188,194 research outputs found
Qubit Complexity of Continuous Problems
The number of qubits used by a quantum algorithm will be a crucial
computational resource for the foreseeable future. We show how to obtain the
classical query complexity for continuous problems. We then establish a simple
formula for a lower bound on the qubit complexity in terms of the classical
query complexityComment: 6 pages, 2 figure
The complexity of dynamic programming
AbstractWe provide tight lower bounds on the computational complexity of discretetime, stationary, infinite horizon, discounted stochastic control problems, for the case where the state space is continuous and the problem is to be solved approximately, within a specified accuracy. We study the dependence of the complexity on the desired accuracy and on the discount factor
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
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