Adaptive Sequential Stochastic Optimization

Wilson, Craig; Veeravalli, Venugopal V.; Nedić, Angelia

doi:10.1109/tac.2018.2816168

Cited by 26 publications

(41 citation statements)

References 28 publications

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“…The rest of this paper is outlined as follows. In Section II, we specialize the work in [3] to the machine learning problem stated in (1). In Section II-B, we consider the problem of minimizing the sequence of functions in (1) with ρ from (2) known.…”

Section: B Paper Outlinementioning

confidence: 99%

“…For the basic version of SGD, generally the number of iterations equals K n , as each sample is used to produce a noisy gradient. See Appendix A of [3] for a discussion of useful b(d 0 , K n ) bounds. For some bounds b(d 0 , K), we may need to know parameters such as the strong convexity parameter.…”

Section: A Assumptionsmentioning

confidence: 99%

“…For some bounds b(d 0 , K), we may need to know parameters such as the strong convexity parameter. Estimating these parameters is discussed in Appendix C of [3]. Finally, for assumption A.4, we can fix K i and set ε i = b(diam(X ), K i ) for i = 1, 2.…”

Section: A Assumptionsmentioning

confidence: 99%

“…Given an estimate of ρ, we determine selection rules for the number of samples K n to achieve a target excess risk ε. This paper is a continuation of the work initiated in [3]. We specialize the results in [3], which were given for general functions f n (w), to the specific form in (1), and provide new results that are specifically relevant to machine learning problems.…”

Section: Introductionmentioning

confidence: 97%

“…This paper is a continuation of the work initiated in [3]. We specialize the results in [3], which were given for general functions f n (w), to the specific form in (1), and provide new results that are specifically relevant to machine learning problems. We develop a bound to show that our estimate ρ is non-trivial provided that the excess risk is small enough.…”

Section: Introductionmentioning

confidence: 97%

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Adaptive sequential machine learning

Wilson

Veeravalli

2019

Sequential Analysis

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A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The stochastic optimization problems arising in these machine learning problems is solved using algorithms such as stochastic gradient descent (SGD). A method based on estimates of the change in the minimizers and properties of the optimization algorithm is introduced for adaptively selecting the number of samples at each time step to ensure that the excess risk, i.e., the expected gap between the loss achieved by the approximate minimizer produced by the optimization algorithm and the exact minimizer, does not exceed a target level. A bound is developed to show that the estimate of the change in the minimizers is nontrivial provided that the excess risk is small enough. Extensions relevant to the machine learning setting are considered, including a cost-based approach to select the number of samples with a cost budget over a fixed horizon, and an approach to applying cross-validation for model selection. Finally, experiments with synthetic and real data are used to validate the algorithms.

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Section: B Paper Outlinementioning

confidence: 99%

Section: A Assumptionsmentioning

confidence: 99%

Section: A Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 97%

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Adaptive sequential machine learning

Wilson

Veeravalli

2019

Sequential Analysis

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Wasserstein‐metric‐based distributionally robust optimization method for unit commitment considering wind turbine uncertainty

Yan

Chen

et al. 2023

Engineering Reports

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The penetration of wind turbines in the power grid is increasing rapidly. Still, the wind turbine output power has uncertainty, leading to poor grid reliability, affecting the grid's dispatching plan, and increasing the total cost. Thus, a distributionally robust optimization method for thermal power unit commitment considering the uncertainty of wind power is proposed. For this method, energy storage and interruptible load are added to simulate increasingly complex electricity consumption scenarios. Furthermore, the amount of load cutting reflects the satisfaction level of electricity consumption on the user side. Based on Wasserstein metric, an ambiguity set is established to reflect the probabilistic distribution information of the wind power uncertainty. An ambiguity set preprocessing method is proposed to depict the probability distribution of ambiguity set more clearly, to minimize the operation cost under the condition that the uncertainty of wind turbine output power obeys the extreme probabilistic distribution of the ambiguity set. The test case in a modified version of the IEEE 6‐bus system shows that the proposed method can flexibly adjust the robustness and economy of optimization decisions by controlling the sample size and the confidence of Wasserstein ambiguity set radius. In addition, the proposed ambiguity set preprocessing method can obtain more economical dispatching decisions with a smaller sample size.

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Stochastic approximation with nondecaying gain: Error bound and data‐driven gain‐tuning

Zhu

Spall

2020

Intl J Robust & Nonlinear

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Our problem of interest is to minimize a sequence of scalar-valued loss functions f k (⋅) or to locate the root(s) of a sequence of vector-valued functions g k (⋅) corresponding to time k with respect to a parameter ∈ R p. The available information for the minimization/root-finding is the noise-corrupted observation(s) of either f k (⋅) or g k (⋅) evaluated at a few of certain design points only. Taking both the dynamics and randomness into consideration, we use stochastic approximation (SA) algorithms to solve the time-varying problem, but with a nondecaying gain (stepsize). The tracking performance of the nondecaying gain SA algorithm is guaranteed by a computable bound for the root-mean-squared error and mean-absolute-deviation. The only assumption imposed on the drifts is that the average distance between two consecutive underlying true parameters is bounded from above-this assumption allows the varying target to change abruptly. The error term arising from using the noisy evaluation of f k (⋅) or g k (⋅) in constructing the search direction is assumed to have bounded second-moment-this allows for biased estimator to be used in the SA algorithms. Given the lenient assumptions on the drift and error term, the error bounds apply to a broad class of time-varying scenarios and are useful for finite-sample analysis. Since the tracking capability characterizes the average performance across all possible sample paths, it may not provide much guidance on the gain-tuning strategies useful for one single run. Hence, we propose a data-dependent gain-tuning strategy based on estimating the Hessian information and the noise level. The adaptive rule is advantageous as it enables the step size to vary with information gathered during the progress of the estimation procedure.

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Adaptive Sequential Stochastic Optimization

Cited by 26 publications

References 28 publications

Adaptive sequential machine learning

Adaptive sequential machine learning

Wasserstein‐metric‐based distributionally robust optimization method for unit commitment considering wind turbine uncertainty

Stochastic approximation with nondecaying gain: Error bound and data‐driven gain‐tuning

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