A Generalization of the Averaging Procedure: The Use of Two-Time-Scale Algorithms

Mokkadem, Abdelkader; Pelletier, Mariane

doi:10.1137/080718395

Cited by 22 publications

(27 citation statements)

References 22 publications

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“…At epoch k, we compute a new iterate µ k+1 by subtracting from the current iterate µ k the product of the Hessian inverse and the gradient of the functionR k+1 (µ k ). For the empirical dual loss functionR k defined in (22), we define the gradient ∇R k (µ) and Hessian ∇ 2R k (µ). The new approximate solution µ k+1 is then found from current approximate solution µ k using the Newton update…”

Section: A Learning Via Newton's Methodsmentioning

confidence: 99%

“…Remark 3 Observe in the text of Proposition 1 that we definẽ R * k to be the optimal point of the loss functionL k (µ k ) regularized with a standard log barrier − log(µ k ), rather than the thresholded barrier − log (µ k ) used in the definition in (22). Indeed, using the thresholded barrier does not explicitly enforce nonnegativity for values smaller than .…”

Section: Erm Over Non-stationary Channelmentioning

confidence: 99%

“…In this section we provide a theoretical analysis of the Newton learning update in (24). We do so by first analyzing the convergence properties of the ERM problem in (22). We subsequently return to the WCP in (WCP k ) and establish a control performance result.…”

Section: Convergence Analysismentioning

confidence: 99%

“…We begin by analyzing the ERM formulation of the power allocation problem in (22) and establish a theoretical result that, under certain conditions, guarantees each iterate µ k is within the statistically accuracy of the risk function at epoch k. Our primary theoretical result characterizes such conditions dependent on statistical accuracy and rate of non-stationarity. We begin by presenting a series of assumptions made in our analysis regarding the dual loss functions f .…”

Section: A Convergence Of Erm Problemmentioning

confidence: 99%

“…This shortcoming of existing sample-based approaches used in [19]- [21] and more general machine learning scenarios motivates the higher-order learning approach proposed in this paper. Some existing machine learning methods account for nonstationarity by optimizing an averaged objective over all time [22]- [24]. Our approach differs in that we seek and track optimality locally with respect to the current channel distribution at every time epoch.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Learning in Wireless Control Systems Over Nonstationary Channels

Eisen

Gatsis

Pappas

et al. 2019

IEEE Trans. Signal Process.

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This paper considers a set of multiple independent control systems that are each connected over a non-stationary wireless channel. The goal is to maximize control performance over all the systems through the allocation of transmitting power within a fixed budget. This can be formulated as a constrained optimization problem examined using Lagrangian duality. By taking samples of the unknown wireless channel at every time instance, the resulting problem takes on the form of empirical risk minimization, a well-studied problem in machine learning. Due to the non-stationarity of wireless channels, optimal allocations must be continuously learned and updated as the channel evolves. The quadratic convergence property of Newton's method motivates its use in learning approximately optimal power allocation policies over the sampled dual function as the channel evolves over time.Conditions are established under which Newton's method learns approximate solutions with a single update, and the subsequent sub-optimality of the control problem is further characterized. Numerical simulations illustrate the near-optimal performance of the method and resulting stability on a wireless control problem.

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Section: A Learning Via Newton's Methodsmentioning

confidence: 99%

Section: Erm Over Non-stationary Channelmentioning

confidence: 99%