, we discussed the advantages and disadvantages of this
strategy compared against current existing approaches such as nonlinear model
predictive control
Why gradient clipping accelerates training: A theoretical justification for adaptivity
We provide a theoretical explanation for the effectiveness of gradient
clipping in training deep neural networks. The key ingredient is a new
smoothness condition derived from practical neural network training examples.
We observe that gradient smoothness, a concept central to the analysis of
first-order optimization algorithms that is often assumed to be a constant,
demonstrates significant variability along the training trajectory of deep
neural networks. Further, this smoothness positively correlates with the
gradient norm, and contrary to standard assumptions in the literature, it can
grow with the norm of the gradient. These empirical observations limit the
applicability of existing theoretical analyses of algorithms that rely on a
fixed bound on smoothness. These observations motivate us to introduce a novel
relaxation of gradient smoothness that is weaker than the commonly used
Lipschitz smoothness assumption. Under the new condition, we prove that two
popular methods, namely, \emph{gradient clipping} and \emph{normalized
gradient}, converge arbitrarily faster than gradient descent with fixed
stepsize. We further explain why such adaptively scaled gradient methods can
accelerate empirical convergence and verify our results empirically in popular
neural network training settings
Gradient Dynamic Approach to the Tensor Complementarity Problem
Nonlinear gradient dynamic approach for solving the tensor complementarity
problem (TCP) is presented. Theoretical analysis shows that each of the defined
dynamical system models ensures the convergence performance. The computer
simulation results further substantiate that the considered dynamical system
can solve the tensor complementarity problem (TCP).Comment: 18pages. arXiv admin note: text overlap with arXiv:1804.00406 by
other author
Scalable Planning with Tensorflow for Hybrid Nonlinear Domains
Given recent deep learning results that demonstrate the ability to
effectively optimize high-dimensional non-convex functions with gradient
descent optimization on GPUs, we ask in this paper whether symbolic gradient
optimization tools such as Tensorflow can be effective for planning in hybrid
(mixed discrete and continuous) nonlinear domains with high dimensional state
and action spaces? To this end, we demonstrate that hybrid planning with
Tensorflow and RMSProp gradient descent is competitive with mixed integer
linear program (MILP) based optimization on piecewise linear planning domains
(where we can compute optimal solutions) and substantially outperforms
state-of-the-art interior point methods for nonlinear planning domains.
Furthermore, we remark that Tensorflow is highly scalable, converging to a
strong plan on a large-scale concurrent domain with a total of 576,000
continuous action parameters distributed over a horizon of 96 time steps and
100 parallel instances in only 4 minutes. We provide a number of insights that
clarify such strong performance including observations that despite long
horizons, RMSProp avoids both the vanishing and exploding gradient problems.
Together these results suggest a new frontier for highly scalable planning in
nonlinear hybrid domains by leveraging GPUs and the power of recent advances in
gradient descent with highly optimized toolkits like Tensorflow.Comment: 9 page
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