3,523 research outputs found
Supporting GENP with Random Multipliers
We prove that standard Gaussian random multipliers are expected to stabilize
numerically both Gaussian elimination with no pivoting and block Gaussian
elimination. Our tests show similar results where we applied circulant random
multipliers instead of Gaussian ones.Comment: 14 page
autoAx: An Automatic Design Space Exploration and Circuit Building Methodology utilizing Libraries of Approximate Components
Approximate computing is an emerging paradigm for developing highly
energy-efficient computing systems such as various accelerators. In the
literature, many libraries of elementary approximate circuits have already been
proposed to simplify the design process of approximate accelerators. Because
these libraries contain from tens to thousands of approximate implementations
for a single arithmetic operation it is intractable to find an optimal
combination of approximate circuits in the library even for an application
consisting of a few operations. An open problem is "how to effectively combine
circuits from these libraries to construct complex approximate accelerators".
This paper proposes a novel methodology for searching, selecting and combining
the most suitable approximate circuits from a set of available libraries to
generate an approximate accelerator for a given application. To enable fast
design space generation and exploration, the methodology utilizes machine
learning techniques to create computational models estimating the overall
quality of processing and hardware cost without performing full synthesis at
the accelerator level. Using the methodology, we construct hundreds of
approximate accelerators (for a Sobel edge detector) showing different but
relevant tradeoffs between the quality of processing and hardware cost and
identify a corresponding Pareto-frontier. Furthermore, when searching for
approximate implementations of a generic Gaussian filter consisting of 17
arithmetic operations, the proposed approach allows us to identify
approximately highly important implementations from possible
solutions in a few hours, while the exhaustive search would take four months on
a high-end processor.Comment: Accepted for publication at the Design Automation Conference 2019
(DAC'19), Las Vegas, Nevada, US
Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Control
Trial-and-error based reinforcement learning (RL) has seen rapid advancements
in recent times, especially with the advent of deep neural networks. However,
the majority of autonomous RL algorithms require a large number of interactions
with the environment. A large number of interactions may be impractical in many
real-world applications, such as robotics, and many practical systems have to
obey limitations in the form of state space or control constraints. To reduce
the number of system interactions while simultaneously handling constraints, we
propose a model-based RL framework based on probabilistic Model Predictive
Control (MPC). In particular, we propose to learn a probabilistic transition
model using Gaussian Processes (GPs) to incorporate model uncertainty into
long-term predictions, thereby, reducing the impact of model errors. We then
use MPC to find a control sequence that minimises the expected long-term cost.
We provide theoretical guarantees for first-order optimality in the GP-based
transition models with deterministic approximate inference for long-term
planning. We demonstrate that our approach does not only achieve
state-of-the-art data efficiency, but also is a principled way for RL in
constrained environments.Comment: Accepted at AISTATS 2018
Preconditioning For Matrix Computation
Preconditioning is a classical subject of numerical solution of linear systems of equations. The goal is to turn a linear system into another one which is easier to solve. The two central subjects of numerical matrix computations are LIN-SOLVE, that is, the solution of linear systems of equations and EIGEN-SOLVE, that is, the approximation of the eigenvalues and eigenvectors of a matrix. We focus on the former subject of LIN-SOLVE and show an application to EIGEN-SOLVE. We achieve our goal by applying randomized additive and multiplicative preconditioning. We facilitate the numerical solution by decreasing the condition of the coefficient matrix of the linear system, which enables reliable numerical solution of LIN-SOLVE. After the introduction in the Chapter 1 we recall the definitions and auxiliary results in Chapter 2. Then in Chapter 3 we precondition linear systems of equations solved at every iteration of the Inverse Power Method applied to EIGEN-SOLVE. These systems are ill conditioned, that is, have large condition numbers, and we decrease them by applying randomized additive preconditioning. This is our first subject.
Our second subject is randomized multiplicative preconditioning for LIN-SOLVE. In this way we support application of GENP, that is, Gaussian elimination with no pivoting, and block Gaussian elimination. We prove that the proposed preconditioning methods are efficient when we apply Gaussian random matrices as preconditioners. We confirm these results with our extensive numerical tests. The tests also show that the same methods work as efficiently on the average when we use random structured, in particular circulant, preconditioners instead, but we show both formally and experimentally that these preconditioners fail in the case of LIN-SOLVE for the unitary matrix of discreet Fourier transform, for which Gaussian preconditioners work efficiently
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