DYNAMIC PROGRAMMING AND LAGRANGE MULTIPLIERS.

By Richard Bellman. 1956

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Citations in the corpus

Batch Policy Gradient Methods for Improving Neural Conversation Models (2017, methodology): “However, if unlabelled data can be used to train a decent initial bot, say via maximum likelihood, we can use policy iteration techniques to reﬁne this bot by making local improvements using the labelled data (Bellman, 1956).”
Safe, Multi-Agent, Reinforcement Learning for Autonomous Driving (2016, methodology): “Most of the RL algorithms rely in some way or another on the mathematically elegant model of a Markov Decision Process (MDP), pioneered by the work of Bellman [4, 5].”
Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms (2015, methodology): “There are two principal ways of solving optimal control problems: either dynamic programming through the Hamilton-Jacobi-Bellman (HJB) equation (Bellman, 1956), or using the Pontryagin’s maximum principle (PMP) (Pon-tryagin, 1987).”
Scaling up budgeted reinforcement learning (2019, background): “A policy π ∗ satisfying Bellman’s optimality equation is optimal [Bellman, 1956]: If γ 1 , it admits a unique solution.”
A Tensor-Based Information Framework for Predicting the Stock Market (2016, methodology): “To optimize J ( V ), we construct a Lagrangian function L and optimize J ( V ) by taking the partial derivative of L with respect to V [Bellman 1956].”
Learning latent structure for activity recognition (2014, background): “In the linear-chain CRF, the exact inference can be performed efficiently using dynamic programming [15].”
Cognitive Control (2012, unknown): “In the second line, based on optimal control and Bellman’s dynamic programming [65]–[67], Bertsekas and Tsitsiklis developed a group of stochastic approximations, which have been known as neurodynamic programming and approximate dynamic programming [68], [69].”
On a Formal Model of Safe and Scalable Self-driving Cars (2017, methodology): “Furthermore, based on the pioneering work of Bellman [2, 3], we can calculate Q(s, a) for every (s, a) ∈ Ŝ × Â, based on dynamic programming procedures (such as the Value Iteration algorithm), and under our assumptions, the total runtime is order of T |Â| |Ŝ|.”
Runtime Neural Pruning (2017, methodology): “Like Inception [41] and ResNet [3], we define the action based on unit of a single block by sharing pruning rate inside the block, which is more scalable and can avoid considering about the sophisticated structures.”
An adaptive scheduling scheme for calculating Bayes factors with thermodynamic integration using Simpson’s rule (2015, background): “As the number of parameters increase, we expect this situation to worsen due to the curse of dimensionality (Bellmann 1986).”
From Dependence to Causation (2016, background): “Bellman (1956) termed this exponential rate of growth in the size of optimization problems the curse of dimensionality.”
Automatic model construction with Gaussian processes (2014, background): “(2006) argued that models based on local kernels are particularly susceptible to the curse of dimensionality (Bellman, 1956), and are generally unable to extrapolate away from the training data.”
Reinforcement Learning: Theory and Algorithms (2019, methodology): “Intuitively, if the Bellman rank is small, then for any level h, the number of linearly independent columns is small. That is, the average Bellman error for any function under most policies can be expressed as linear combination of the Bellman errors of that function on a small set of policies corre”
Attention-Aware Deep Reinforcement Learning for Video Face Recognition (2017, methodology): “According to the Bellman equation [2], we apply the Qlearning method to train the frame evaluation network by”