Stochastic Estimation of the Maximum of a Regression Function

By J. Kiefer, J. Wolfowitz. 1952

Subfields: Statistics and Probability, Mathematical Optimization

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Citations in the corpus

Overcoming Catastrophic Forgetting in Incremental Few-Shot Learning by Finding Flat Minima (2021, methodology): “Standard supervised training with SGD as the optimizer tends to converge to a sharp local minima.”
Lifelong Graph Learning (2020, neutral): “In the experiments, we find that GCN, APPNP obtain the best overall performance using the SGD optimizer, while MLP, GAT, and FGN performed the best using the Adam optimizer.”
Continual Learning by Asymmetric Loss Approximation With Single-Side Overestimation (2019, methodology): “With a naı̈ve stochastic gradient descent (SGD) method, deep neural networks easily forget the knowledge obtained from the earlier tasks while adapting to the new information quickly from the incoming tasks [26, 8].”
Episodic Exploration for Deep Deterministic Policies: An Application to StarCraft Micromanagement Tasks (2016, methodology): “…comes from stochastic gradient-free optimization [14, 21, 30, 9, 11], where the gradient of a diﬀerentiable function x ∈ R d (cid:55)→ f ( x ) can be estimated with ﬁnite diﬀerence methods by where the expectation is taken over the vector u sampled on the unit sphere [21, chapter 9.3].”
Regret Analysis of Stochastic and Nonstochastic Multi-armed Bandit Problems (2012, neutral): “3 is inspired by gradient-free optimization, a topic extensively studied since [118, 147] — see [31, 67, 138, 140] for recent accounts on this theory.”
Behaviour Suite for Reinforcement Learning (2019, background): “• sgd : vanilla stochastic gradient descent with learning rate 1e-2 (Kiefer & Wolfowitz, 1952).”
SequenceR: Sequence-to-Sequence Learning for End-to-End Program Repair (2018, methodology): “Back propagation is used to update the parameters in the network with stochastic gradient decent during training [19].”
Nearly Tight Bounds for the Continuum-Armed Bandit Problem (2004, methodology): “(3)Readers familiar with Kiefer-Wolfowitz stochastic approximation [17] will note the similarity with our algorithm.”
QUANTILE ESTIMATION WITH ADAPTIVE IMPORTANCE SAMPLING (2010, methodology): “The solution θ∗ is estimated by a sequence (θn)n≥0, generated, for instance, by a stochastic approximation algorithm of Kiefer–Wolfowitz or Robbins–Monro type.”
Domain Agnostic Learning with Disentangled Representations (2019, methodology): “We train the class and domain disentanglement component, MINE and the reconstruction component iteratively with Stochasitc Gradient Descent (Kiefer et al., 1952) or Adam (Kingma & Ba, 2014) optimizer.”
Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses (2020, background): “ is known that one-pass SGD is guaranteed to have optimal excess risk, which can be shown via martingale arguments that trace back to the stochastic approximation literature (Robbins and Monro, 1951; Kiefer and Wolfowitz, 1952). Using our UAS bound, we show that Algorithms 2 and 3 can recover nearly”
Efficient sparse collective communication and its application to accelerate distributed deep learning (2020, background): “The most common DDL approach is data-parallel training via stochastic gradient descent (SGD) [33].”
Predicting the Computational Cost of Deep Learning Models (2018, methodology): “Thus, we separately evaluate predictions for only forward passes (Figure 4a,b), and predictions for forward and backward passes with stochastic gradient descent [14] (Figure 4c,d).”
Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms (2009, unknown): “Under suitable technical conditions on the function M(·) and the sequences {ak} and {ck}, Kiefer and Wolfowitz (1952) showed that the sequence zk → z ∗ in probability as k → ∞.”
Monte Carlo sampling-based methods for stochastic optimization (2014, methodology): “Robbins and Monro’s problem was actually to find a zero of a given noisy function; Kiefer and Wolfowitz [129] applied the idea to optimization and used finite-difference estimators of the gradient.”