Gradient Theory of Optimal Flight Paths

By H. Kelley. 1960

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In Mathematical Optimization

Citations in the corpus

Recurrent World Models Facilitate Policy Evolution (2018, methodology): “The backpropagation algorithm [39, 50, 103] can be used to train a large M in form of a neural network (NN).”
Deep learning in neural networks: An overview (2014, background): “…at least since the early 1960s (e.g., Amari, 1967; Bryson, 1961; Bryson & Denham, 1961; Bryson & Ho, 1969; Director & Rohrer, 1969; Dreyfus, 1962; Kelley, 1960; Pontryagin, Boltyanskii, Gamrelidze, & Mishchenko, 1961; Wilkinson, 1965), initially within the framework of Euler–Lagrange equations…”
World Models (2018, methodology): “The backpropagation algorithm (Lin-nainmaa, 1970; Kelley, 1960; Werbos, 1982) can be used to train large neural networks efﬁciently.”
Are Markets Truly Efficient? Experiments Using Deep Learning Algorithms for Market Movement Prediction (2018, neutral): “The evolution of the backpropagation algorithm covers the past 50 years, through seminal work by [9]; [10]; [11]; [12], the latter being the implementation that is widely used.”
On Learning to Think: Algorithmic Information Theory for Novel Combinations of Reinforcement Learning Controllers and Recurrent Neural World Models (2015, methodology): “To maximize differentiable objective functions of SL and UL, NN researchers almost invariably use backpropagation (BP) [125, 30, 52] in discrete graphs of nodes with differentiable activation functions [151, 265][245, Sec.”
Kornia: an Open Source Differentiable Computer Vision Library for PyTorch (2019, methodology): “An image processing algorithm that can be defined as a Direct Acyclic Graph (DAG) structure can, thanks to the reverse-mode [53] auto-differentiation [19], compute gradients via backpropagation [27].”
The numerical solution of variational problems (1962, background): “This approach is known to a few practitioners of the numerical art such as Kelley [3] and Bryson [4].”
Machine Learning in Finance : The Case of Deep Learning for Option Pricing (2017, methodology): “To find these, taking numerical gradients for optimization is computationally infeasible, and luckily, we are able to do so analytically with linear computation, using the backpropagation algorithm (Kelley (1960); Bryson (1961); Dreyfus (1973); Rumelhart et al. (1986)).”
My First Deep Learning System of 1991 + Deep Learning Timeline 1962-2013 (2013, background): “Gradient descent [42] in such systems can be performed [13, 50, 12] by iterating the ancient chain rule [57, 58] in dynamic programming style [9] (compare simpliﬁed derivation using chain rule only [27]).”
Adversarial examples for models of code (2019, unknown): “code2vec”
Universal Planning Networks (2018, background): “The idea of planning by gradient descent has existed for decades (Kelley, 1960).”
Reinforcement Learning Upside Down: Don't Predict Rewards - Just Map Them to Actions (2019, methodology): “Replay-based training on previous behaviors and commands compatible with observed time horizons and costs: For all pairs {(k, j); 1 ≤ k ≤ j ≤ t}: train C through gradient descent-based backpropagation [29, 25, 71][53, Sec.”
Plant Disease Detection and Classification by Deep Learning (2019, unknown): “During the first phase, several developments like backpropagation [2,3], chain rule [4], Neocognitron [5], hand written text recognition (LeNET architecture) [6], and resolving the training problem [7,8] were observed (as shown in Figure 1).”
Neural Networks and Deep Learning (2018, unknown): “The original idea of backpropagation was based on idea of differentiation of composition of functions as developed in control theory [54, 237] under the ambit of automatic differentiation.”