5,416 research outputs found
Stochastic optimization methods for the simultaneous control of parameter-dependent systems
We address the application of stochastic optimization methods for the
simultaneous control of parameter-dependent systems. In particular, we focus on
the classical Stochastic Gradient Descent (SGD) approach of Robbins and Monro,
and on the recently developed Continuous Stochastic Gradient (CSG) algorithm.
We consider the problem of computing simultaneous controls through the
minimization of a cost functional defined as the superposition of individual
costs for each realization of the system. We compare the performances of these
stochastic approaches, in terms of their computational complexity, with those
of the more classical Gradient Descent (GD) and Conjugate Gradient (CG)
algorithms, and we discuss the advantages and disadvantages of each
methodology. In agreement with well-established results in the machine learning
context, we show how the SGD and CSG algorithms can significantly reduce the
computational burden when treating control problems depending on a large amount
of parameters. This is corroborated by numerical experiments
Sensor-based robot deployment algorithms
Abstract — In robot deployment problems, the fundamental issue is to optimize a steady state performance measure that depends on the spatial configuration of a group of robots. For such problems, a classical way of designing high-level feedback motion planners is to implement a gradient descent scheme on a suitably chosen objective function. This can lead to computationally expensive algorithms that may not be adaptive to uncertain dynamic environments. We address these challenges by showing that algorithms for a variety of deployment scenarios in uncertain stochastic environments and with noisy sensor measurements can be designed as stochastic gradient descent algorithms, and their convergence properties analyzed via the theory of stochastic approximations. This approach yields often surprisingly simple algorithms that can accommodate complicated objective functions, and work without a detailed model of the environment. To illustrate the richness of the framework, we discuss two applications, namely source seeking with realistic stochastic wireless connectivity constraints, and coverage with heterogeneous sensors. I
A Molecular Implementation of the Least Mean Squares Estimator
In order to function reliably, synthetic molecular circuits require
mechanisms that allow them to adapt to environmental disturbances. Least mean
squares (LMS) schemes, such as commonly encountered in signal processing and
control, provide a powerful means to accomplish that goal. In this paper we
show how the traditional LMS algorithm can be implemented at the molecular
level using only a few elementary biomolecular reactions. We demonstrate our
approach using several simulation studies and discuss its relevance to
synthetic biology.Comment: Molecular circuits, synthetic biology, least mean squares estimator,
adaptive system
Distributed Learning for Stochastic Generalized Nash Equilibrium Problems
This work examines a stochastic formulation of the generalized Nash
equilibrium problem (GNEP) where agents are subject to randomness in the
environment of unknown statistical distribution. We focus on fully-distributed
online learning by agents and employ penalized individual cost functions to
deal with coupled constraints. Three stochastic gradient strategies are
developed with constant step-sizes. We allow the agents to use heterogeneous
step-sizes and show that the penalty solution is able to approach the Nash
equilibrium in a stable manner within , for small step-size
value and sufficiently large penalty parameters. The operation
of the algorithm is illustrated by considering the network Cournot competition
problem
SuperSpike: Supervised learning in multi-layer spiking neural networks
A vast majority of computation in the brain is performed by spiking neural
networks. Despite the ubiquity of such spiking, we currently lack an
understanding of how biological spiking neural circuits learn and compute
in-vivo, as well as how we can instantiate such capabilities in artificial
spiking circuits in-silico. Here we revisit the problem of supervised learning
in temporally coding multi-layer spiking neural networks. First, by using a
surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based
three factor learning rule capable of training multi-layer networks of
deterministic integrate-and-fire neurons to perform nonlinear computations on
spatiotemporal spike patterns. Second, inspired by recent results on feedback
alignment, we compare the performance of our learning rule under different
credit assignment strategies for propagating output errors to hidden units.
Specifically, we test uniform, symmetric and random feedback, finding that
simpler tasks can be solved with any type of feedback, while more complex tasks
require symmetric feedback. In summary, our results open the door to obtaining
a better scientific understanding of learning and computation in spiking neural
networks by advancing our ability to train them to solve nonlinear problems
involving transformations between different spatiotemporal spike-time patterns
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